Optimization of Structural Topology, Shape, and Material

1. Front Matter

   Pages I-XI

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2. Introduction

   • Martin P. Bendsøe

   Pages 1-4

3. The homogenization approach to topology design

   • Martin P. Bendsøe

   Pages 5-77

4. Optimized energy functionals for the design of topology and shape

   • Martin P. Bendsøe

   Pages 79-107

5. Extremal energy functionals for a free parametrization of material, shape and topology

   • Martin P. Bendsøe

   Pages 109-137

6. Topology design of truss structures

   • Martin P. Bendsøe

   Pages 139-180

7. Extensions of topology design methodologies

   • Martin P. Bendsøe

   Pages 181-226

8. Bibliographical notes

   • Martin P. Bendsøe

   Pages 227-236

9. Back Matter

   Pages 237-273

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In the past, the possibilities of structural optimization were restricted to an optimal choice of profiles and shape. Further improvement can be obtained by selecting appropriate advanced materials and by optimizing the topology, i.e. finding the best position and arrangement of structural elements within a construction.
The optimization of structural topology permits the use of optimization algorithms at a very early stage of the design process.
The method presented in this book has been developed by Martin Bendsoe in cooperation with other researchers and can be considered as one of the most effective approaches to the optimization of layout and material design.

• Materials
• Mathematical Optimization
• Structures
• Topological
• algorithms
• applied mechanics
• design
• design process
• engineering design
• mechanics
• optimization
• structural optimization
• topology

From the reviews of the second edition:

"The book consists of two parts. The first part deals with the topology design within the framework of searching for optimum ‘classical designs’ for isotropic materials … . The second part concentrates on compliance design … . The book is accessible to the novice and expert, alike, and can be used by students, engineers and scientists working in aerospace, automotive, and mechanical and civil engineering." (Stefan Jendo, Zentralblatt MATH, Vol. 1059 (10), 2005)

"This is a ‘practical’ book. Apart from mathematical models, it includes the necessary computational procedures, verified by extensive practical experience. Each section is illustrated by many examples … . The bibliography … represents a rich source for readers who want to study details of particular topics. I find the book to be very useful for … mathematicians, civil and structural engineers, materials scientists and others. … it is a rich source of problem formulations, examples, and computational techniques … ." (Michal Kocvara, Mathematical Reviews, Issue 2005 e)

• Mathematical Institute, Technical University of Denmark, Lyngby, Germany

  Martin P. Bendsøe

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