Mathematical Problems in Shape Optimization and Shape Memory Materials
Published on 1. August 1992
Book
Paperback/Softback
120 pages
978-3-631-45085-7 (ISBN)
Description
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.
Reviews / Votes
«This is a very informative and interesting book giving good insight into new developments in the area under consideration.» (Fredi Tröltzsch, Mathematical Review)More details
Person
The Author: Antoni Zochowski was born in 1951 in Szczecin, Poland, and has graduated from the Applied Mathematics Faculty of the Warsaw Technical University. In 1976 he obtained the Ph.D. and now works in the Systems Research Institute of the Polish Academy of Sciences. From 1981 to 1983 he visited Hiroshima University supported by the Japanese Society for the Promotion of Science. From 1990 to 1991 he was the Humboldt scholar at the Augsburg University. His current fields of interest include mathematical problems in nonlinear elasticity, shape design, phase transitions, reaction-diffusion systems.
Content
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.