Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics

Vladimir F. Dem’yanov, Georgios E. Stavroulakis, Ludmila N. Polyakova, Panagiotis D. Panagiotopoulos (auth.)0792340930, 9780792340935

Nonsmooth energy functions govern phenomena which occur frequently in nature and in all areas of life. They constitute a fascinating subject in mathematics and permit the rational understanding of yet unsolved or partially solved questions in mechanics, engineering and economics.
This is the first book to provide a complete and rigorous presentation of the quasidifferentiability approach to nonconvex, possibly nonsmooth, energy functions, of the derivation and study of the corresponding variational expressions in mechanics, engineering and economics, and of their numerical treatment. The new variational formulations derived are illustrated by many interesting numerical problems. The techniques presented will permit the reader to check any solution obtained by other heuristic techniques for nonconvex, nonsmooth energy problems. A civil, mechanical or aeronautical engineer can find in the book the only existing mathematically sound technique for the formulation and study of nonconvex, nonsmooth energy problems.
Audience: The book will be of interest to pure and applied mathematicians, physicists, researchers in mechanics, civil, mechanical and aeronautical engineers, structural analysts and software developers. It is also suitable for graduate courses in nonlinear mechanics, nonsmooth analysis, applied optimization, control, calculus of variations and computational mechanics.

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Table of contents :
Front Matter….Pages i-xvii
Nonsmooth Analysis….Pages 1-48
Quasidifferentiable Functions and Sets….Pages 49-91
Nonsmooth Mechanics I….Pages 93-137
Nonsmooth Mechanics II….Pages 139-176
Additional Topics….Pages 177-203
Nonsmooth Optimization Algorithms….Pages 205-252
Nonsmooth Computational Mechanics….Pages 253-295
Nonsmooth Computational Mechanics….Pages 297-344
Back Matter….Pages 345-349