Hemivariational Inequalities: Applications in Mechanics and Engineering - Softcover

Inhaltsangabe

I Introductory Topics.- 1 Elements of Nonsmooth Analysis.- 1.1 Convexity and Sub differential.- 1.2 Generalized Gradient and Related Calculus.- 1.3 Minimization Problems. Duality of Convex Functionals.- 1.4 Miscellanea: Fans, Quasidifferentials, Codifferentials.- II Mechanical Theory.- 2 Nonsmooth Mechanics I.- 2.1 Convex Superpotentials.- 2.2 Nonconvex Superpotentials.- 2.3 Boundary Conditions Expressed via Convex Superpotentials.- 2.4 Boundary Conditions Expressed via Nonconvex Superpotentials.- 2.5 Extensions to Function Spaces.- 3 Nonsmooth Mechanics II.- 3.1 Material Laws Expressed via Convex Superpotentials. An Overview.- 3.2 Material Laws Expressed via Nonconvex Superpotentials I.- 3.3 Material Laws Expressed via Nonconvex Superpotentials II.- 3.4 Loading and Unloading Problems. The Advantage of the Use of Superpotentials.- 3.5 Material Laws and Boundary Conditions Expressed via Fans, Quasi differentials and Codifferentials.- 4 Hemivariational Inequalities.- 4.1 The Derivation of Hemivariational Inequalities in Mechanical Problems.- 4.2 Hemivariational and Variational-Hemivariational Inequalities.- 4.3 Substationarity Problems for the Potential or the Complementary Energy.- 4.4 Loading and Unloading Problems, Eigenvalue Problems for Hemivariational Inequalities and Dynamic Problems.- 4.5 On the F-superpotential and the V-superpotential. Quasidiffer-entiability in Mechanics.- 5 Multivalued Boundary Integral Equations.- 5.1 The Indirect and the Direct Method for Nonmonotone Boundary Conditions.- 5.2 Complement for Adhesively Bonded Cracks.- III Mathematical Theory.- 6 Static Hemivariational Inequalities.- 6.1 Coercive Hemivariational Inequalities.- 6.2 Semicoercive Hemivariational Inequalities.- 6.3 On the Substationarity of the Energy.- 6.4 Variational Hemivariational Inequalities.- 6.5 Applications to Engineering Problems.- 7 Eigenvalue and Dynamic Problems.- 7.1 On the Eigenvalue Problem for Hemivariational Inequalities.- 7.2 Dynamic Hemivariational Inequalities.- 7.3 Applications to Engineering Problems: Von Kármán Plates and Thermoelasticity.- 8 Optimal Control and Identification Problems.- 8.1 Formulation of the Problem.- 8.2 Mathematical Study of the Optimal Control Problem Governed by Hemivariational Inequalities.- 8.3 Applications to Engineering Problems.- IV Numerical Applications.- 9 On the Numerical Treatment of Hemivariational Inequalities.- 9.1 The First Numerical Attempts and the Questions of Stability and Uniqueness.- 9.2 The Microspring Approximation Method of the Decreasing Branch.- 9.3 The Method of Decreasing Branch Approximation by Monotone Laws.- 9.4 Application I: Cleavage in Laminated Composites and the Non-monotone Unilateral Contact Problem.- 9.5 Application II: The Nonmonotone Friction Problem and the Combined Unilateral Contact Problem with Nonmonotone Friction.- 10 On the Approximation of Hemivariational Inequalities by Variational Inequalities.- 10.1 General Formulation of the Method.- 10.2 Application III: Nonmonotone Friction Interface Conditions with Debonding.- 10.3 Application IV:Adhesive Joints in Structural Mechanics.- 10.4 Application V: Comparison with the Path Following Method.- 10.5 Application VI: Nonmonotone Stress-Strain Laws. The Sawtooth Behaviour of Composites.- 10.6 Application VII: Shear Connectors in Composite Beams.- 11 The Method of Substationary Point Search.- 11.1 General Formulation of the Method.- 11.2 On the Numerical Implementation of the Algorithm.- 11.3 Application VIII: Delamination and Adhesive Joints in Structural Mechanics.- 11.4 Application IX: Semirigid Connections in Steel Structures.- 12 On a Decomposition Method into Two Convex Problems.- 12.1 General Formulation of the Method.- 12.2 Application X: The Stamp Problem and the Interfacial Debonding in Composites.- 13 Dynamic Hemivariational Inequalities and Crack Problems.- 13.1 Application XI: Numerical Treatment of Dynamic Hemivariational Inequalities.- 13.2 Application XII: The Unilateral Contact and N

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