Overview

The aim of this text is the formulation, mathematical study and numerical treatment of static and dynamic problems in mechanical and engineering sciences involving nonconvex and nonsmooth energy functions, or nonmonotone and multivalued stress-strain laws. Such problems lead to a new type of variational forms, the hemivariational inequalities, which also lead to multivalued differential or integral equations. Innovative numerical methods are presented for the treatment of realistic engineering problems. The text deals with the variational theory of engineering problems involving nonmonotone multivalue relations, their mechanical foundation, their mathematical study (existence and certain approximation results) and the corresponding eigenvalue and optimal control problems. All the numerical applications give innovative answers to as yet unsolved or partially solved engineering problems, such as the adhesive contact in cracks, the delamination problem, the sawtooth stress-strain laws in composites, the shear connectors in composite beams, the semirigid connections in steel structures, the adhesive grasping in robotics, etc. The book closes with a consideration of hemivariational inequalities for fractal type geometries and with the neural network approach to the numerical treatment of hemivariational inequalities.

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9783540549635

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