E-raamat: Nonsmooth/Nonconvex Mechanics: Modeling, Analysis and Numerical Methods

Contributing Authors xi Preface xv In Memoriam, Professor P.D. Panagiotopoulos xix Stability of a quasi-static evolution 1(14) F. Abed-Meraim Q.S. Nguyen Introduction 1(2) Stability of an evolution and linearization method 3(1) Stability of a visco-elastic evolution 4(4) Stability of a visco-plastic evolution 8(2) Stability of an elastic-plastic evolution 10(1) Criterion of second variation of free energy 11(4) Variational principles for self-adjoint elliptic eigenproblems 15(28) G. Auchmuty Introduction 15(2) Quadratic Forms and Closed Linear Operators 17(5) Morse Index of a Quadratic Form 22(2) Unconstrained Variational Principles for Self-Adjoint Eigenproblems 24(5) Types of Critical Points and Morse Indices 29(2) Constrained Variational Principles for Higher Eigenvalues 31(1) Indefinite Weighted Eigenproblems 32(3) Linear, Second-order, Self-adjoint Elliptic Eigenproblems 35(8) A sensitivity equation method for conduction and phase change problems 43(26) J. Borggaard D. Pelletier Introduction 43(2) Sensitivity Analysis for Conduction 45(7) A Phase Change Problem 52(8) An Enthalpy FEM for Sensitivities 60(5) Conclusions 65(4) Rocks interface problem including adhesion 69(14) Y. Dumont D. Goeleven K. L. Kuttler M. Rochdi M. Shillor Introduction 69(1) The model 70(3) Weak formulation 73(2) Regularized problems 75(4) Passing to the limit 79(4) On a Class of Differential-Hemivariational Inequalities 83(12) M. Foundo Introduction 83(1) Formulation of Problem 84(2) Some auxiliary results 86(2) The main existence theorem 88(7) Nonsmooth/Nonconvex dynamics: Duality, polarity, complementary extrema 95(46) D.Y. Gao Problems and Motivations 95(9) Framework in Nonconvex, Nonsmooth Dynamical Systems 104(6) Canonical Hamiltonian, Extended Lagrangian and Dual Action 110(4) Triality Theory in Fully Nonlinear Systems 114(1) Duality Theory in Geometrically Linear Dynamical Systems 115(7) Applications in 3-D Elastodynamics 122(10) Concluding Remarks 132(9) Signorini problem with a given friction 141(32) J. Haslinger Z. Dostal R. Kucera Introduction 141(4) Reciprocal variational formulation of the Signorini problem with a given friction 145(4) Approximations of the Signorini problem 149(6) Solution of box constrained quadratic programming problems 155(3) Numerical results 158(15) Debonding of Adhesively Bonded Composite Structures 173(16) D.N. Kaziolas M.J. Kontoleon C.C. Baniotopoulos Introduction 173(2) The substationarity problem 175(3) Numerical applications 178(11) Effect of nonlinearity in nonsmooth and nonconvex structural behaviour 189(42) M. Kurutz Introduction 189(1) Nonlinearity of state variable functions 190(3) Nonsmoothness and nonconvexity in structural analysis 193(3) Analysis of nonlinearities based on the Hu-Washizu-Principle 196(11) Extension of the Hu-Washizu-Principle to nonsmooth cases 207(7) Mathematical programming formulation of nonsmooth problems 214(4) Illustration of the effect of nonlinearity in nonconvex and nonsmooth problems 218(7) Conclusion 225(6) Pseudoelastic solutions for one-dimensional martensite phase transitions 231(16) K.A. Lazopoulos Introduction 231(1) The bar model 232(4) Reversals 236(2) The necking of a cylindrical bar 238(9) Inverse Coefficient Problem 247(16) S. Migorski A. Ochal Introduction 247(3) Preliminaries 250(3) Formulation of the inverse problem 253(2) The boundary homogenization 255(3) Main result 258(5) Solutions to eigenvalue problems for hemivariational inequalities 263(14) D. Motreanu Introduction 263(4) Main Results 267(3) Proofs 270(7) Non-smooth changes in elastic material properties under finite deformation 277(24) R.W. Ogden Introduction 277(2) Pseudo-elasticity 279(6) Material symmetry 285(3) A simple model 288(2) Inflation and deflation of a spherical shell 290(11) Nonlinear Rescaling in discrete minimax 301(32) R.A. Polyak I. Griva J. Sobieszczanski-Sobieski Introduction 302(2) Problem formulation and basic assumptions 304(1) Smoothing technique in discrete minimax 305(5) Nonlinear Rescaling method 310(3) Convergence of the NR method 313(4) Numerical realization of the NR algorithm 317(5) Numerical results 322(4) Concluding remarks 326(7) Multivalued problems with strong resonance 333(16) V. Radulescu Introduction 333(2) Abstract framework and main results 335(2) Auxiliary results 337(8) Proof of Theorems 345(4) Freely propagating waves in a supported nonlinear elastic beam 349(20) D.L. Russell Introduction 349(2) Equations of Motion for the Elastic Beam with the Support Constraint 351(3) Freely Propagating Steady State Waves in the Supported Beam 354(1) Results for the Linearized System 355(4) Computational Study of Simple Solutions of the Nonlinear System 359(3) Computational Study of General Solutions 362(7) Shape sensitivities for optimal design: A case study 369(22) L.G. Stanley Introduction 369(1) Optimal Design Model 370(3) Sensitivity Equation Methods 373(4) Numerical Results 377(7) Conclusions 384(7) Optimal design and identification problems in nonsmooth mechanics 391(20) G.E. Stavroulakis Introduction 392(1) Nonsmooth Mechanics 393(7) Optimal Design Problems 400(11) Adhesively Supported von Karman Plate 411(16) K. Tsilika Introduction 411(1) Formulation of the problem 412(4) The existence of the solutions 416(3) The bifurcation problem 419(8) Optimality conditions of semi-invex functions 427(10) V. Vetrivel J. Dutta Introduction 427(2) Optimality Conditions 429(5) Duality with Semi-invexity 434(3) The chaotic behaviour of a physically nonlinear beam 437(10) Y.-H. Xu Introduction 437(1) Formulation of problem 438(3) Chaotic Vibration and Parameters Combinations 441(1) Existence of homoclinic orbits 442(2) Discussion 444(3) Duality principle in nonholonomic mechanical systems 447(1) H. Yoshimura T. Kawase Introduction 447(2) Nonenergic Condition 449(2) Invariance of Virtual Work 451(2) Ideal Constraints and Connection Matrices 453(4) Duality Principle and System Structure 457(6) Dual Formalisms for Nonholonomic Systems 463