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Case-Studies in Topology Optimisation of Bracing Systems ROBERT BALDOCK

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Case-Studies in Topology Optimisation of Bracing Systems ROBERT BALDOCK STRUCTURAL OPTIMISATION IN BUILDING DESIGN PRACTICE : CASE -STUDIES IN TOPOLOGY OPTIMISATION OF BRACING SYSTEMS Robert Baldock Corpus Christi College June 2007 A dissertation submitted for the Degree of Doctor of Philosophy Cambridge University Engineering Department Declaration Except where otherwise stated, this thesis is the result of my own research and does not include the outcome of work done in collaboration. This thesis has not been submitted in whole or in part for consideration for any other degree of qualification at the University or any other institute of learning. The thesis contains 49 figure, 14 tables and less than 42,000 words. Robert Baldock Corpus Christi College Cambridge June 2007 Abstract Keywords: structural topology optimisation, structural design practice, bracing design, Evolutionary Structural Optimisation, Pattern Search, Optimality Criteria, Genetic Programming, computer-aided design, large-scale structural size optimisation This thesis aims to contribute to the reduction of the significant gap between the state- of-the-art of structural design optimisation in research and its practical application in the building industry. The research has focused on structural topology optimisation, investigating three distinct methods through the common example of bracing design for lateral stability of steel building frameworks. The research objective has been aided by collaboration with structural designers at Arup. It is shown how Evolutionary Structural Optimisation can be adapted to improve applicability to practical bracing design problems by considering symmetry constraints, rules for element removal and addition, as well as the definition of element groups to enable inclusion of aesthetic requirements. Size optimisation is added in the optimisation method to improve global optimality of solutions. A modified Pattern Search algorithm is developed, suitable for the parameterised, grid-based, topological design problem of a live, freeform tower design project. The alternative objectives of minimising bracing member piece count or bracing volume are considered alongside an efficient simultaneous size and topology optimisation approach, through integration of an Optimality Criteria method. A range of alternative optimised designs, suitable for assessment according to unmodelled criteria, are generated by stochastic search, parametric studies and changes in the initial design. This study is significant in highlighting practical issues in the application of structural optimisation in the building industry. A Genetic Programming formulation is presented, using design modification operators as modular "programmes", and shown to be capable of synthesising a range of novel, optimally-directed designs. The method developed consistently finds the global optimum for a small 2D planar test problem, generates high-performance designs for larger scale tasks and shows the potential to generate designs meeting user-defined aesthetic requirements. The research and results presented contribute to establishing a structural optimisation toolbox for design practice, demonstrating necessary method extensions and considerations and practical results that are directly applicable to building projects. Acknowledgements I wish to thank my academic supervisor, Kristina Shea, for her dedicated support, guidance and encouragement throughout the course of this project. I am also greatly indebted to Geoff Parks for his efficiency and advice in the role of advisor and subsequently as administrative supervisor. Thanks are due to Marina Gourtovaia and Andrew Flintham for their valuable assistance in computing matters and to all my friends and colleagues in the Engineering Design Centre, Cambridge for many stimulating discussions. The collaboration with Arup has been fundamental to this research. I therefore wish to express my sincere gratitude to Ed Clark and Alvise Simondetti, as industrial supervisors, as well as Damian Eley, Chris Neighbour, Steve McKechnie, Martin Holt, Colin Jackson, Jan-Peter Koppitz, Chris Carroll, Pat Dallard and Peter Young, all of whom generously gave time to aid me in various aspects of this project. Additionally, the support of Chris Kaethner and Stephen Hendry, in relation to Oasys GSA, has been very beneficial. I could not have completed this thesis without the fantastic friends who have inspired, distracted and kept me sane. I have been blessed with loving and loyal parents who have supported me from my first steps to the conclusion of this thesis. I owe them the greatest thanks of all. This research has been made possible through funding by the Engineering and Physical Sciences Research Council and an Industrial CASE studentship from Arup. Additional financial support from Cambridge University Engineering Department, Corpus Christi College, Cambridge and the Royal Commission for the Exhibition of 1851 is also gratefully acknowledged. Contents 1. INTRODUCTION ………………………………………………………….. 1 1.1. The nature of design optimisation ……………………………………. 1 1.2. Optimisation of structures ……………………………………………. 3 1.3. The design process for building structures ………………………… ... 5 1.4. Drivers and barriers for structural optimisation in the building industry 7 1.5. Summary of research contributions .………………………….……… 10 1.6. Thesis structure …………………………………………….………… 11 2. STATE-OF-THE-ART: RESEARCH AND PRACTICE OF DESIGN OPTIMISATION IN STRUCTURAL ENGINEERING …………………... 12 2.1. Structural design optimisation research ……………………………… 12 2.1.1. Section-size optimisation ………………………………………... 14 Optimality Criteria ………………………………………………… 14 Mathematical Programming ………………………………………. 14 Fully Stressed Design ……………………………………………… 15 Additional considerations ………………………………………….. 15 2.1.2. Discrete topology optimisation methods ………………………… 16 Ground structure approach ………………………………………… 16 Ruled-based approaches …………………………………………… 18 2.1.3. Evolutionary Algorithms in topology optimisation ……………… 19 Genetic Algorithms …………………………………………...….... 19 Genetic Programming ……………………………………………… 20 Evolutionary Strategies …………………………………………….. 21 Evolutionary Programming ……………………………………….... 21 2.1.4. Continuum-based optimisation methods …………………………. 21 Homogenisation …………………………………………………….. 22 Bubble method ……………………………………………………… 22 Evolutionary Structural Optimisation ……………………………… 22 2.1.5. Computer-based conceptual design methods …………………….. 24 2.2. Optimisation in building engineering design practice ………………… 25 2.2.1. Comparison of structural design in the automotive and aeronautical industries versus the building industry …………………………… 25 2.2.2. Commercial optimisation software ……………………………….. 27 2.2.3. Published literature on industrial applications ……………………. 29 Section-size optimisation …………………………………………… 29 Evolutionary Structural Optimisation (ESO) ……………………….. 30 Parametric optimisation …………………………………………….. 31 Non-parametric optimisation ……………………………………….. 31 2.2.4. Facilitating structural optimisation ……………………………….. 32 Software …………………………………………………………….. 32 Parametric optimisation case studies ……………………………….. 33 Non-parametric discrete optimisation and design generation case studies ………………………………………………………………………. 33 2.3. Conclusions …………………………………………………………….. 34 2.4. Justification of case study ……………………………………………… 35 2.5. Context of research contributions ……………………………………... 37 Evolutionary Structural Optimisation ………………………………. 37 Pattern Search and Optimality Criteria ……………………………... 37 Genetic Programming using design modification operators ………... 38 3. CONTINUUM TOPOLOGY OPTIMISATION OF BRACED STEEL FRAMES ……………………………………………………………………….. 40 3.1. Introduction …………………………………………………………….. 40 3.2. Background …………………………………………………………….. 40 4.7.1 Method overview ………………………………………………….. 40 3.2.1. Addition considerations and extensions …………………………... 41 3.2.2. Evolutionary Structural Optimisation (ESO) for stiffness and displacement constraints ………………………………………….. 43 3.2.3. Bi-directional Evolutionary Structural Optimisation (BESO) …… 45 3.3. Benchmark problem: structural model specifications ………………… 45 3.4. Optimisation for minimal mean compliance ………………………….. 46 3.5. Optimisation for displacement constraint …… ……………………….. 47 3.6. Including optimisation of domain thickness …………………………... 53 3.7. Including architectural requirements and pattern definition …………... 58 3.8. Discrete interpretation of continuum topologies ………………………. 60 3.9. Conclusions ……………………………………………………………. 64 3.10. Guidelines for practical use …………………………………………… 64 4. BRACING TOPOLOGY AND SECTION-SIZE OPTIMISATION BY A HYBRID ALGORITHM: AN INDUSTRIAL CASE-STUDY ………………………... 67 4.1. Introduction …………………………………………………………… 67 4.2. Background ………………………………………… ………………… 68 4.4.1. Overview of studies ……………………………………………… 69 4.3. Design task definition …………………………………………………. 69 4.3.1. Structural models ………………………………………………… 69 4.3.2. Topology optimisation models …………………………………… 72 Optimisation model A ……………………………………………… 72 Optimisation model B ……………………………………………… 72 4.4. Pattern Search method ………………………………………………… 73 4.5. Live project optimisation ……………………………………………… 75 4.5.1. Topology optimisation by Modified Pattern Search ……………... 75 4.5.2. Parametric studies ………………………………………………… 76 4.5.3. Outline proposals …………………………………………………. 77 4.6. Characterisation of design space ………………………………………. 78 4.7. Topology optimisation method development …………………………. 80 4.7.1. Objective function formulation …………………………………... 83 Formulation 1 ………………… ……………………………………. 83 Formulation 2 ………………… ……………………………………. 83 4.7.2. Comparative investigation ………………………………………... 84 Evolving
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