Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics
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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Quasidifferentiable Functions and Sets
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adhesive algorithms Analogously applications assume boundary conditions calculus Cartesian coordinate system classical compact sets cone constraints contact law continuously codifferentiable convex analysis convex compact sets convex function convex sets d.c. functions defined deformation denotes df(x differentiable function Dini Dini derivatives directional derivative directionally differentiable displacements duality elastic elastoplasticity equation equivalent Example exists fi(x Find finite following problem friction law gradient hemivariational inequalities holds hypodifferential inequality problems interface laws Let us consider linear Lipschitz material laws max vg method minimization problem monotone Moreover nonlinear nonmonotone friction normal open set optimality conditions optimization problem pair of convex Panagiotopoulos P.D. plasticity plate possibly multivalued potential energy QD-superpotential quasidifferentiable function real number relation resp satisfy Sect set ft solution space Stavroulakis G.E. stresses subdifferential sublinear functions subset superdifferential superpotentials system of variational tangential tensor Theorem theory tion unilateral contact variational formulation variational inequalities vector yield surface