A Mathematical Introduction to Sizing and Shape Optimization

• Published in: Introduction to Shape Optimization p. 1
• Main Authors: Mäkinen R. A. E, Haslinger J
• Format: Book Chapter
• Language: English
• Published: Society for Industrial and Applied Mathematics (SIAM) 2003; Society for Industrial and Applied Mathematics
• Series: Advances in Design and Control
• Subjects: General Engineering & Project Administration; Manufacture & Processing; Structural optimization—Mathematics
• ISBN: 0898715369; 9780898715361
• DOI: 10.1137/1.9780898718690.ch2

The aim of this chapter is to present ideas that are used in existence and convergence analysis in sizing and shape optimization (SSO). As we shall see, the basic ideas are more or less the same: we first prove that solutions of state problems depend continuously on design variables (and we shall sp...

Table of Contents:

• 2.1 Thickness Optimization of an Elastic Beam: Existence and Convergence Analysis 2.2 A Model Optimal Shape Design Problem 2.3 Abstract Setting of Sizing Optimization Problems: Existence and Convergence Results 2.4 Abstract Setting of Optimal Shape Design Problems and Their Approximations 2.5 Applications of the Abstract Results Problems
• 2.1 Thickness optimization of an elastic beam: Existence and convergence analysis 2.2 A model optimal shape design problem 2.3 Abstract setting of sizing optimization problems: Existence and convergence results 2.4 Abstract setting of optimal shape design problems and their approximations 2.5 Applications of the abstract results Problems