Computational Design of Lightweight Structures E-Book

Benoit Descamps

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 154

Veröffentlichungsjahr: 2014

Beschreibung

The author of this book presents a general, robust, and easy-to-use method that can handle many design parameters efficiently. Following an introduction, Chapter 1 presents the general concepts of truss layout optimization, starting from topology optimization where structural component sizes and system connectivity are simultaneously optimized. To fully realize the potential of truss layout optimization for the design of lightweight structures, the consideration of geometrical variables is then introduced. Chapter 2 addresses truss geometry and topology optimization by combining mathematical programming and structural mechanics: the structural properties of the optimal solution are used for devising the novel formulation. To avoid singularities arising in optimal configurations, this approach disaggregates the equilibrium equations and fully integrates their basic elements within the optimization formulation. The resulting tool incorporates elastic and plastic design, stress and displacement constraints, as well as self-weight and multiple loading. The inherent slenderness of lightweight structures requires the study of stability issues. As a remedy, Chapter 3 proposes a conceptually simple but efficient method to include local and nodal stability constraints in the formulation. Several numerical examples illustrate the impact of stability considerations on the optimal design. Finally, the investigation on realistic design problems in Chapter 4 confirms the practical applicability of the proposed method. It is shown how we can generate a range of optimal designs by varying design settings.

Leseprobe

Table of Contents

Preface

Introduction

1 Truss Layout Optimization

1.1. Standard theory of mathematical programming

1.2. Governing equations of truss structures

1.3. Layout and topology optimization

1.4. Generalization

1.5. Truss geometry and topology optimization

1.6. Concluding remarks

2 Unified Formulation

2.1. Literature review

2.2. Disaggregation of equilibrium equations

2.3. Minimum volume problem

2.4. Minimum compliance problem

2.5. Reduced formulation for single loading

2.6. Nonlinear programming

2.7. Design settings

2.8. Concluding remarks

3 Stability Considerations

3.1. Literature review

3.2. Lower bound plastic design formulation

3.3. Nominal force method for local stability

3.4. Local buckling criterion

3.5. Formulation including stability constraints

3.6. Numerical examples

3.7. Concluding remarks

4 Structural Design Applications

4.1. Reticulated dome

4.2. Lateral bracing of Winter’s type column

4.3. Arch bridge

4.4. Suspension bridge

4.5. Dutch Maritime Museum

Conclusions and Future Prospects

Appendix

A1.1. Structural form-finding methods

A1.2. Metaheuristics for truss design

A1.3. Example of implementation

Bibliography

Index

First published 2014 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA

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© ISTE Ltd 2014

The rights of Benoît Descamps to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2013957304

British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISSN 2051-2481 (Print)ISSN 2051-249X (Online)ISBN 978-1-84821-674-7

Preface

Designing structures as light as possible is an intelligent and responsible way for engineers and architects to conceive structural systems. The key ingredient to achieve lightness relies on a thorough study of the structural form, which establishes a dialogue with forces. Nowadays, these structures are able to cross incredibly wide spans with the least amount of materials. Still, the quest for lightness must cope with current design constraints, which give sense to modern structures.

This book presents a computational method for the preliminary shape design of lightweight structures. The strategy relies on fundamental concepts of structural design to formulate an optimization problem combining the theories of mathematical programming and structural mechanics. The method considers many design settings including stress and displacement constraints, self-weight, multiple loading conditions and structural stability considerations. In addition, the conceptual framework is well suited to accommodate project-specific constraints. These building blocks result in an integrated design process at a midway between form finding and structural optimization. Several large-scale applications of three-dimensional bridge and dome structures emphasize the versatility and robustness of the proposed method.

This book is primarily written for graduate students and researchers in architectural, civil and mechanical engineering. It is also of significance for practioners in structural design who are concerned with the design of lightweight structures. Readers are assumed to have some basic knowledge of mathematical optimization and structural computational mechanics for a better understanding of this book.

Classical computational methods for designing lightweight structures are focused either on finding an equilibrium shape or are restricted to fairly small design applications. In this book, we aim to develop a general, robust and easy-to-use method that can handle many design parameters efficiently. These considerations have led to truss layout optimization, the goal of which is to find the best material distribution within a given design domain discretized by a grid of nodal points and connected by tentative bars.

Chapter 1 presents the general concepts of truss layout optimization, starting from topology optimization where structural component sizes and system connectivity are simultaneously optimized. The range of applications covers limit analysis and the identification of failure mechanisms in soils and masonries. To fully realize the potential of truss layout optimization for the design of lightweight structures, the consideration of geometrical variables is then introduced. The resulting truss geometry and topology optimization problem raises several fundamental and computational challenges, which are identified.

Then, Chapter 2 addresses truss geometry and topology optimization by combining mathematical programming and structural mechanics: the structural properties of the optimal solution are used for devising the novel formulation. To avoid singularities arising in optimal configurations, the present approach disaggregates the equilibrium equations and fully integrates their basic elements within the optimization formulation. The resulting tool incorporates elastic and plastic design, stress and displacement constraints, as well as self-weight and multiple loading.

In addition, the inherent slenderness of lightweight structures requires the study of stability issues. As a solution, Chapter 3 proposes a conceptually simple but efficient method to include local and nodal stability constraints in the formulation. Several numerical examples illustrate the impact of stability considerations on the optimal design.

Finally, the investigation of realistic design problems in Chapter 4 confirms the practical applicability of the proposed method. It is shown how we can generate a range of optimal designs by varying design settings. In this regard, the computational design method mostly requires the designer to have a good knowledge of structural design to provide an initial guess.

Benoît DESCAMPSJanuary 2014

Introduction

This introduction first describes lightweight structures in a historical context and points out current design issues. To tackle these challenges, section I.2 briefly discusses an empirical design process along with available methods for form finding and structural optimization. As a prelude to the novel method presented in this work, section I.3 introduces the conceptual framework of hanging models, plastic design and layout optimization leading to the computational design problem. The main achievements of the book are finally given in section I.4.

I.1. About lightweight structures

Structural design is an inseparable discipline of the art of building, whose governing factors are of a social, cultural, environmental, technical and financial nature. Given the considerable impact of the construction sector in terms of resources, today’s expectations are directed toward “meeting growing demand with limited resources”. In this context, designing structures as light as possible may greatly contribute to more sustainability: by reducing the structural mass, we not only reduce the quantity of raw material, but we also decrease the embodied energy used for its production, transport, assembly, maintenance, and demolition or reuse, as well as the impact on the ground and foundations [KAN 07].