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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
Engineering design is an iterative process, in which the design is continuously modified until it meets the criteria set by the engineers. The traditional design process is carried out by the so called ‘trial and error’ method, in which the designer uses his experience and intuition to lead the design process. This manual based design process has the advantage that the designer’s knowledge can be utilized in the design, and this approach still dominates the design method. But as the design problem becomes more complex, design modification becomes much more difficult. Therefore there is a urgent need for a new tool to guide the design modification.
Zhiye Zhao

Chapter 2. Basic Numerical Optimization Techniques

Abstract
The aim of this chapter is to provide the basic concepts and terminology in shape optimization by the mathematical programming method, which will be used throughout the thesis. Various algorithms of the mathematical programming methods are presented to give a general view of the numerical methods available today. The information presented here is mainly from References [1]–[5], in which more details can be found.
Zhiye Zhao

Chapter 3. The Boundary Element Method in Elastostatics

Abstract
This chapter introduces the basic theory and numerical aspects of the boundary element method in elastostatics which will be used later on as a numerical analysis tool for shape optimization. After a historical review of the boundary element method in elastostatics, the boundary element formulation for elasticity is presented, followed by the numerical implementation. Final concluding remarks discuss the advantages and drawbacks of the boundary element method over the finite element method in the field of structural analysis, especially in the application of shape optimum design.
Zhiye Zhao

Chapter 4. Shape Design Sensitivity Analysis using the Boundary Element Method

Abstract
The mathematical programming (MP) methods for shape optimization are iterative methods, in which the designs are modified successively until all the criteria are satisfied. A key issue during the design modification is to predict how the response of the structure changes due to the shape change of the structure. This information is called shape design sensitivity, which is defined as the rates of change of structural responses with respect to the design variables. It is essential to provide accurate design sensitivity information in order to use those MP methods discussed in Chapter 2.
Zhiye Zhao

Chapter 5. Shape Optimization Using the Boundary Element Method

Abstract
In the previous chapters, different elements of shape optimization are discussed, including mathematical programming methods, the boundary element method and shape design sensitivity analysis. An integrated shape optimization system contains a number of subproblems which must be treated properly in order to obtain a satisfied optimum design. The five main subproblems of a shape optimization system are described as following:
1)
Structural Analysis Structural analysis provides the response of a structure under certain loads.
 
Zhiye Zhao

Backmatter

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