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I General Introduction.- 1 On Solving Problems of Mechanics by Computer Methods.- 2 Basic Equations of Nonlinear Solid Mechanics.- 2.1 Introductory Comments.- 2.2 Description of Strain.- 2.3 State of Stress.- 2.4 Equations of Motion.- 2.5 Constitutive Equations.- 2.6 Fundamental System of Equations for Nonlinear Mechanics of Deformable Bodies.- 2.7 Variational Formulation.- 2.8 Heat Conduction.- 3 On Approximate Solving Systems of Differential Equations.- References.- II Finite Element Method.- 1 Introduction.- 2 Selected Topics from the Mathematical Theory of Finite Elements.- 2.1 Variational Formulation.- 2.2 Regularity of the Solution. Sobolev Spaces.- 2.3 Existence, Uniqueness and Regularity Results.- 2.4 Fundamental Notions of the Mathematical Theory of Finite Elements.- 2.5 Convergence Analysis for Conforming Elements. Cea´s Lemma.- 2.6 Convergence in Norm L2. The Aubin-Nitsche Argument.- 2.7 Numerical Integration. Strang´s First Lemma.- 2.8 Nonconforming Elements. Strang´s Second Lemma.- 2.9 Steady State Vibrations as an Example of a Non-coercive Problem.- 2.10 Conclusions.- 2.10.1 Relaxing Regularity Assumptions.- 2.10.2 Summary.- 3 Fundamentals of nonlinear analysis.- 3.1 Solid Mechanics Problems.- 3.2 Heat Conduction Problem.- 4 Problems of Dynamics.- 4.1 Classification of Computer Methods Used for Analysis of Dynamic Problems.- 4.2 Formulation of Equations of Motion Using Rigid Finite Element Method.- 4.3 Eigenvalue Problem.- 4.4 Fourier Transformation.- 4.5 Numerical Integration.- 4.6 The Modal Method.- 4.7 Vibration Analysis of Systems with Changing Configuration.- 4.8 Investigation of Dynamic Stability of a Linear System.- 5 Space-Time Element Method.- 5.1 Introductory Remarks and General Relations.- 5.2 Principle of Virtual Action.- 5.3 Rectangular Space-Time Elements.- 5.4 Non-rectangular Space-Time Elements.- 5.5 Uncoupled Equilibrium Equations for Impulses.- 5.6 Non-stationary Heat Flow.- 6 Plasticity Problems.- 6.1 Forms of Constitutive Equations.- 6.1.1 Introductory Comments.- 6.1.2 Thermo-Elasto-Plasticity with Isotropic Hardening...- 6.1.3 Mixed Isotropic-Kinematic Hardening.- 6.1.4 Creep and Visco-Plasticity.- 6.1.5 Elasto-Plasticity with Damage.- 6.1.6 Large Elastic-Plastic Deformations.- 6.1.7 Rigid-Plasticity and Rigid Visco-Plasticity.- 6.2 Solving Plasticity Problems by FEM.- 6.2.1 Boundary-Value Problem of Plasticity.- 6.2.2 Finite Element Equations.- 6.2.3 Time Integration of the Constitutive Equations.- 6.2.4 The Consistent (Algorithmic) Tangent Matrix.- 6.3 Computational Illustrations.- 7 Stability Problems and Methods of Analysis of FEM Equations.- 7.1 Remarks on Stability Analysis of Mechanical Systems Equilibrium States.- 7.1.1 Loads in Stability Analysis of Mechanical Systems.- 7.1.2 Equilibrium Paths and Buckling of Structures.- 7.1.3 A More General Stability Analysis of Structures.- 7.1.4 Instability under Multiple Parameter Loads.- 7.1.5 Instability of Elastic-Plastic Systems.- 7.1.6 Further Remarks.- 7.2 FEM Equations for Structural Stability.- 7.2.1 Generalisation of FE Incremental Equations.- 7.2.2 Eigenproblems in the Buckling Analysis.- 7.2.3 Extended Sets of Equations.- 7.3 Solution Methods for Nonlinear FEM Equations.- 7.3.1 Incremental Methods.- 7.3.2 Computation of Equilibrium Paths by Incremental Methods.- 7.3.3 Methods of Reduced Basis.- 7.4 Initial Buckling and Evaluation of Solution of Nonlinear and Nonconservative Problems.- 7.5 Numerical Examples.- 7.6 Final Remarks.- References.- III Finite Difference Method.- 1 Introduction.- 1.1 Formulation of Boundary-value Problems for Finite Difference Analysis.- 1.2 FDM Discretization.- 1.3 The Basic FDM Procedure.- 2 The Classical FDM.- 2.1 Domain Discretization.- 2.2 Selection of Stars and Generation of FD Operators.- 2.3 Generation of the FD Equations.- 2.4 Imposition of Boundary Conditions.- 2.5 Solution of Simultaneous FD Equations.- 2.6 Postprocessing - Evaluation of the Required Final Results...- 2.7 Numerical Examples.- 2

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