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Author:   P.D. Panagiotopoulos ,  Panagiotopoulos
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   1985 ed.
Dimensions:   Width: 17.80cm , Height: 2.30cm , Length: 25.40cm
Weight:   0.985kg
ISBN:  

9780817630942

ISBN 10:   0817630945
Pages:   412
Publication Date:   01 January 1985
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

1. Introductory Topics.- 1. Essential Notions and Propositions of Functional Analysis.- 1.1 Topological Vector Spaces and Related Subjects.- 1.1.1 Topological Spaces and Continuous Mappings.- 1.1.2 Locally Convex Topological Vector Spaces, Normed Spaces and Linear Mappings.- 1.2 Duality in Topological Vector Spaces.- 1.2.1 Duality. Weak and Strong Topologies.- 1.2.2 Topologically Dual Pairs of Vector Spaces.- 1.2.3 Duality in Normed and Hilbert Spaces.- 1.2.4 Transpose of a Continuous Linear Mapping Scales of Hilbert Spaces. The Lax-Milgram Theorem.- 1.3 Certain Function Spaces and Their Properties.- 1.3.1 The Spaces $$ {C^m}\left( \Omega \right),{C^m}\left( {\overline \Omega } \right),D\left( \Omega \right),D\left( {\overline \Omega } \right)and{L^p}\left( \Omega \right) $$.- 1.3.2 Spaces of Distributions.- 1.3.3 Sobolev Spaces.- 1.3.4 Trace Theorem. Imbedding Properties of Sobolev Spaces.- 1.3.5 The Space of Functions of Bounded Deformation.- 1.4 Additional Topics.- 1.4.1 Elements of the Theory of Vector-valued Functions and Distributions.- 1.4.2 Elements of Differential Calculus.- 1.4.3 Supplementary Notions and Propositions.- 2. Elements of Convex Analysis.- 2.1 Convex Sets and Functionals.- 2.1.1 Definitions.- 2.1.2 Lower Semicontinuous Convex Functionals.- 2.2 Minimization of Convex Functionals.- 2.2.1 Existence of a Minimum.- 2.2.2 Variational Inequalities.- 2.3 Subdifferentiability.- 2.3.1 Definitions and Related Propositions.- 2.3.2 One-Sided Directional Gateaux-Differential.- 2.4 Subdifferential Calculus.- 2.4.1 The Subdifferential of a Sum of Functionals and of a Composite Functional.- 2.4.2 The Relative Interior of R(?f).- 2.5 Conjugates of Convex Functionals.- 2.5.1 The Classes ?(X) and ?0(X).- 2.5.2 The Conjugacy Operation.- 2.6 Maximal Monotone Operators.- 2.6.1 Definitions and Fundamental Results.- 2.6.2 Maximal Monotone Graphs in ?2.- 2. Inequality Problems.- 3. Variational Inequalities and Superpotentials.- 3.1 Mechanical Laws and Constraints.- 3.1.1 Generalized Forces and the Principle of Virtual Power.- 3.1.2 Multivalued Laws and Constraints in Mechanics.- 3.1.3 Minimization Problems and Variational Inequalities Characterizing the Equilibrium Configurations.- 3.1.4 Dissipative Laws. A Note on the Eigenvalue Problem for Superpotential Laws.- 3.2 Superpotentials and Duality.- 3.2.1 The Hypothesis of Normal Dissipation.- 3.2.2 Duality of Variational Principles.- 3.3 Subdifferential Boundary Conditions and Constitutive Laws.- 3.3.1 Subdifferential Boundary Conditions.- 3.3.2 Subdifferential Constitutive Laws I.- 3.3.3 Subdifferential Constitutive Laws II.- 3.3.4 Extension of Subdifferential Relations to Function Spaces.- 4. Variational Inequalities and Multivalued Convex and Nonconvex Problems in Mechanics.- 4.1 Two General Variational Inequalities and the Derivation of Variational Inequality Principles in Mechanics.- 4.1.1 Variational Inequalities of the Fichera Type.- 4.1.2 Variational Inequalities of Other Types.- 4.1.3 The Derivation of Variational Inequality Principles in Mechanics.- 4.2 Coexistent Phases. The Morphology of Material Phases.- 4.2.1 Neoclassical Processes and Gibbsian States. Rules for Coexistent Phases.- 4.2.2 Minimum Problems for Gibbsian States.- 4.2.3 Comparison of Gibbsian States. Some Results of the Dynamic Problem.- 4.3 Nonconvex Superpotentials.- 4.3.1 Introduction and Brief Survey of the Basic Mathematical Properties.- 4.3.2 Nonconvex Superpotentials. Hemivariational Inequalities and Substationarity Principles.- 4.3.3 Generalizations of the Hypothesis of Normal Dissipation.- 4.4 The Integral Inclusion Approach to Inequality Problems.- 5. Friction Problems in the Theory of Elasticity.- 5.1 The Static B.V.P.- 5.1.1 The Classical Formulation.- 5.1.2 The Variational Formulation.- 5.2 Existence and Uniqueness Propositions.- 5.2.1 Equivalent Minimum Problem. The case mes ?U>0.- 5.2.2 Study of the Case ?U=O.- 5.2.3 Further Properties of the Solution.- 5.3 Dual Formulation. Complementary Energy.- 5.3.1 Minimization of the Complementary Energy.- 5.3.2 Duality.- 5.4 The Dynamic B.V.P.- 5.4.1 Classical and Variational Formulations of the Problem.- 5.4.2 Existence of Solution.- 5.4.3 The Regularized Problem.- 5.4.4 The Uniqueness of the Solution.- 5.5 A Note on Other Types of Friction Problems.- 6. Subdifferential Constitutive Laws and Boundary Conditions.- 6.1 Subdifferential Material Laws and Classical Boundary Conditions.- 6.1.1 Formulation of the Problem.- 6.1.2 The Existence and Uniqueness of the Solution.- 6.1.3 Duality.- 6.2 Linear Elastic Material Law and Subdifferential Boundary Conditions.- 6.2.1 Formulation of the Boundary Conditions.- 6.2.2 Existence and Uniqueness Propositions.- 6.2.3 Duality.- 6.3 Subdifferential Material Laws and Subdifferential Boundary Conditions. Minimum Propositions for Nonmonotone Laws.- 6.3.1 Formulation and Study of the Problem.- 6.3.2 Nonmonotone Laws.- 6.4 The Corresponding Dynamic and Incremental Problems.- 7. Inequality Problems in the Theory of Thin Elastic Plates.- 7.1 Static Unilateral Problems of von Karman Plates.- 7.1.1 Generalities.- 7.1.2 Boundary Conditions and Corresponding Variational Formulations.- 7.1.3 The Existence of the Solution.- 7.1.4 In-Plane Unilateral Boundary Conditions.- 7.2 The Unilateral Buckling Problem. Eigenvalue Problems for Variational Inequalities.- 7.2.1 Formulation of the Problem.- 7.2.2 A General Proposition on the Existence of the Solution.- 7.2.3 Application to the Buckling Problem.- 7.2.4 Extension of the Rayleigh-Quotient Rule to Unilateral Problems.- 7.3 Dynamic Unilateral Problems of von Karman Plates.- 7.3.1 Boundary Conditions and Variational Inequalities.- 7.3.2 Existence Proposition.- 7.3.3 Uniqueness Proposition.- 8. Variational and Hemivariational Inequalities in Linear Thermoelasticity.- 8.1 B.V.P.s and their Variational Formulations.- 8.1.1 Classical Formulations.- 8.1.2 Variational Formulations.- 8.2 Existence and Uniqueness Propositions.- 8.2.1 Study of Problem 1.- 8.2.2 Study of Problem 2. Some Remarks on Related Problems.- 8.3 Generalizations and Related Variational Inequalities.- 8.4 Hemivariational Inequalities in Linear Thermoelasticity.- 8.4.1 Formulation of Certain General Problems.- 8.4.2 An Existence Result for a Hemivariational Inequality.-A Model Problem.- 9. Variational Inequalities in the Theory of Plasticity and Viscoplasticity.- 9.1 Elastic Viscoplastic Materials.- 9.1.1 Formulation of the Dynamic Problem, Existence and Uniqueness of the Solution.- 9.1.2 The Quasi-static Problem.- 9.2 Elastic Perfectly Plastic Materials.- 9.2.1 Formulation of the Quasi-static Problem.- 9.2.2 Existence and Uniqueness Propositions.- 9.3 Rigid Viscoplastic Flow Problems.- 9.3.1 Classical Formulation of the General Dynamic Problem.- 9.3.2 The Functional Framework and Existence Propositions.- 9.3.3 The Relation Between Velocity and Stress Fields.- 9.4 Other Problems on Bingham Fluids.- 9.4.1 Laminar Flow in a Cylindrical Pipe.- 9.4.2 Heat Transfer in Rigid Viscoplastic Flows.- 9.4.3 Variational Inequalities in the Case of the General Law ? ? ?w(D).- 3. Numerical Applications.- 10. The Numerical Treatment of Static Inequality Problems.- 10.1 Unilateral Contact and Friction Problems.- 10.1.1 Discrete Forms of the Problems of Minimum Potential and Complementary Energy.- 10.1.2 Applications.- 10.2 Torsion of Cylindrical or Prismatic Bars With Convex Strain-Energy Density.- 10.2.1 Formulation of the Problem.- 10.2.2 Discretization and Numerical Application.- 10.3 A Linear Analysis Approach to Certain Classes of Inequality Problems.- 10.3.1 Description of the Method.- 10.3.2 Applications.- 11. Incremental and Dynamic Inequality Problems.- 11.1 The Elastoplastic Calculation of Cable Structures.- 11.1.1 Formulation of the Problem as a Linear Complementarity Problem and Related Expressions.- 11.1.2 Multilevel Decomposition Techniques.- 11.1.3 Application.- 11.2 Incremental Elastoplastic Analysis.L.C.P.s, Variational Inequalities and Minimum Propositions.- 11.3 Dynamic Unilateral Contact 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.

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