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Full Description
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.
Contents
Preface. Introduction. Guidelines for the Readers. 1. Nonsmooth Analysis. The One-Dimensional Case. 2. Quasidifferentiable Functions and Sets. Quasidifferentiable Optimization and Optimality Conditions. 3. Nonsmooth Mechanics I. Nonsmooth Modelling in Mechanics. 4. Nonsmooth Mechanics II. Variational Formulations Using Quasidifferentiability. 5. Additional Topics. Stability, Economics, Flow Problems, Dynamic Problems. 6. Nonsmooth Optimization Algorithms. Quasidifferentiable and Codifferentiable Optimization. 7. Nonsmooth Computational Mechanics I. Modelling and Applications. 8. Nonsmooth Computational Mechanics II. Algorithms and Examples. Subject Index.
