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Mathematical Problems in Shape Optimization and Shape Memory Materials


Antoni Zochowski

The book is devoted to nonlinear mathematical problems encountered in modern structural design: shape optimization and «smart» materials. In the first part a method of sensitivity calculations for singular elliptic problems is proposed and its correctness as well as some properties are proved. Examples of applications are given. The second part concerns structures reinforced with shape memory materials. The existence, uniqueness and differentiability properties of solutions to dynamic problems are proved, based on the Landau-Devonshire shape memory effect model. Finally, an approach to the description of noncristalline shape memory materials with preliminary existence results is presented.
Contents: Shape sensitivity for singular elliptic problems - Existence results for structures reinforced with shape memory materials - Control problems with shape memory actuators - A model of the noncristalline shape memory material.