# Shape Design Sensitivity Analysis and Optimization Using the Boundary Element Method

• Zhiye Zhao
Book

Part of the Lecture Notes in Engineering book series (LNENG, volume 62)

1. Front Matter
Pages N2-VIII
2. Zhiye Zhao
Pages 1-25
3. Zhiye Zhao
Pages 26-37
4. Zhiye Zhao
Pages 38-62
5. Zhiye Zhao
Pages 63-139
6. Zhiye Zhao
Pages 140-186
7. Back Matter
Pages 187-196

### Introduction

This book investigates the various aspects of shape optimization of two­ dimensional continuum structures, including shape design sensitivity analysis, structural analysis using the boundary element method (BEM), and shape optimization implementation. The book begins by reviewing the developments of shape optimization, followed by the presentation of the mathematical programming methods for solving optimization problems. The basic theory of the BEM is presented which will be employed later on as the numerical tool to provide the structural responses and the shape design sensitivities. The key issue of shape optimization, the shape design sensitivity analy­ sis, is fully investigated. A general formulation of stress sensitivity using the continuum approach is presented. The difficulty of the modelling of the ad­ joint problem is studied, and two approaches are presented for the modelling of the adjoint problem. The first approach uses distributed loads to smooth the concentrated adjoint loads, and the second approach employs the singu­ larity subtraction method to remove the singular boundary displacements and tractions from the BEM equation. A novel finite difference based approach to shape design sensitivity is pre­ sented, which overcomes the two drawbacks of the conventional finite difference method. This approach has the advantage of being simple in concept, and eas­ ier implementation. A shape optimization program for two-dimensional continuum structures is developed, including structural analysis using the BEM, shape design sensitiv­ ity analysis, mathematical programming, and the design boundary modelling.

### Keywords

Gestaltoptimierung Randelementmethode analysis boundary element method calculus design design sensitivity mathematical programming model modeling optimization programming shape optimization

#### Authors and affiliations

• Zhiye Zhao
• 1
1. 1.School of Civil and Structural EngineeringNanyang Technological UniversitySingapore

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-84382-2
• Copyright Information Springer-Verlag Berlin Heidelberg 1991
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-540-53518-8
• Online ISBN 978-3-642-84382-2
• Series Print ISSN 0176-5035