Проектирование композитных конструкций произвольной формы /Design of freeform composite structures тема диссертации и автореферата по ВАК РФ 00.00.00, кандидат наук Москалева Анастасия Викторовна

• Москалева Анастасия Викторовна
• кандидат наук
• 2024

Оглавление диссертации кандидат наук Москалева Анастасия Викторовна

Contents

1 Introduction

2 The state of the art

2.1 What are freeform structures?

2.2 Fiber reinforced polymer composites

2.3 Applications of FRP composites in freeform structures

2.4 Freeform structures created by using the geometric approach

2.4.1 What is the geometric approach?

2.4.2 Geometrical composite freeform structures: case studies

2.5 Freeform structures created by using the biomimetic approach

2.5.1 What is biomimetic approach?

2.5.2 Biomimetic composite freeform structures: case studies

2.6 Freeform structures created by using the form-finding approach

2.6.1 What is form-finding approach?

2.6.2 Numerical form-finding methods

2.6.3 Form-found composite freeform structures: case studies

2.7 Discussion and future trends

3 Composite freeform shell structures: design, construction and testing

3.1 Form-finding of the composite shell structure

3.2 Manufacturing of the composite shell structure

3.3 Mechanical testing of the composite shell structure

3.3.1 Testing of test coupons

3.3.2 Testing of prototype shells

3.4 Finite element analysis

3.5 Comparison of the structural behavior with other structural shapes

3.6 Discussion and outlook

4 Evolving design workflow: optimization of rib patterns for a freeform composite structure

4.1 Methods

4.2 Results

4.3 Discussion and outlook

5 Stiffening patterns for freeform composite shell structures

5.1 Design of rib patterns

5.2.1 Regular rib pattern

5.2.2 Biomimetic rib pattern

5.2.3 Cross-vault rib pattern

5.2.4 Topology optimized rib patterns

5.2 Manufacturing

5.4 Mechanical testing

5.5 Finite element analysis

5.6 Asymmetric loading scenarios

5.7 Integration of stiffening patterns

5.8 Discussion and future research

6 Conclusion

Acknowledgements

List of abbreviations

List of symbols

List of figures

List of tables

Bibliography

The author's publications on the dissertation topic:

Appendix A. Algorithm for post-processing of the Cross-vault and Optimization stiffening patterns, realized on the Grasshopper platform

Appendix B. Algorithm for generation of the Voronoi stiffening pattern, realized on the Grasshopper platform

Введение диссертации (часть автореферата) на тему «Проектирование композитных конструкций произвольной формы /Design of freeform composite structures»

1 Introduction

The pursuit of freeform shell structures, or complex geometry shells with double curvature, is driving advancements at the intersection of structural engineering and modern design innovation. In the realm of construction, a primary goal is the deployment of progressive building constructions that minimize material consumption and labor while reducing both the cost and duration of building projects. As international experience has shown over recent decades, among the most progressive are shell structures, known for their efficiency in roofing systems for various types of buildings. These structures not only contribute to the creation of buildings with a distinct architectural identity but also address significant spatial challenges. Nonetheless, their construction requires a calculated approach leveraging the latest advancements in structural mechanics. The incorporation of composite materials, notably fiber-reinforced polymers (FRPs), into the design of these freeform structures presents a strategic innovation. FRPs bring a new dimension to structural capabilities with their superior strength-to-weight ratios, durability, and design flexibility. Their application in freeform shells offers the potential to push beyond traditional limits, providing engineers and designers with the tools to realize structures that were once considered unfeasible. Consequently, an in-depth understanding of the behavior of composites under varied loading conditions is crucial.

Relevance of research topic. In constructing buildings with expansive halls covered by various shell structures, these coverings represent a considerable share of material use and labor. Consequently, advancements in the structural designs of these coverings are pivotal for progress across the construction industry. There is a critical need to develop innovative structural forms and leverage new materials that can reduce labor requirements on construction sites, cut costs, and expedite building timelines. Moreover, challenges in modeling and calculating thin-walled structures with complex shapes are prevalent not only in construction, but in various industrial sectors, such as aviation, aerospace, shipbuilding, and others. This research is driven by the urgent need to develop comprehensive methodologies to enhance the stiffness and stability of freeform shell

structures, particularly given their vulnerability to load changes, buckling, and environmental stresses. The emergence of fiber-reinforced polymers provides new opportunities for both architectural and structural design by combining superior mechanical properties with material versatility. Integrating FRPs into the design of freeform structures represents a strategic approach to overcoming the analytical and design challenges these structures present. While traditional form-finding methodologies lay the groundwork for defining the initial contours of freeform architectures, they often fall short in addressing the complexities of structural performance under diverse loading conditions. This gap highlights the need for innovative solutions that extend beyond mere form generation to include structural optimization and reinforcement as core elements of the design process. Addressing these challenges necessitates a comprehensive approach that transcends the limitations of traditional design methodologies, which typically focus only on the form-finding stage. This research aims to contribute significantly by offering a design methodology that integrates form finding with subsequent optimization and reinforcement under various loading conditions. By doing so, it strives to reconcile aesthetic aspirations with structural necessities, ensuring that the resulting structures are not only visually impressive but also meet the highest standards of structural performance.

Research development status. The design and realization of freeform structures, characterized by their complex geometries, represent a significant challenge within the construction industry. These structures, often embodying forms with double curvature or sculptural qualities unattainable through traditional methods, necessitate a fusion of highlevel structural analysis, design ingenuity, and advanced construction techniques. Despite the potential for architecturally expressive and spatially efficient large-span roofing structures, the reliance on conventional materials such as reinforced concrete or steel has historically limited the architectural and structural ambitions of such designs. Fiber-reinforced polymers opened new possibilities in this realm, offering superior mechanical and insulating properties that can significantly expand the application and functionality of shells and other freeform structures. The distinctive challenges of designing shell structures, which demand intricate analysis and a nuanced understanding of material

behavior under complex loading conditions, underscore the need for innovative approaches that go beyond mere form generation to encompass structural optimization and reinforcement. Traditionally, the design of freeform structures has been anchored in geometric, biomimetic, and form-finding methodologies. While effective in defining initial forms, these approaches often fall short in addressing the nuanced demands of structural performance, particularly under varied and dynamic loading conditions. The gap between initial form-finding and subsequent structural optimization and reinforcement is notable, highlighting an area ripe for development.

Moreover, the integration of FRPs within these design frameworks remains underexplored, with current applications mostly limited to experimental projects and a few pioneering constructions. This nascent field of inquiry promises to harness the unique properties of FRPs — such as high elasticity and the ability to form complex, optimized shapes through form-finding methods — to revolutionize freeform architectural design. The distinction between force-active and force-passive structural systems, as applied to freeform structures, further illustrates the nuanced considerations necessary for designing these complex geometries. Force-active systems, which adapt their shape in response to external loads, and force-passive systems, which maintain their form under loading, require tailored approaches to design and optimization that can leverage the benefits of FRPs. In essence, the current status of research and application in the field of freeform structures is at a pivotal juncture, where the potential for innovation is immense, yet the path forward requires a comprehensive strategy that not only embraces advanced materials like FRPs but also integrates cutting-edge design methodologies. This strategy must address the full spectrum of design considerations, from initial form generation and structural analysis to optimization and reinforcement, to realize the full potential of freeform structures in contemporary architecture.

The primary aim of this research is to elevate the structural efficacy of freeform shell structures through the integration of fiber-reinforced polymers and advanced form-finding methodologies. This effort seeks to balance the aesthetic and functional requirements of contemporary architecture by delivering solutions that enhance the

durability, stability, and sustainability of these constructions under different factors. In order to achieve this goal, the following tasks have been defined:

- To establish a complex methodology that combines experimental and theoretical research on composite shells formed through advanced shape-finding techniques. This should accurately reflect their structural behavior under load and the impact of various factors on the strength, stability, and deformability.

- To develop a systematic design workflow, that integrates form-finding, optimization, and reinforcement strategies. This objective focuses on crafting a methodology that ensures that the freeform shells achieve optimal structural performance. The workflow should be designed to adaptively respond to varying structural and environmental conditions.

- To investigate the potential of fiber-reinforced polymers in enhancing the structural design of freeform shells. This includes exploring innovative applications of FRPs to exploit their superior mechanical properties, such as high strength-to-weight ratios and corrosion resistance, which are critical for improving the durability of structures.

- To perform detailed structural analyses and empirical testing to validate the effectiveness of the proposed design methodologies. This objective involves rigorous testing of prototypes and scaled models under varied loading scenarios to empirically confirm their structural integrity, safety, and performance capabilities.

- To optimize the design of freeform shells to maximize their structural efficiency, performance and sustainability. This includes developing intelligent reinforcement strategies and using optimization algorithms to reduce material use and waste, thereby promoting sustainability in architectural design.

The scientific novelty of the work is the following:

First, this research critically examines freeform structures from the perspectives of form generation and conceptual design, and discusses the influential role of FRP composites in the design process. This analysis extends to both a scientific literature review and a historical overview of constructed projects, underscoring the transformative potential of FRPs in construction innovation.

Second, the study introduces a novel classification system for freeform composite structures, anchored in the methodologies employed in the conceptual design stage. This classification, which includes geometric, biomimetic, and form-finding approaches, provides a structured framework for understanding and navigating the diverse strategies underlying freeform design. It also highlights the unique challenges and potentials of each approach.

Next, this study addresses the research gap in the use of FRP materials with form-finding for shell structures. While there is some research done in the field of form-finding of structures with composite materials, this area remains narrowly explored. This work significantly contributes to filling this research gap, focusing on the integration of form-finding processes with FRP materials to create efficient freeform shell structures.

Further, a novel comprehensive design algorithm is presented that encapsulates the full spectrum of the design process from initial form finding to structural optimization and reinforcement. This algorithmic approach represents a methodological advance in creating designs that balance aesthetic appeal with structural integrity, emphasizing intelligent reinforcement strategies to maximize stiffness and stability.

Finally, a significant part of this work involves the development and implementation of reinforcement strategies that employ complex rib patterns for improving buckling resistance and overall stability of freeform shell structures. By applying geometric, biomimetic and topological optimization approaches, this research has developed solutions that not only address structural weaknesses, but also contribute to the sustainability and material efficiency of architectural designs.

Together, these contributions signal a shift toward a more integrated and innovative approach to the design and construction of freeform structures. By using the synergies between advanced materials such as FRPs, advanced form-finding techniques, and strategic reinforcement methods, this research paves the way for a new era of sustainable and efficient designs.

From a theoretical perspective, the value of this work investigates the analysis of freeform structures, examining them through the dual lenses of form generation and

conceptual design. It explores the revolutionary impact of fiber-reinforced polymer composites on design processes, weaving together historical insights and contemporary challenges to expand the academic discourse on material innovation. Moreover, by introducing a novel classification system based on the methodologies employed at the conceptual design stage, the study provides a structured framework that sheds light on various design strategies. This framework not only facilitates a deeper understanding of these strategies but also highlights the distinct challenges and opportunities presented by geometric, biomimetic, and form-finding approaches. Furthermore, the research addresses a notable gap in the integration of FRP materials with form-finding processes for shell structures, thereby contributing to a richer theoretical understanding of how materials can influence and elevate the architectural form and function.

The practical value of the dissertation is the development of a comprehensive design algorithm that spans from initial form-finding through to structural optimization and reinforcement. This algorithm equips architects and engineers with practical tools for creating structures that are both aesthetically pleasing and structurally sound. By emphasizing intelligent strategies to enhance stiffness and stability, the algorithm addresses the complex challenges associated with designing intricate geometries. Additionally, the study's focus on developing and implementing innovative reinforcement strategies using complex rib patterns provides practical solutions for improving the buckling resistance and overall stability of freeform shell structures. The effectiveness of these strategies, derived from geometric, biomimetic, and topology optimization approaches, underscores their potential to significantly improve structural performance. This practical contribution is of particular value to professionals seeking sustainable and material-efficient design options. Finally, the research plays a crucial role in bridging the gap between the conceptual design and the construction stages. The dissertation narrows the divide between creative aspirations of initial design and technical requirements of structural feasibility. It presents a validated framework for realizing freeform shell structures, supported by empirical evidence of enhanced performance and sustainability.

This dissertation work used the following research methods:

• Literature Review: A thorough examination of relevant literature, focusing on advancements in freeform shell structure design, optimization techniques, and smart design strategies. This review establishes the research foundation and identifies gaps in existing knowledge.

• Form-Finding Methods: Application of specific form-finding methods to establish the initial shapes of shell structures, emphasizing the use of:

- Force Density Method (FDM): Utilized for generating equilibrium shapes based on predefined force densities.

- Topological Mapping (TM): Used for generating initial geometric configurations, allowing for the flexible adaptation of structure topology to meet design and performance criteria.

• Optimization Methods: Application of sophisticated optimization algorithms to refine structural designs for enhanced performance, involving:

- Topology Optimization: Performed using the Abaqus/CAE Optimization module with a general (sensitivity-based) algorithm, focusing on optimizing material distribution within the structure for improved structural efficiency.

- Parametric Optimization: Executed within the Grasshopper environment, enabling the dynamic adjustment of design parameters to achieve optimal structural performance based on specific criteria.

• Verification: Verification of the optimized designs through:

- Numerical Simulations: Employing computational models to verify the designs against established performance criteria and ensure they meet structural efficiency requirements. Analysis of the structural integrity, stiffness, and stability of the designed shapes under various loading conditions, using finite element analysis (FEA) in Abaqus software suite.

- Physical Prototyping and Testing: Fabrication of scale models or prototypes for empirical testing, validating the computational models and optimization outcomes through real-world experiments.

In this dissertation, the author defends the following statements:

1. Development of an integrated design methodology: this dissertation introduces a comprehensive workflow that seamlessly integrates form-finding, optimization, and reinforcement strategies to tailor freeform shell structures for high structural performance. The approach is demonstrated through a case study where finite element analysis validates the structural integrity and response under applied loads. The workflow encompasses initial geometric configurations using topological mapping and force density methods to optimize the structural form, ensuring that both aesthetic qualities and functional demands are met efficiently. Notably, the iterative design process reflects in how modifications in the form-finding phase influence subsequent optimization steps, enhancing the overall stability and load-bearing capacity of the structures.

2. Innovative use of fiber-reinforced polymers in form-found shells: the dissertation provides novel insights into using fiber-reinforced polymers to overcome traditional material constraints in freeform architecture. The empirical data includes mechanical properties derived from extensive testing, which underpin the simulation models used to predict structural behavior accurately. The use of FRPs enabled the creation of designs that were previously unachievable, offering enhanced durability and resilience while maintaining lightweight properties.

3. Advancements in structural optimization techniques: advancements were made by introducing sophisticated optimization techniques combining topology and parametric optimization within the design process. the effectiveness of these techniques was illustrated through finite element models that displayed improved distribution of material and stress, leading to structures that maximize structural integrity while minimizing material use. Case studies detailed in the dissertation show how these optimized structures perform under simulated physical conditions, confirming their efficiency and the effectiveness of the optimization algorithms.

4. Smart reinforcement strategies: this dissertation advances the development of smart reinforcement strategies that utilize complex rib patterns, engineered to

significantly improve buckling resistance and structural stability in freeform shell structures. Through detailed finite element analysis, the research demonstrated how these reinforcements strategically improve load-bearing capacities without compromising the design's integrity. Case studies included in the dissertation illustrate how different reinforcement configurations affect structural performance, providing a deep understanding of the interactions between material properties, geometric configurations, and reinforcement strategies.

The author's personal contribution consists in setting the objectives, planning the experimental activities, systematization and analysis of literature data. The author conducted an extensive literature review and classification of composite freeform structures. The author conducted manufacturing of shell prototypes, mechanical testing of shells and finite element analysis, processing and interpretation of the obtained scientific results. The author participated in the preparation and presentation of oral and poster presentations at scientific conferences, writing articles for international peer-reviewed scientific journals.

Reliability and validation of the research results. The robust methodological framework of this dissertation, combined with empirical testing and validation through peer-reviewed publications, ensures the reliability and applicability of its findings. The research has been evaluated through the publication of four scientific papers in highranking international journals [228 - 231], indexed in Scopus and Web of Science. The scientific results were presented at four international conferences:

- 25th International Conference on Composite Structures. 19-21 July 2022. Faculty of Engineering, University of Porto, Portugal.

- The 13th International Conference on Key Engineering Materials. 24 - 26 March 2023. Istanbul University, Istanbul, Turkey.

- The 14th International Conference on Key Engineering Materials. 6 - 8 March 2024, Dubai, UAE.

- The 4th International Workshop of Advanced Manufacturing Technologies. 15-16 April 2024, Skolkovo Institute of Science and Technology, Moscow, Russia.

The research contributions have been critically reviewed by experts. Additionally, the integration of empirical testing with advanced simulation techniques, provides a solid foundation for the practical implementation of the proposed solutions.

Volume and structure of the dissertation. The dissertation consists of an abstract, six chapters, list of symbols and abbreviations, list of 231 references, and two appendices comprising of 7 figures. The dissertation is illustrated by 55 figures and 9 tables. The full volume of the dissertation is 174 pages.

The first chapter substantiates the relevance and significance of the dissertation topic. New provisions introduced by the author into the development of the problem of form-finding of complex geometry composite structures are outlined, the main results of the work that are submitted for defense are listed, their scientific significance and practical value are noted. Information on the implementation of research results is provided.

The second chapter provides the results of theoretical studies of the state of the art in the freeform composite structures, describes the methods which are used in the design of freeform structures, and provides the classification of these methods according to the methodology used at the first conceptual design stage. We define three general approaches: geometric approach, biomimetic approach, form-finding (equilibrium) approach. In geometric approach, the shapes of the structures are created as mathematically described surfaces, independently from the flow of forces acting in them. Biomimetic approach implies the analysis and understanding of natural processes and phenomena, and the creative implementation of natural principles to solve the challenges in other areas of science and technology. Form-finding approach is a design process when the defined shape of the structure follows the forces acting in it. In other worlds, it is a finding the shape in equilibrium under design loads. Also, this chapter analyses world experience in the design, structural analysis and construction of freeform composite structures, designed by each of these methodologies. Moreover, numerical form-finding methods used in the dissertation, are also discussed in the second chapter.

The third chapter details the adaptation of form-finding methods, particularly the force density method and topological mapping, for design of composite shell structures. This approach, though previously unused for composite shells, was adapted to generate the equilibrium shape. The model used for the experimental study is a square-plan, double-curvature shell supported at four points, made from carbon fiber-reinforced polymer. The initial design involved setting up support points, followed by defining the network topology and finding the equilibrium shape, which was then refined using Rhinoceros software to generate a non-uniform rational B-spline (NURBS) surface for manufacturing. The prototype shells were fabricated using vacuum infusion with two layers of biaxial carbon fabric. In total six shell prototypes were tested. The tests were conducted using two types of boundary conditions: unconstrained and constrained supports. A special test assembly was developed, with samples loaded centrally under displacement control. Digital image correlation was used to analyze the strain distribution on the surface of the shells during the tests. Finally, finite element simulations were conducted using ABAQUS software, replicating the mechanical tests to compare experimental data with numerical results. The simulations considered geometric nonlinearity and used the material properties derived from mechanical tests of elementary samples. Load-displacement curves demonstrated close agreement between the physical tests and the simulations, confirming the reliability of the adapted form-finding method for designing freeform composite shells. Strain analysis also showed a high degree of correlation between experimental and simulated results.

Chapter 4 presents an algorithm that integrates form-finding, structural analysis, and optimization to improve the stiffness and stability of freeform shell structures. The workflow involves several steps: defining the design boundaries, conducting form-finding, performing structural analysis, and applying optimization to improve performance, particularly under various load conditions. A case study demonstrates how a composite shell structure is optimized by incorporating a rib pattern. The design starts with the initial shell structure described in the previous chapter. To increase stiffness, a topology optimization was carried out using Abaqus, which generated an optimized

material distribution. The results were translated into rib patterns via parametric optimization in Grasshopper. The ribs were integrated into the finite element model for further analysis. The results showed significant improvements in structural performance. Even with the addition of ribs constituting just 10% of the original shell volume, the maximum buckling load increased from 600N to 1100N, and with 25% rib volume, it reached 2394N. The shell's rigidity also improved, with reduced displacement under loading when ribs were introduced. The reinforced designs underwent finite element analysis under the same conditions as the original, non-optimized shell, demonstrating the substantial benefits of rib reinforcement.

Chapter 5 explores methods to improve the structural integrity of form-found shells using rib-based reinforcements. It compares five different rib configurations: a regular rectangular grid pattern, a biomimetic Voronoi pattern, two patterns derived from topology optimization, and a historically inspired design based on the rib vaults of the Cathedral of Granada. The goal was to improve the stiffness and strength of the shell described in Chapter 3, while maintaining the constraint of using no more than 50% of the original shell's, ensuring a fair comparison between all designs. Rib thickness and material volume were standardized to ensure comparability. The regular stiffening pattern was designed using a 6x6 rectangular rib grid, inspired by coffered ceilings. The biomimetic Voronoi pattern was generated by placing 32 points on the shell surface to initiate a natural rib layout, achieving a material volume close to the other designs. The historically inspired rib pattern mirrored the rib pattern on one of the vaults in the Cathedral of Granada, with adjustments made to rib dimensions to fit the volume constraints. Two additional patterns were created using the Abaqus topology optimization module. In the first case, the shell itself is the design space for optimization, and in the second case, two shells were interconnected using tie constraint, while only the lower shell was the optimization design space. Prototypes for these designs were manufactured using carbon fiber reinforced polymers with vacuum infusion technology. CNC-milled rib patterns were bounded to the shells from below as a reinforcement with VK-9 glue under vacuum. These prototypes were tested under similar conditions to those described

in Chapter 3, using an Instron testing machine. Results showed that all rib patterns significantly improved the critical buckling load compared to the unreinforced shell, with the topology optimized patterns providing the highest increase. The most effective design achieved a maximum load of 2853 N, over 4.5 times greater than the unreinforced shell's capacity. Finite element simulations were performed to validate these results. The simulations confirmed the experimental findings, showing close alignment between the physical and numerical tests. The simulations also demonstrated the advantage of strategic rib reinforcement over simply increasing shell thickness: a thicker, unreinforced shell of equivalent mass was also analyzed and performed much worse than the rib-reinforced designs. The study also considered the performance of these patterns under asymmetrical loading. All rib-reinforced shells showed a reduction in performance under these conditions, but the value of reduction varied significantly. Finally, a new rib design was created by combining the optimized rib layout (designed by second optimization case) with a Voronoi pattern (which showed the least reduction in performance), inspired by the hierarchical structure of dragonfly wings. This biomimetic approach resulted in a pattern that performed well under both central and asymmetrical loading, highlighting the potential of integrating natural design principles into structural optimization.

Заключение диссертации по теме «Другие cпециальности», Москалева Анастасия Викторовна

6 Conclusion

This dissertation has addressed key challenges in the design and optimization of freeform composite shell structures by focusing on four main areas: the development of an integrated design methodology, the innovative use of fiber-reinforced polymers in form-found shells, advancements in structural optimization techniques, and the development of smart reinforcement strategies. The research critically examined freeform structures from the perspectives of form generation and design, highlighting the transformative role of FRP composites in the design process. This analysis encompassed a comprehensive literature review and a historical overview of constructed projects, underscoring the innovative potential of FRPs in this field and the scientific gap of applications of FRPs in structures designed with form-finding. Also, the study introduces a novel classification system for freeform composite structures, anchored in the methodologies employed at the conceptual design stage. This system categorizes designs into geometric, biomimetic, and form-finding approaches, providing a structured framework for understanding and navigating diverse design strategies while highlighting the unique challenges and opportunities each approach presents.

Below is a summary of the main contributions of the dissertation:

1. Development of an integrated design methodology. An integrated design workflow was developed that seamlessly combines form-finding, structural analysis, optimization, and verification processes. This methodology allows for the efficient design of freeform shell structures that meet both aesthetic and structural requirements. The approach was demonstrated through the design and analysis of a composite shell structure, where form-finding techniques were integrated with finite element analysis and structural optimization to achieve the most effective structural form. The validity of this methodology was confirmed with a case study through both numerical simulations and physical experiments.

2. Innovative use of fiber-reinforced polymers in form-found shells. The research explored the potential of fiber-reinforced polymers in improving the structural design of

form-found shells. By integrating FRPs and form-finding design process, the study demonstrated significant improvements in stiffness and structural performance compared to traditional forms. The use of FRPs enabled the creation of lightweight structures with better durability and resilience. Experimental results confirmed that such shells exhibit superior performance, validating the innovative application of composite materials in freeform shell structures. Comparative analysis showed that the form-found shell exhibited higher stiffness compared to other traditional shapes such as spherical and cylindrical vaults.

3. Advancements in structural optimization techniques. Significant progress was made in integrating topology and parametric optimization into the design process. Topology optimization was performed using ABAQUS software, and a parametric algorithm was developed for post-processing of raw optimization results to align with real-world manufacturing constraints and functional requirements. This approach facilitated the transition from theoretical models to practical, manufacturable solutions. The optimized rib patterns developed through this process significantly improved the structural performance of the shells, increasing the maximum buckling load by up to four times compared to unreinforced structures. These findings demonstrate the effectiveness of integrating advanced optimization techniques into the design process.

4. Smart reinforcement strategies. The dissertation advanced the development of smart reinforcement strategies utilizing complex rib patterns engineered to improve buckling resistance and structural stability. Five different rib patterns were designed based on geometric, biomimetic, and topology optimization approaches, each adhering to a 50% volume constraint relative to the original shell. Mechanical testing and FEA of the reinforced shells demonstrated significant increases in stiffness and buckling resistance. The most effective pattern, derived from topology optimization, achieved a maximum load before buckling of 2853 N, over 4.5 times that of the unreinforced shell. Through finite element analysis and physical testing, it was shown that these reinforcements significantly improve buckling resistance and load-bearing capacity without compromising design integrity. The case studies demonstrated how different rib

configurations impact structural performance, providing valuable insights into how reinforcements can be strategically applied to improve the stability of freeform shells.

Looking forward, several promising directions for further development of this dissertation have been identified, and work has already begun on them:

1. One significant area is the integration of rib patterns at the form-finding stage, thereby affecting the overall shape of the shell. By incorporating reinforcement strategies early in the design process, the form of the structure can be inherently optimized for both load distribution and material efficiency.

2. Further perspective studies are investigating the scalability of the design algorithms and reinforcement strategies developed in this dissertation, focusing on the transition from small-scale prototypes to full-scale constructions and addressing the challenges of manufacturing and assembly in diverse architectural applications. Addressing issues such as material behavior at larger scales, connection design, and practical construction methods for complex geometries are crucial for real-world implementation.

3. Furthermore, an important direction for future research is the deeper exploration of hierarchical structures observed in nature to improve the biomimetic approach to rib pattern design. While this dissertation has begun to apply biomimetic concepts — such as the variable thickness and cross-sectional geometry of fibers in dragonfly wings — there remains significant potential for advancement. By conducting more in-depth studies, including precise measurements of thicknesses, cross-sections, and the hierarchical organization of load-resisting biological structures, we can further develop and refine our biomimetic strategies. This deeper understanding would enable the creation of reinforcement patterns that offer improved performance under a wider range of loading conditions. Advancing this biomimetic approach could lead to shells with better mechanical properties, adaptability, and resilience, pushing the boundaries of current structural design methodologies.

Список литературы диссертационного исследования кандидат наук Москалева Анастасия Викторовна, 2024 год

Bibliography

1. Abramczyk J. Folded Sheets as a Universal Material for Shaping Transformed Shell Roofs / J. Abramczyk // Materials 2021, Vol. 14, Page 2051. - 2021. - Vol. 14. -№ 8. - P. 2051.

2. Abramczyk J. Symmetric Free Form Building Structures Arranged Regularly on Smooth Surfaces with Polyhedral Nets / J. Abramczyk // Symmetry. - 2020. - Vol. 12. -№ 5. - P. 763.

3. Abramczyk J. Transformed Corrugated Shell Units Used as a Material Determining Unconventional Forms of Complex Building Structures / J. Abramczyk // Materials 2021, Vol. 14, Page 2402. - 2021. - Vol. 14. - № 9. - P. 2402.

4. Abramczyk J. Transformed Shell Structures Determined by Regular Networks as a Complex Material for Roofing / J. Abramczyk // Materials 2021, Vol. 14, Page 3582. -2021. - Vol. 14. - № 13. - P. 3582.

5. Adaptive Mould D300 - Adapa - adaptive moulds [Электронный ресурс]. -Режим доступа: https://adapa.dk/portfolio-item/adaptive-mould-d300-2/.

6. Addis B. Physical modelling and form finding / B. Addis // Shell Structures for Architecture: Form Finding and Optimization. - 2014. - Vol. 9781315849270.

7. Adriaenssens S. Shell structures for architecture: Form finding and optimization. Vol. 9781315849270 / S. Adriaenssens [et al.]. - 2014.

8. Alajarmeh O. Compressive behaviour of hollow box pultruded FRP columns with continuous-wound fibres / O. Alajarmeh [et al.] // Thin-Walled Structures. - 2021. -Vol. 168.

9. Alexander K.D. The Structural Behavior of Medieval Ribbed Vaulting / K.D. Alexander, R. Mark, J.F. Abel // Journal of the Society of Architectural Historians. -1977. - Vol. 36. - № 4. - P. 241-251.

10. Al-Obaidi K.M. Biomimetic building skins: An adaptive approach. Vol. 79 / K.M. Al-Obaidi [et al.]. - 2017.

11. Angjeliu G. A parametric model for ribbed masonry vaults / G. Angjeliu, G. Cardani, D. Coronelli // Automation in Construction. - 2019. - Vol. 105. - P. 102785.

12. Arjangpay A. An experimental and numerical investigation on low velocity impact response of a composite structure inspired by dragonfly wing configuration / A. Arjangpay [et al.] // Composite Structures. - 2018. - Vol. 184. - P. 327-336.

13. ASTM. ASTM D5379 Standard Test Method for Shear Properties of Composite Materials by the V-Notched / ASTM // Annual Book of ASTM Standards. - 2005. -Vol. i. - № March. - P. 1-13.

14. ASTM Standard. ASTM D6641 / D6641M-16e1, Standard Test Method for Compressive Properties of Polymer Matrix Composite Materials Using a Combined Loading Compression (CLC) Test Fixture, ASTM International, West Conshohocken, PA / ASTM Standard. - 2016. - Vol. i. - № Clc.

15. Badarnah L. A methodology for the generation of biomimetic design concepts / L. Badarnah, U. Kadri // Architectural Science Review. - 2015. - Vol. 58. - № 2. -P. 120-133.

16. Bakis C.E. Fiber-Reinforced Polymer Composites for Construction - State-of-the-Art Review / C.E. Bakis [et al.] // Perspectives in Civil Engineering: Commemorating the 150th Anniversary of the American Society of Civil Engineers. - 2003. - P. 369-383.

17. Bank L.C. Composites for Construction: Structural Design with FRP Materials / L.C. Bank. - John Wiley and Sons, 2007. - 1-551 p.

18. Barnes M.R. Form-finding and analysis of prestressed nets and membranes / M.R. Barnes // Computers and Structures. - 1988. - Vol. 30. - № 3.

19. Barnes M.R. Form finding and analysis of tension structures by dynamic relaxation / M.R. Barnes // International Journal of Space Structures. - 1999. - Vol. 14. - № 2.

20. Baumeister D. Biomimicry Resource Handbook: A seed bank of knowledge and best practices / D. Baumeister. - 2011.

21. BBVA Headquarters / Herzog & de Meuron | ArchDaily [Электронный ресурс]. - Режим доступа: https://www.archdaily.com/893996/bbva-headquarters-herzog-and-de-meuron.

22. Bedon C. Review on the use of FRP composites for façades and building skins. Vol. 9 / C. Bedon. - 2016.

23. Bedon C. Thermo-mechanical Investigation of Novel GFRP-glass Sandwich Facade Components / C. Bedon [et al.] // Challenging Glass 6: Conference on Architectural and Structural Applications of Glass, CGC 2018 - Proceedings. - TU Delft Open, 2018. - Vol. 6. - P. 501-512.

24. Beites S. Morphological behavior of shape memory polymers toward a deployable, adaptive architecture / S. Beites // ACADIA 2013: Adaptive Architecture -Proceedings of the 33rd Annual Conference of the Association for Computer Aided Design in Architecture. - 2013.

25. Bends0e M.P. Topology Optimization : Theory, Methods, and Applications / M.P. Bends0e, Ole. Sigmund. - Springer Berlin Heidelberg, 2004. - 370 p.

26. Benefits of composite materials - Solico [Электронный ресурс]. - Режим доступа: https://www.solico.nl/about-us/benefits-of-composite-materials.

27. Bertolesi E. Research and practice on masonry cross vaults - A review / E. Bertolesi [et al.] // Engineering Structures. - 2019. - Vol. 180. - P. 67-88.

28. BIG's 2016 Serpentine Pavilion Opens Alongside 4 Summerhouses | ArchDaily [Электронный ресурс]. - Режим доступа: https://www.archdaily.com/789018/bigs-2016-serpentine-pavilion-opens-alongside-4-summerhouses.

29. Bletzinger K.U. Computational form finding and optimization / K.U. Bletzinger, E. Ramm // Shell Structures for Architecture: Form Finding and Optimization. - 2014. -Vol. 9781315849270.

30. Bletzinger K.U. Form finding of shells by structural optimization / K.U. Bletzinger, E. Ramm // Engineering with Computers. - 1993. - Vol. 9. - № 1.

31. Block P. NEST HiLo: Investigating lightweight construction and adaptive energy systems / P. Block [et al.] // Journal of Building Engineering. - 2017. - Vol. 12. -P. 332-341.

32. Block P. Thrust network analysis: A new methodology for three-dimensional equilibrium / P. Block, J. Ochsendorf // Journal of the International Association for Shell and Spatial Structures. - 2007. - Vol. 48.

33. Block P. Thrust Network Analysis: Exploring Three-dimensional Equilibrium / P. Block. - 2009.

34. Bohlooly M. Buckling and postbuckling of advanced grid stiffened truncated conical shells with laminated composite skins / M. Bohlooly [et al.] // Thin-Walled Structures. - 2020. - Vol. 149. - P. 106528.

35. Bolbotowski K. Optimal vault problem - form finding through 2D convex program / K. Bolbotowski // Computers & Mathematics with Applications. - 2022. -Vol. 109. - P. 280-324.

36. Bruggi M. A constrained force density method for the funicular analysis and design of arches, domes and vaults / M. Bruggi // International Journal of Solids and Structures. - 2020. - Vols. 193-194. - P. 251-269.

37. Caetano I. Architecture meets computation: an overview of the evolution of computational design approaches in architecture / I. Caetano, A. Leitao // Architectural Science Review. - 2020. - Vol. 63. - № 2. - P. 165-174.

38. Carbonell-Marquez J.F. Topological design of compression structures / J.F. Carbonell-Marquez [et al.] // Archive of Applied Mechanics. - 2016. - Vol. 86. - № 8. -P. 1495-1508.

39. Chanel Mobile Art Pavilion / Zaha Hadid Architects | ArchDaily [Электронный ресурс]. - Режим доступа: https://www.archdaily.com/144378/chanel-mobile-art-pavilion-zaha-hadid-architects.

40. Chen J. Lightweight composite structures in the forewings of beetles / J. Chen [et al.] // Composite Structures. - 2007. - Vol. 79. - № 3. - P. 331-337.

41. Christie J. Filigree Shell Slabs Material and Fabrication-aware Shape Optimisation for CFRP Coreless- wound Slab Components / J. Christie [et al.] // AAG Advances in Architectural Geometry. - 2021. - P. 244-263.

42. Chu S. Simultaneous layout and topology optimization of curved stiffened panels / S. Chu [et al.] // AIAA Journal. - 2021. - Vol. 59. - № 7.

43. Chu S. Simultaneous size, layout and topology optimization of stiffened panels under buckling constraints / S. Chu [et al.] // AIAA Scitech 2021 Forum. - 2021.

44. Cleary R. Review: Seven Structural Engineers: The Felix Candela Lectures by Guy Nordenson, editor / R. Cleary // Journal of the Society of Architectural Historians. -2011. - Vol. 70. - № 3.

45. Coster A. De. Exploring the three-dimensional space with modular concrete shells: Form-finding, design and structural analysis / A. De Coster, L. De Laet, T. Tysmans // Thin-Walled Structures. - 2024. - Vol. 195. - P. 111336.

46. Cuvilliers P. Hybrid structural skin: Prototype of a gfrp elastic gridshell braced by a fiber-reinforced concrete envelope / P. Cuvilliers [et al.] // Journal of the International Association for Shell and Spatial Structures. - 2017. - Vol. 58. - № 1.

47. D7078/D7078M-12. Standard Test Method for Shear Properties of Composite Materials by V-Notched Rail Shear Method / D7078/D7078M-12 // ASTM Book of Standards. - 2012. - Vol. i. - P. 1-15.

48. Dambrosio N. Buga Fibre Pavilion Towards an architectural application of novel fiber composite building systems / N. Dambrosio [et al.] // Ubiquity and Autonomy -Paper Proceedings of the 39th Annual Conference of the Association for Computer Aided Design in Architecture, ACADIA 2019. - 2019.

49. Doerstelmann M. ICD/ITKE Research Pavilion 2014-15: Fibre placement on a pneumatic body based on a water spider web / M. Doerstelmann [et al.] // Architectural Design. - 2015. - Vol. 85. - № 5. - P. 60-65.

50. Douthe C. Form-finding of a grid shell in composite materials / C. Douthe, O. Baverel, J.F. Caron // Journal of the International Association for Shell and Spatial Structures. - 2006. - Vol. 47. - № 150.

51. Douthe C. Gridshell structures in glass fibre reinforced polymers / C. Douthe, J.F. Caron, O. Baverel // Construction and Building Materials. - 2010. - Vol. 24. - № 9.

52. Douthe C. Étude de structures élancées précontraintes en matériaux composites : Application à la conception des gridshells / C. Douthe // Doctoral Thesis. - 2007. -№ November 2007.

53. Eekhout A.J.C.M. Lord of the Wings: The Making of Free Form Architecture / A.J.C.M. Eekhout, S. Wichers. - IOS Press - Delft University Press, 2016.

54. Eekhout M. Composite stressed skin roofs for liquid design architecture / M. Eekhout // International Journal of Structural Engineering. - 2010. - Vol. 1. - № 3-4.

55. Eekhout M. Form as a Bridge between Architectural, Structural and Industrial Design / M. Eekhout // Proceedings of the 4th International colloqium on Structural Morphology IASS: Spatial Lattice and Tension Structures. - Delft, 2000. - P. 1000-1010.

56. Eekhout M. Case Study E Management of Complex Free Form Design and Engineering Processes / M. Eekhout, B. Gelder // Architectural Management: International Research and Practice. - Wiley-Blackwell, 2009. - P. 244-267.

57. Ehlig D. Textilbeton - Ausgeführte Projekte im Überblick / D. Ehlig [et al.] // Beton- und Stahlbetonbau. - 2012. - Vol. 107. - № 11. - P. 777-785.

58. Ehsani A. Multi-objective design optimization of variable ribs composite grid plates / A. Ehsani, H. Dalir // Structural and Multidisciplinary Optimization 2020 63:1. -2020. - Vol. 63. - № 1. - P. 407-418.

59. Engelsmann S. Eine Geometrisch Komplexe Plastik-skulptur mit Modularem Tragwerk / S. Engelsmann, V. Spalding // Bautechnik. - 2008. - Vol. 85. - № 5.

60. Engelsmann S. PLASTICS in Architecture and Construction / S. Engelsmann, V. Spalding, S. Peters.

61. Farin G. From Conics to NURBS: A Tutorial and Survey / G. Farin // IEEE Computer Graphics and Applications. - 1992. - Vol. 12. - № 5.

62. Fernandez-Ruiz M.A. Design and form-finding of compression structures with prestressing tendons / M.A. Fernandez-Ruiz [et al.] // Engineering Structures. - 2019. -Vol. 197.

63. Fernández-Ruiz M.A. From octagonal connection graphs belonging to the Z-Octahedron family to new tensegrity structures / M.A. Fernández-Ruiz, E. Hernández-Montes, L.M. Gil-Martín // International Journal of Solids and Structures. - 2022. -Vols. 254-255. - P. 111901.

64. Fernández-Ruiz M.A. Topological design of the octahedron tensegrity family / M.A. Fernández-Ruiz, E. Hernández-Montes, L.M. Gil-Martín // Engineering Structures. - 2022. - Vol. 259. - P. 114211.

65. Fernández-Ruiz M.A. Patterns of force:length ratios for the design of compression structures with inner ribs / M.A. Fernández-Ruiz [et al.] // Engineering Structures. - 2017. - Vol. 148.

66. Fiberline Factory | Lay Light by Fiberline | Archello [Электронный ресурс]. -Режим доступа: https://archello.com/project/fiberline-factory.

67. Fischer J.-R. Optimizing Digital Organic Freeform Modelling for Fabrication by Using Parameterization With Glass Fibre Reinforced Plastics / J.-R. Fischer // eCAADe 30. - 2012. - Vol. 2.

68. Früh N. Multi-stage filament winding: Integrative design and fabrication method for fibre-reinforced composite components of complex geometries / N. Früh, J. Knippers // Composite Structures. - 2021. - Vol. 268. - P. 113969.

69. Gaetani A. Design and Analysis of Cross Vaults Along History / A. Gaetani [et al.] // International Journal of Architectural Heritage. - 2016. - Vol. 10. - № 7.

70. Galizia F.G. The evolution of molds in manufacturing: From rigid to flexible / F.G. Galizia [et al.] // Procedia Manufacturing. - Elsevier B.V., 2019. - Vol. 33. - P. 319326.

71. Gates P. Advanced composites for façade retrofit / P. Gates [et al.] // Structural Engineer. - 2012. - Vol. 90. - № 1. - P. 46-48.

72. Gebeshuber I.C. An attempt to reveal synergies between biology and mechanical engineering / I.C. Gebeshuber, M. Drack // Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. - 2008. - Vol. 222. - №2 7.

73. Gero J.S. Computational Models of Innovative and Creative Design Processes / J.S. Gero // Technological Forecasting and Social Change. - 2000. - Vol. 64. - № 2-3. -P. 183-196.

74. Gil Pérez M. Structural design, optimization and detailing of the BUGA fibre pavilion / M. Gil Pérez [et al.] // International Journal of Space Structures. - 2020.

75. Haber R.B. Initial equilibrium solution methods for cable reinforced membranes part I-formulations / R.B. Haber, J.F. Abel // Computer Methods in Applied Mechanics and Engineering. - 1982. - Vol. 30. - № 3.

76. Hameed A. Architectural potentiality of free-form structures / A. Hameed, H. Al Alwan, N. Oukaili // 3rd European and Mediterranean Structural Engineering and Construction Conference 2020, Euro-Med-Sec 2020. - 2020.

77. Hamm C. Evolution of lightweight structures: analyses and technical applications / C. Hamm. - 2015.

78. Hao P. An integrated framework of exact modeling, isogeometric analysis and optimization for variable-stiffness composite panels / P. Hao [et al.] // Computer Methods in Applied Mechanics and Engineering. - 2018. - Vol. 339. - P. 205-238.

79. Hao R. A novel three-dimensional structure model of biomimetic staggered composites / R. Hao, D.X. Li, W. Liu // Composite Structures. - 2020. - Vol. 239. -P. 112042.

80. Harries K.A. FRP INTERNATIONAL the official newsletter of the International Institute for FRP in Construction / K.A. Harries [et al.].

81. Hawkins W. Design, Construction and Testing of a Low Carbon Thin-Shell Concrete Flooring System / W. Hawkins [et al.] // Structures. - 2019. - Vol. 18.

82. Henriksen T. A new method to advance complex geometry thin-walled glass fibre reinforced concrete elements / T. Henriksen, S. Lo, U. Knaack // Journal of Building Engineering. - 2016. - Vol. 6.

83. Henriksson V. Rationalizing freeform architecture - Surface discretization and multi-objective optimization / V. Henriksson, M. Hult. - 2015.

84. Hernández-Montes E. Full and folded forms: a compact review of the formulation of tensegrity structures / E. Hernández-Montes [et al.] // Mathematics and Mechanics of Solids. - 2018. - Vol. 23. - № 6.

85. Hernández-Montes E. Topological Mapping for Tension Structures / E. Hernández-Montes, R. Jurado-Piña, E. Bayo // Journal of Structural Engineering. - 2006.

- Vol. 132. - № 6.

86. Hernández-Montes E. Structural Knowledge within the 6th Century AD Arch of Taq-iKisra / E. Hernández-Montes [et al.] // International Journal of Architectural Heritage. - 2017. - Vol. 11. - № 6.

87. Heydar Aliyev Center / Zaha Hadid Architects | ArchDaily [Электронный ресурс]. - Режим доступа: https://www.archdaily.com/448774/heydar-aliyev-center-zaha-hadid-architects?ad_medium=gallery.

88. Heyman J. The stone skeleton / J. Heyman // International Journal of Solids and Structures. - 1966. - Vol. 2. - № 2. - P. 249-279.

89. Hirschler T. Isogeometric sizing and shape optimization of thin structures with a solid-shell approach / T. Hirschler [et al.] // Structural and Multidisciplinary Optimization. - 2019. - Vol. 59. - № 3. - P. 767-785.

90. Hollaway L.C. The evolution of and the way forward for advanced polymer composites in the civil infrastructure / L.C. Hollaway // Construction and Building Materials. - Elsevier, 2003. - Vol. 17. - P. 365-378.

91. Hu J. Axial compression response of multi-cell tube reinforced by parallel leaf veins inspired secondary ribs / J. Hu [et al.] // Thin-Walled Structures. - 2023. - Vol. 185.

- P. 110557.

92. ICD and ITKE's new lightweight pavilion mimics the structure of water spider's underwater nests [Электронный ресурс]. - Режим доступа: https://inhabitat.com/icd-and-itkes-lightweight-pavilion-mimics-the-structure-of-water-spiders-underwater-nests/.

93. ICD/ITKE Research Pavilion 2012 | Institute for Computational Design and Construction | University of Stuttgart [Электронный ресурс]. - Режим доступа: https://www.icd. uni-stuttgart. de/proj ects/icditke-research-pavilion-2012/.

94. INTERNATIONAL STANDARD. EN ISO 527-4:1997 Plastics. Determination of tensile properties Test conditions for isotropic and orthotropic fibre-reinforced plastic composites. Vol. 1 / INTERNATIONAL STANDARD. - 1997.

95. Islam M.K. Biomimetic armour design strategies for additive manufacturing: A review. Vol. 205 / M.K. Islam [et al.]. - 2021.

96. Isler H. Concrete Shells Derived from Experimental Shapes / H. Isler // Structural Engineering International. - 1994. - Vol. 4. - № 3.

97. Jiang C. Computational design and optimization of quad meshes based on diagonal meshes / C. Jiang [et al.] // Advances in Architectural Geometry. - 2021. - P. 3861.

98. Jurado-Piña R. Topological mesh for shell structures / R. Jurado-Piña, L.M. Gil-Martín, E. Hernández-Montes // Applied Mathematical Modelling. - 2009. - Vol. 33. -№ 2.

99. Kavuma A. Factors influencing Time and Cost Overruns on Freeform Construction Projects / A. Kavuma, J. Ock, H. Jang // KSCE Journal of Civil Engineering. - 2019. - Vol. 23. - № 4. - P. 1442-1450.

100. Kiendl J. Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting / J. Kiendl [et al.] // Computer Methods in Applied Mechanics and Engineering. - 2014. - Vol. 274. - P. 148-167.

101. Kiendl J.M. Isogeometric Analysis and Shape Optimal Design of Shell Structures / J.M. Kiendl. - 2011.

102. Kilian A. Particle-spring systems for structural form finding / A. Kilian, J. Ochsendorf // Journal of the International Association for Shell and Spatial Structures. -2005. - Vol. 46. - № 148.

103. Kim K. Current trends and future directions of free-form building technology / K. Kim [et al.] // Architectural Science Review. - 2015. - Vol. 58. - № 3.

104. Kim S. Development of Sustainable Production Technology of Free-Form Concrete Panels Using a Multi-Point Press CNC Machine / S. Kim, S. Son, D. Lee // Sustainability. - 2021. - Vol. 13. - № 4. - P. 1990.

105. Knippers J. Construction Manual for Polymers + Membranes / J. Knippers [et al.]. - 2013.

106. Knippers J. Design and construction principles in nature and architecture / J. Knippers, T. Speck // Bioinspiration and Biomimetics. - 2012. - Vol. 7. - № 1.

107. Komkov V. Design sensitivity analysis of structural systems / V. Komkov [et al.] // Mathematics in Science and Engineering. - 1986. - Vol. 177. - № C.

108. Korotkov R. Shape memory behavior of unidirectional pultruded laminate / R. Korotkov [et al.] // Composites Part A: Applied Science and Manufacturing. - 2021. -Vol. 150.

109. Krivoshapko S.N. Encyclopedia of Analytical Surfaces / S.N. Krivoshapko, V.N. Ivanov. - 2015.

110. Krogh C. A simple MATLAB draping code for fiber-reinforced composites with application to optimization of manufacturing process parameters / C. Krogh [et al.] // Structural and Multidisciplinary Optimization 2021 64:1. - 2021. - Vol. 64. - № 1. -P. 457-471.

111. Lai M. Corrugated shells: An algorithm for generating double-curvature geometric surfaces for structural analysis / M. Lai [et al.] // Thin-Walled Structures. -2022. - Vol. 173. - P. 109019.

112. Lee S. A novel method for topology design of tensegrity structures / S. Lee, J. Lee // Composite Structures. - 2016. - Vol. 152.

113. Lefevre B. Buckling of elastic gridshells / B. Lefevre, C. Douthe, O. Baverel // Journal of the International Association for Shell and Spatial Structures. - 2015. -Vol. 56. - № 3.

114. Lengyel G. Numerical analysis of the mechanical role of the ribs in groin vaults / G. Lengyel, K. Bagi // Computers & Structures. - 2015. - Vol. 158. - P. 42-60.

115. Libonati F. Understanding the structure-property relationship in cortical bone to design a biomimetic composite / F. Libonati, L. Vergani // Composite Structures. -2016. - Vol. 139. - P. 188-198.

116. Lienhard J. Flectofin: A hingeless flapping mechanism inspired by nature / J. Lienhard [et al.] // Bioinspiration and Biomimetics. - 2011. - Vol. 6. - № 4.

117. Linkwitz K. About formfinding of double-curved structures / K. Linkwitz // Engineering Structures. - 1999. - Vol. 21. - № 8.

118. Linkwitz K. Einige Bemerkungen zur Berechnung von vorgespannten Seilnetzkonstruktionen / K. Linkwitz, H.J. Schek // Ingenieur-archiv. - 1971. - Vol. 40. - № 3. - P. 145-158.

119. Li Q. How to understand "structural morphology"? / Q. Li, A. Borgart, Y. Wu // Journal of the International Association for Shell and Spatial Structures. - 2016. -Vol. 57. - № 2.

120. Li Q. Form Follows Force: A theoretical framework for Structural Morphology, and Form-Finding research on shell structures / Q. Li // A+BE | Architecture and the Built Environment. - 2018. - Vol. 8. - № 2. - P. 1-278.

121. Li X. The modified force density method for form-finding of cable net structure / X. Li [et al.] // Thin-Walled Structures. - 2023. - P. 111363.

122. López López D. "Brick-topia", the thin-tile vaulted pavilion / D. López López, M. Domènech Rodríguez, M. Palumbo Fernández // Case Studies in Structural Engineering. - 2014. - Vol. 2.

123. López M. How plants inspire façades. From plants to architecture: Biomimetic principles for the development of adaptive architectural envelopes. Vol. 67 / M. López [et al.]. - Elsevier Ltd, 2017.

124. Malakhov A. V. Design of composite structures reinforced curvilinear fibres using FEM / A. V. Malakhov, A.N. Polilov // Composites Part A: Applied Science and Manufacturing. - 2016. - Vol. 87. - P. 23-28.

125. Ma X. Post-buckling optimization of bending-induced variable stiffness composite cylinders considering worst geometric imperfections / X. Ma [et al.] // Thin-Walled Structures. - 2021. - Vol. 169. - P. 108489.

126. McCulloch W.S. Living prototypes - the key to new technology. Symposium on bionics / W.S. McCulloch, P.M.; Kelly // Bionics-Symposium. - 1960.

127. Mele E. Hexagrid-Voronoi transition in structural patterns for tall buildings / E. Mele [et al.] // Frattura ed Integrita Strutturale. - 2019. - Vol. 13. - № 47.

128. Méndez Echenagucia T. A Cable-Net and Fabric Formwork System for the Construction of Concrete Shells: Design, Fabrication and Construction of a Full Scale Prototype / T. Méndez Echenagucia [et al.] // Structures. - 2019. - Vol. 18.

129. Milwich M. Biomimetics and technical textiles: Solving engineering problems with the help of nature's wisdom. Vol. 93 / M. Milwich [et al.]. - 2006.

130. Minchenkov K. Effects of the quality of pre-consolidated materials on the mechanical properties and morphology of thermoplastic pultruded flat laminates / K. Minchenkov [et al.] // Composites Communications. - 2022. - Vol. 35.

131. Minchenkov K. Experimental and numerical analyses of the thermoplastic pultrusion of large structural profiles / K. Minchenkov [et al.] // Materials & Design. -2023. - Vol. 232. - P. 112149.

132. Minchenkov K. Thermoplastic pultrusion: A review. Vol. 13 / K. Minchenkov [et al.]. - 2021.

133. Mobile Art Chanel Contemporary Art Container - Zaha Hadid Architects [Электронный ресурс]. - Режим доступа: https://www.zaha-hadid.com/architecture/chanel-art-pavilion/.

134. Naaman A.E. Thin TRC Products: Status, Outlook, and Future Directions / A.E. Naaman // Textile Fibre Composites in Civil Engineering. - 2016.

135. New Christian Dior Flagship Store In Seoul Reflects Dior's Soft And Flowing Style [Электронный ресурс]. - Режим доступа: https://worldarchitecture.org/articles/ccmpc/new-christian-dior-flagship-store-in-seoul-reflects-diors-soft-and-flowing-style.html.

136. Ney L. Shaping forces / L. Ney, S. Adriaenssens // Shell Structures for Architecture: Form Finding and Optimization. - 2014. - Vol. 9781315849270.

137. Nguyen K.T.Q. Fire safety of composites in prefabricated buildings: From fibre reinforced polymer to textile reinforced concrete. Vol. 187 / K.T.Q. Nguyen [et al.]. -Elsevier Ltd, 2020.

138. Niu B. Discrete material optimization of composite structures subjected to initial excitation for minimum residual vibration / B. Niu [et al.] // Thin-Walled Structures. - 2022. - Vol. 173. - P. 108901.

139. Nomura T. General topology optimization method with continuous and discrete orientation design using isoparametric projection / T. Nomura [et al.] // International Journal for Numerical Methods in Engineering. - 2015. - Vol. 101. - №2 8. - P. 571-605.

140. O'Dwyer D. Funicular analysis of masonry vaults / D. O'Dwyer // Computers & Structures. - 1999. - Vol. 73. - № 1-5. - P. 187-197.

141. One Ocean, Thematic Pavilion EXPO 2012 / soma | ArchDaily [Электронный ресурс]. - Режим доступа: https://www.archdaily.com/236979/one-ocean-thematic-pavilion-expo-2012-soma?ad_medium=gallery.

142. Ostanin I. Natural erosion of sandstone as shape optimisation / I. Ostanin, A. Safonov, I. Oseledets // Scientific Reports. - 2017. - Vol. 7. - № 1.

143. Palombini F.L. Bionic design of thin-walled structure based on the geometry of the vascular bundles of bamboo / F.L. Palombini, J.E. de A. Mariath, B.F. de Oliveira // Thin-Walled Structures. - 2020. - Vol. 155.

144. Pantazis E. Beyond geometric complexity: a critical review of complexity theory and how it relates to architecture engineering and construction / E. Pantazis, D.J. Gerber // Architectural Science Review. - 2019. - Vol. 62. - № 5. - P. 371-388.

145. Pazdur-Czarnowska A. Ecological Properties of Glass Fibre Reinforced Materials Based on Architecture of Zaha Hadid / A. Pazdur-Czarnowska // IOP Conference Series: Materials Science and Engineering. - 2019. - Vol. 471.

146. Peloux L. Du. Construction of a large composite gridshell structure: A lightweight structure made with pultruded glass fibre reinforced polymer tubes / L. Du Peloux [et al.] // Structural Engineering International. - 2016. - Vol. 26. - № 2.

147. Peloux L. Du. Modeling of bending-torsion couplings in active-bending structures. Application to the design of elastic gridshells. / L. Du Peloux. - 2017.

148. Pohl G. Fibre Reinforced Building Envelopes Inspired by Nature: Pavilion COCOON FS / G. Pohl. - 2015.

149. Pohl G. Biomimetics for Architecture & Design / G. Pohl, W. Nachtigall. -

2015.

150. Pohl G. The role of textiles in providing biomimetic solutions for construction / G. Pohl [et al.] // Textiles, Polymers and Composites for Buildings. - 2010.

151. Poirriez C. Parametrization, integration and buildability: Design and construction of a 50M span freeform roof in Bangkok / C. Poirriez, M. Franceschi, Y. Bouzida // Journal of the International Association for Shell and Spatial Structures. -2019. - Vol. 60. - № 4. - P. 287-293.

152. Poppinga S. Biomimetic deployable systems in architecture / S. Poppinga [et al.] // IFMBE Proceedings. - 2010. - Vol. 31 IFMBE.

153. Poppinga S. Compliant Mechanisms in Plants and Architecture / S. Poppinga [et al.]. - 2016.

154. Poppinga S. Plant movements as concept generators for deployable systems in architecture / S. Poppinga [et al.] // WIT Transactions on Ecology and the Environment.

- 2010. - Vol. 138.

155. Pottmann H. Architectural geometry / H. Pottmann [et al.] // Computers and Graphics (Pergamon). - 2015. - Vol. 47. - P. 145-164.

156. Pottmann H. Freeform architecture and discrete differential geometry / H. Pottmann, J. Wallner // Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - Springer Verlag, 2017. - Vol. 10502 LNCS. - P. 3-8.

157. Raupach M. Textile-Reinforced Concrete: Selected Case Studies / M. Raupach, C. Morales Cruz // Textile Fibre Composites in Civil Engineering. - Elsevier Inc., 2016.

- P. 275-299.

158. Reichert S. Fibrous structures: An integrative approach to design computation, simulation and fabrication for lightweight, glass and carbon fibre composite structures in architecture based on biomimetic design principles / S. Reichert [et al.] // CAD Computer Aided Design. - 2014. - Vol. 52.

159. Reitinger R. Buckling and imperfection sensitivity in the optimization of shell structures / R. Reitinger, E. Ramm // Thin-Walled Structures. - 1995. - Vol. 23. - № 14.

160. Restoration of Buckminster Fuller's iconic Fly's Eye Dome at America's Cup | ArchDaily [Электронный ресурс]. - Режим доступа: https://www.archdaily.com/13923 8/restoration-of-buckminster-fuller%25e2%2580%2599s-iconic-fly%25e2%2580%2599s-eye-dome-at-america%25e2%2580%2599s-cup.

161. Rogers D.F. An introduction to NURBS: with historical perspective / D.F. Rogers. - 2001.

162. Rozvany G.I.N. A critical review of established methods of structural topology optimization / G.I.N. Rozvany // Structural and Multidisciplinary Optimization 2008 37:3. - 2008. - Vol. 37. - № 3. - P. 217-237.

163. Safonov A.A. 3D topology optimization of continuous fiber-reinforced structures via natural evolution method / A.A. Safonov // Composite Structures. - 2019. - Vol. 215. - P. 289-297.

164. Safonov A. Modeling of cracking during pultrusion of large-size profiles / A. Safonov [et al.] // Composite Structures. - 2020. - Vol. 235. - P. 111801.

165. Safonov A. Numerical modeling of the evolution of arcades and rock pillars / A. Safonov [et al.] // Geomorphology. - 2020. - Vol. 365.

166. San B. Shape optimization of concrete free-form shells considering material damage / B. San, D. Feng, Y. Qiu // https://doi.org/10.1080/0305215X.2021.1968854. -2021. - P. 1-18.

167. Schek H.J. The force density method for form finding and computation of general networks / H.J. Schek // Computer Methods in Applied Mechanics and Engineering. - 1974. - Vol. 3. - № 1.

168. Schikore J. Kinetics and Design of Semi-Compliant Grid Mechanisms / J. Schikore [et al.] // Advances in Architectural Geometry. - 2021. - P. 108-129.

169. Schipper R. Kine-Mould: Manufacturing technology for Curved Architectural Elements in Concrete / R. Schipper [et al.]. - 2015.

170. Schleicher S. Adaptive façade shading systems inspired by natural elastic kinematics / S. Schleicher [et al.] // Inernational Adaptive Architecture Conference (IAAC). - 2011. - № March.

171. Schleicher S. Bio-inspired Kinematics for Adaptive Shading Systems on Free Form Facades / S. Schleicher [et al.] // IABSE-IASS Symposium. - 2011.

172. Schleicher S. Constructing hybrid gridshells using bending-active formwork: / S. Schleicher, M. Herrmann // https://doi.org/10.1177/0956059920924189. - 2020. -Vol. 35. - № 3. - P. 80-89.

173. Schling E. Freie form - Experimentelle tragstruktur - entwurf und umsetzung von modularen flächentragwerken / E. Schling, R. Barthel, J. Tutsch // Bautechnik. -2014. - Vol. 91. - № 12.

174. Schling E. Bending-activated tensegrity / E. Schling [et al.] // Proceedings of the 7th International Conference on Textile Composites and Inflatable Structures, STRUCTURAL MEMBRANES 2015. - 2015.

175. Scholzen A. Thin-walled shell structures made of textile-reinforced concrete: Part II: Experimental characterization, ultimate limit state assessment and numerical simulation / A. Scholzen, R. Chudoba, J. Hegger // Structural Concrete. - 2015. - Vol. 16. - № 1.

176. Scholzen A. Thin-walled shell structures made of textile-reinforced concrete: Part I: Structural design and construction / A. Scholzen, R. Chudoba, J. Hegger // Structural Concrete. - 2015. - Vol. 16. - № 1.

177. Setoodeh S. Combined topology and fiber path design of composite layers using cellular automata / S. Setoodeh, M.M. Abdalla, Z. Gürdal // Structural and Multidisciplinary Optimization 2005 30:6. - 2005. - Vol. 30. - № 6. - P. 413-421.

178. Sharei E. Structural behavior of a lightweight, textile-reinforced concrete barrel vault shell / E. Sharei [et al.] // Composite Structures. - 2017. - Vol. 171.

179. Sharma S. Biomimicry: Exploring research, challenges, gaps, and tools / S. Sharma, P. Sarkar // Smart Innovation, Systems and Technologies. - 2019. - Vol. 134.

180. Shi J.X. Design optimization of cable-membrane structures for form-finding and stiffness maximization / J.X. Shi [et al.] // Composite Structures. - 2018. - Vol. 192.

181. Solly J. Structural design of a lattice composite cantilever / J. Solly [et al.] // Structures. - 2019. - Vol. 18.

182. Sorina T.G. Pecularities of using carbon glass-reinforced plastic in pultrusion composite profiles for bridge engineering / T.G. Sorina, A.A. Safonov, A.K. Khairetdinov // Journal of Machinery Manufacture and Reliability. - 2010. - Vol. 39. - № 1.

183. Sowinski K. Buckling of shells with special shapes with corrugated middle surfaces - FEM study / K. Sowinski // Engineering Structures. - 2019. - Vol. 179.

184. Speck T. Plant stems: Functional design and mechanics / T. Speck, I. Burgert // Annual Review of Materials Research. - 2011. - Vol. 41.

185. Speck T. Process sequences in biomimetic research / T. Speck, O. Speck // WIT Transactions on Ecology and the Environment. - 2008. - Vol. 114.

186. Starr T.F. Pultrusion for engineers / T.F. Starr. - 2000.

187. Stedelijk Museum Amsterdam / Benthem Crouwel Architects | ArchDaily [Электронный ресурс]. - Режим доступа: https://www.archdaily.com/3 50843/stedelijk-museum-amsterdam-benthem-crouwel-architects.

188. Tayeb F. Design and realisation of composite gridshell structures / F. Tayeb [et al.] // Journal of the International Association for Shell and Spatial Structures. - Int. Association for Shell and Spatial Structures, 2015. - Vol. 56. - P. 49-59.

189. Tayeb F. Stability and robustness of a 300 m2 composite gridshell structure / F. Tayeb [et al.] // Construction and Building Materials. - 2013. - Vol. 49.

190. Tellier X. Fabrication-aware design of architectural envelopes using surfaces with planar curvature lines / X. Tellier [et al.] // IASS Symposium 2019 - 60th Anniversary Symposium of the International Association for Shell and Spatial Structures;

Structural Membranes 2019 - 9th International Conference on Textile Composites and Inflatable Structures, FORM and FORCE. - 2019.

191. Tinkov D. V. Design optimization of truss bridge structures of composite materials / D. V. Tinkov, A.A. Safonov // Journal of Machinery Manufacture and Reliability. - 2017. - Vol. 46. - № 1. - P. 46-52.

192. Tung C.C. Optimization of mechanical properties of bio-inspired Voronoi structures by genetic algorithm / C.C. Tung [et al.] // Journal of Materials Research and Technology. - 2023. - Vol. 26. - P. 3813-3829.

193. Tysmans T. Form finding methodology for force-modelled anticlastic shells in glass fibre textile reinforced cement composites / T. Tysmans, S. Adriaenssens, J. Wastiels // Engineering Structures. - 2011. - Vol. 33. - № 9. - P. 2603-2611.

194. Vacmobile 2SHD vacuum system for resin infusion & bagging [Электронный ресурс]. - Режим доступа: https://www.vacmobiles.com/shop/vacmobile-vacuum-systems/Vacmobile-2SHD.html.

195. Vasey L. BEHAVIORAL DESIGN AND ADAPTIVE ROBOTIC FABRICATION OF A FIBER COMPOSITE COMPRESSION SHELL WITH PNEUMATIC FORMWORK / L. Vasey [et al.] // ACADIA 2015 - Computational Ecologies: Design in the Anthropocene: Proceedings of the 35th Annual Conference of the Association for Computer Aided Design in Architecture. - 2015. - Vols. 2015-October.

196. Vattam S.S. Nature of creative analogies in biologically inspired innovative design / S.S. Vattam, M.E. Helms, A.K. Goel // C and C 2009 - Proceedings of the 2009 ACM SIGCHI Conference on Creativity and Cognition. - 2009.

197. Vedernikov A. Effects of additives on the cure kinetics of vinyl ester pultrusion resins / A. Vedernikov [et al.] // Journal of Composite Materials. - 2021.

198. Vedernikov A. Effects of pulling speed on structural performance of L-shaped pultruded profiles / A. Vedernikov [et al.] // Composite Structures. - 2021. - Vol. 255. -№ July 2020. - P. 112967.

199. Vedernikov A. Effects of the Pre-Consolidated Materials Manufacturing Method on the Mechanical Properties of Pultruded Thermoplastic Composites / A. Vedernikov [et al.] // Polymers. - 2022. - Vol. 14. - № 11.

200. Vedernikov A. Modeling spring-in of l-shaped structural profiles pultruded at different pulling speeds / A. Vedernikov [et al.] // Polymers. - 2021. - Vol. 13. - № 16.

201. Vedernikov A. Pultruded materials and structures: A review. Vol. 54 / A. Vedernikov [et al.]. - 2020.

202. Veenendaal D. An overview and comparison of structural form finding methods for general networks / D. Veenendaal, P. Block // International Journal of Solids and Structures. - 2012. - Vol. 49. - № 26.

203. Veltkamp M. Free form structural design: Schemes, systems & prototypes of structures for irregular shaped buildings. Vol. 6 / M. Veltkamp. - Amsterdam, the Netherlands: IOS Press BV, 2007.

204. Venkayya V.B. Structural optimization: A review and some recommendations / V.B. Venkayya // International Journal for Numerical Methods in Engineering. - 1978. - Vol. 13. - № 2. - P. 203-228.

205. Verwimp E. Experimental and numerical buckling analysis of a thin TRC dome. Vol. 94 / E. Verwimp [et al.]. - Elsevier Ltd, 2015.

206. Voigt P. Die Pionierphase des Bauens mit glasfaserverstärkten Kunststoffen (GFK) 1942 bis 1980 / P. Voigt. - 2007.

207. Waimer F. Integrated design methods for the simulation of fibre-based structures / F. Waimer [et al.] // Rethinking Prototyping - Proceedings of the Design Modelling Symposium Berlin 2013. - 2013. - P. 1-9.

208. Waimer F. The railway station stuttgart 21 - Computational design and digital fabrication of freeform concrete shells / F. Waimer [et al.] // IASS Symposium 2019 -60th Anniversary Symposium of the International Association for Shell and Spatial Structures; Structural Membranes 2019 - 9th International Conference on Textile Composites and Inflatable Structures, FORM and FORCE. - 2019.

209. Wakasa M. Free-form optimization for controlling time-dependent responses of shell structures / M. Wakasa, M. Shimoda // Structural and Multidisciplinary Optimization 2019 60:4. - 2019. - Vol. 60. - № 4. - P. 1545-1560.

210. Wang X. Improved multi-objective Hybrid Genetic Algorithm for Shape and Size Optimization of Free-form latticed structures / X. Wang [et al.] // Journal of Building Engineering. - 2021. - Vol. 43. - P. 102902.

211. Wang Z. Shape optimization of free-form grid structures based on the sensitivity hybrid multi-objective evolutionary algorithm / Z. Wang [et al.] // Journal of Building Engineering. - 2021. - Vol. 44. - P. 102538.

212. Weigele J. Fibrous Morphologies / J. Weigele [et al.] // Computation and Performance - Proceedings of the 31st eCAADe Conference / eds. R. Stouffs, S. Sariyildiz. - Faculty of Architecture, Delft University of Technology, 2013. - P. 549-558.

213. Wenzel F. Frei Otto: Forschen, Bauen, Inspirieren / a Life of Research, Construction and Inspiration. Vol. 96 / F. Wenzel [et al.]. - 2019.

214. Wester T. Nature of structural morphology and some interdisciplinary examples / T. Wester // Proceedings of the IASS-ASCE International Symposium 1994 on Spatial, Lattice and Tension Structures. - Publ by ASCE, 1994. - P. 1000-1009.

215. Wester T. Nature of structural morphology and some interdisciplinary examples / T. Wester // Proceedings of the IASS-ASCE International Symposium 1994 on Spatial, Lattice and Tension Structures. - Publ by ASCE, 1994. - P. 1000-1009.

216. Williams C. What is a shell? / C. Williams // Shell Structures for Architecture: Form Finding and Optimization. - New York: Routledge, 2014. - Vol. 9781315849270.

- P. 21-31.

217. Xiang S. An analytic approach to predict the shape and internal forces of barrel vault elastic gridshells during lifting construction / S. Xiang [et al.] // Structures. - 2021.

- Vol. 29. - P. 628-637.

218. Yang Y. Recycling of composite materials / Y. Yang [et al.] // Chemical Engineering and Processing: Process Intensification. - 2012. - Vol. 51.

219. Yoon J. Design-to-fabrication with thermo-responsive shape memory polymer applications for building skins / J. Yoon // Architectural Science Review. - 2021. -Vol. 64. - № 1-2. - P. 72-86.

220. Zhang L.Y. Analytical form-finding of tensegrities using determinant of force-density matrix / L.Y. Zhang [et al.] // Composite Structures. - 2018. - Vol. 189.

221. Zhao Z. A novel numerical method for form-finding analysis of branching structures / Z. Zhao [et al.] // Journal of the Brazilian Society of Mechanical Sciences and Engineering. - 2017. - Vol. 39. - № 6.

222. Zhao Z. Efficient form-finding algorithm for free form grid structures based on inverse hanging method / Z. Zhao [et al.] // Structures. - 2022. - Vol. 44.

223. Zhao Z. Topology establishment, form finding, and mechanical optimization of branching structures / Z. Zhao, B. Liang, H. Liu // Journal of the Brazilian Society of Mechanical Sciences and Engineering. - 2018. - Vol. 40. - № 11.

224. Zhao Z. Shape optimization of reticulated shells with constraints on member instabilities / Z. Zhao [et al.] // Engineering Optimization. - 2019. - Vol. 51. - № 9.

225. Zhao Z. A form-finding method for spatial arch bridges based on inverse hanging method / Z. Zhao, T. Zhang, W. Wang // Structures. - 2022. - Vol. 46.

226. Zhou Y. Two-scale buckling topology optimization for grid-stiffened cylindrical shells / Y. Zhou [et al.] // Thin-Walled Structures. - 2020. - Vol. 151. -P. 106725.

227. Погалов А. Моделирование и прочностной анализ многокристального модуля в трехмерном исполнении / А. Погалов [et al.] // elibrary.ruAM Погалов, АМ Грушевский, ГА Блинов, ПА ЖуковОборонный комплекс-научно-техническому прогрессу России, 2007^ elibrary.ru.