Nonsmooth/Nonconvex Mechanics: Modeling, Analysis and Numerical Methods
Nonsmooth and nonconvex models arise in several important applications of mechanics and engineering. The interest in this field is growing from both mathematicians and engineers. The study of numerous industrial applications, including contact phenomena in statics and dynamics or delamination effects in composites, require the consideration of nonsmoothness and nonconvexity.\ The mathematical topics discussed in this book include variational and hemivariational inequalities, duality,...
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Nonsmooth and nonconvex models arise in several important applications of mechanics and engineering. The interest in this field is growing from both mathematicians and engineers. The study of numerous industrial applications, including contact phenomena in statics and dynamics or delamination effects in composites, require the consideration of nonsmoothness and nonconvexity. The mathematical topics discussed in this book include variational and hemivariational inequalities, duality, complementarity, variational principles, sensitivity analysis, eigenvalue and resonance problems, and minimax problems. Applications are considered in the following areas among others: nonsmooth statics and dynamics, stability of quasi- static evolution processes, friction problems, adhesive contact and debonding, inverse problems, pseudoelastic modeling of phase transitions, chaotic behavior in nonlinear beams, and nonholonomic mechanical systems. This volume contains 22 chapters written by various leading researchers and presents a cohesive and authoritative overview of recent results and applications in the area of nonsmooth and nonconvex mechanics. Audience: Faculty, graduate students, and researchers in applied mathematics, optimization, control and engineering.
Contributing AuthorsPrefaceIn Memoriam, Professor P. D. Panagiotopoulos1Stability of a quasi-static evolution12Variational principles for self-adjoint elliptic eigenproblems153A sensitivity equation method for conduction and phase change problems434Rock's interface problem including adhesion695On a Class of Differential-Hemivariational Inequalities836Nonsmooth/Nonconvex dynamics: Duality, polarity, complementary extrema957Signorini problem with a given friction1418Debonding of Adhesively Bonded Composite Structures1739Effect of nonlinearity in nonsmooth and nonconvex structural behaviour18910Pseudoelastic solution for one-dimensional martensite phase transitions23111Inverse Coefficient Problem24712Solutions to eigenvalue problems for hemivariational inequalities26313Non-smooth changes in elastic material properties under finite deformation27714Nonlinear Rescaling in discrete minimax30115Multivalued problems with strong resonance33316Freely propagating waves in a supported nonlinear elastic beam34917Shape sensitivities for optimal design: A case study36918Optimal design and identification problems in nonsmooth mechanics39119Adhesively Supported von Karman Plate41120Optimality conditions of semi-invex functions42721The chaotic behaviour of a physically nonlinear beam43722Duality principle in nonholonomic mechanical systems447
