The objective of this book is to thoroughly document and discuss the influence of the most important computer-oriented techniques on formulating and solving boundary-value problems typical for contemporary solid and structural mechanics. The book is also intended to serve as an up-to-date introduction into current research on the subject. It will be useful to university researchers and graduate students, as well as to industrial engineers interested in effective solution methods in solid mechanics.
The objective of this book is to thoroughly document and discuss the influence of the most important computer-oriented techniques on formulating and solving boundary-value problems typical for contemporary solid and structural mechanics. The book is also intended to serve as an up-to-date introduction into current research on the subject. It will be useful to university researchers and graduate students, as well as to industrial engineers interested in effective solution methods in solid mechanics.
I General Introduction.- 1 On Solving Problems of Mechanics by Computer Methods.- 2 Basic Equations of Nonlinear Solid Mechanics.- 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.- 3 Fundamentals of nonlinear analysis.- 4 Problems of Dynamics.- 5 Space-Time Element Method.- 6 Plasticity Problems.- 7 Stability Problems and Methods of Analysis of FEM Equations.- References.- III Finite Difference Method.- 1 Introduction.- 2 The Classical FDM.- 3 Curvilinear Finite Difference Method.- 4 FD Method Generalized for Arbitrary Irregular Grids.- 5 Adaptive GFDM Approach.- 6 On Mathematical Foundations of the FDM for Elliptic Problems.- 7 Final Remarks.- References.- IV Boundary Element Method.- 1 Introduction.- 2 Mathematical Foundations.- 3 BEM in Linear Theory of Elasticity.- 4 BEM in Nonlinear Problems.- 5 BEM in Synthesis Problems.- 6 Final Remarks.- References.- V Optimization Methods.- 1 Numerical Approaches to Structural Optimization.- 2 Applications of Linear Programming.- 3 Applications of Nonlinear Programming.- 4 Discrete Programming in Structural Optimization.- References.- VI Methods of Sensitivity Analysis.- 1 Introduction.- 2 Classification of Structural Design Variables and Parameters.- 3 Fundamental Variational Theorems.- 4 Sensitivity Analysis for Varying Material Parameters.- 5 Structural Shape Variation.- 6 Sensitivity Analysis for Beam Structures.- 7 Sensitivity Analysis in Static and Dynamic Thermo-elasticity.- 8 Numerical Aspects of Sensitivity Analysis.- References.
I General Introduction.- 1 On Solving Problems of Mechanics by Computer Methods.- 2 Basic Equations of Nonlinear Solid Mechanics.- 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.- 3 Fundamentals of nonlinear analysis.- 4 Problems of Dynamics.- 5 Space-Time Element Method.- 6 Plasticity Problems.- 7 Stability Problems and Methods of Analysis of FEM Equations.- References.- III Finite Difference Method.- 1 Introduction.- 2 The Classical FDM.- 3 Curvilinear Finite Difference Method.- 4 FD Method Generalized for Arbitrary Irregular Grids.- 5 Adaptive GFDM Approach.- 6 On Mathematical Foundations of the FDM for Elliptic Problems.- 7 Final Remarks.- References.- IV Boundary Element Method.- 1 Introduction.- 2 Mathematical Foundations.- 3 BEM in Linear Theory of Elasticity.- 4 BEM in Nonlinear Problems.- 5 BEM in Synthesis Problems.- 6 Final Remarks.- References.- V Optimization Methods.- 1 Numerical Approaches to Structural Optimization.- 2 Applications of Linear Programming.- 3 Applications of Nonlinear Programming.- 4 Discrete Programming in Structural Optimization.- References.- VI Methods of Sensitivity Analysis.- 1 Introduction.- 2 Classification of Structural Design Variables and Parameters.- 3 Fundamental Variational Theorems.- 4 Sensitivity Analysis for Varying Material Parameters.- 5 Structural Shape Variation.- 6 Sensitivity Analysis for Beam Structures.- 7 Sensitivity Analysis in Static and Dynamic Thermo-elasticity.- 8 Numerical Aspects of Sensitivity Analysis.- References.
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