In a remarkably short time, the field of inequality problems has seen considerable development in mathematics and theoretical mechanics. Applied mechanics and the engineering sciences have also benefitted from these developments in that open problems have been treated and entirely new classes of problems have been formulated and solved. This book is an outgrowth of seven years of seminars and courses on inequality problems in mechanics for a variety of audiences in the Technical University of Aachen, the Aristotle University of Thessaloniki, the University of Hamburg and the Technical University of Milan. The book is intended for a variety of readers, mathematicians and engineers alike, as is detailed in the Guidelines for the Reader. It goes without saying that the work of G. Fichera, J. L. Lions, G. Maier, J. J. Moreau in originating and developing the theory of inequality problems has considerably influenced the present book. I also wish to acknowledge the helpful comments received from C. Bisbos, J. Haslinger, B. Kawohl, H. Matthies, H. O. May, D. Talaslidis and B. Werner. Credit is also due to G. Kyriakopoulos and T. Mandopoulou for their exceptionally diligent work in the preparation of the fmal figures. Many thanks are also due to T. Finnegan and J. Gateley for their friendly assistance from the linguistic standpoint. I would also like to thank my editors in Birkhiiuser Verlag for their cooperation, and all those who helped in the preparation of the manuscript
CONTENT
1. Introductory Topics -- 1. Essential Notions and Propositions of Functional Analysis -- 2. Elements of Convex Analysis -- 2. Inequality Problems -- 3. Variational Inequalities and Superpotentials -- 4. Variational Inequalities and Multivalued Convex and Nonconvex Problems in Mechanics -- 5. Friction Problems in the Theory of Elasticity -- 6. Subdifferential Constitutive Laws and Boundary Conditions -- 7. Inequality Problems in the Theory of Thin Elastic Plates -- 8. Variational and Hemivariational Inequalities in Linear Thermoelasticity -- 9. Variational Inequalities in the Theory of Plasticity and Viscoplasticity -- 3. Numerical Applications -- 10. The Numerical Treatment of Static Inequality Problems -- 11. Incremental and Dynamic Inequality Problems -- Epilogue -- Appendices -- Appendix I. Some Basic Notions [20] [112] [321] [322] -- Appendix II. Rigidifying Velocity Fields. Objectivity [112] [197] [322] -- Appendix III. Dissipation [112]. -- Appendix IV. Plasticity and Thermodynamics [75] [196] -- List of Notations -- References
Mathematics
Physics
Mechanics
Mathematics
Mathematics general
Mechanics
Theoretical Mathematical and Computational Physics
