Introduction to Shape Optimization by Jan Sokolowski

Introduction to Shape Optimization by Jan Sokolowski

This book is motivated largely by a desire to solve shape optimization prob- lems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems. Many such problems can be formulated as the minimization of functionals defined over a class of admissible domains. Shape optimization is quite indispensable in the design and construction of industrial structures. For example, aircraft and spacecraft have to satisfy, at the same time, very strict criteria on mechanical performance while weighing as little as possible. The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. g. such as the weight of the structure) and yet simultaneously satisfies specific constraints (like thickness, strain energy, or displacement bounds). The geometry of the structure can be considered as a given domain in the three-dimensional Euclidean space. The domain is an open, bounded set whose topology is given, e. g. it may be simply or doubly connected. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed. In general the cost functional takes the form of an integral over the domain or its boundary where the integrand depends smoothly on the solution of a boundary value problem.

Antonio Andr� Novotny is a Senior Researcher at the National Laboratory for Scientific Computing, Petr�polis, Brazil. His research topics include the theoretical development and applications of the topological derivative method to shape and topology optimization; inverse problems; imaging processing; multi-scale material design; and mechanical modeling, including damage and fracture phenomena.

Jan Sokolowski is a Full Professor at the Institute of Mathematics (IECL) at the Universit� de Lorraine in Nancy, France, and at the Polish Academy of Sciences' Systems Research Institute. He has published five monographs with Springer and Birkhauser, and over 200 research papers in international journals. His research focuses on shape and topology optimization for the systems described by partial differential equations.

SKU	Unavailable
ISBN 13	9783540541776
ISBN 10	3540541772
Title	Introduction to Shape Optimization
Author	Jan Sokolowski
Series	Springer Series In Computational Mathematics
Condition	Unavailable
Binding Type	Hardback
Publisher	Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Year published	1992-06-01
Number of pages	254
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.