Meshless Methods in Solid Mechanics

Introduction: Foundation of Physical Theories.- Atomic Scale Modeling and Computation.- PDE-based Continuum Modeling and Computation.- Fundamentals of Continuum Mechanics: Kinematics.- Balance Laws of Motion.- Constitutive Theory.- Thermo-Visco-Elastic Solid.- Integral Formulation of Continuum Problems: Introduction.- Weighted Residual Methods.- Variational Principle.- Basic Concepts of Finite Element Methods: Introduction.- Shape Functions.- Finite Element Formulation.- Numerical Integration.- An Overview of Meshless Methods: Approximation Functions.- Smooth particle hydrodynamics method (SPH) .- Reproducing kernel particle method (RKPM) .- Moving least squares approximation (EFG) .- Partition of unity methods (PU) .- Other meshless methods.- The common feature of the approximations.- Numerical Implementations.- Collocation method.- Galerkin method with quadrature integration scheme.- Nodal integration of Galerkin method.- Local boundary integral equation method and local Petrov-Galerkin method.- Imposition of essential boundary conditions.- Applications.- Procedures of Meshless Analysis: Construction of the Approximation.- Choice of Weight Functions.- Formulation of Meshless Analysis.- Evaluation of the Integral.- Treatment of Discontinuity.- Treatment of Mirror Symmetry.- H- and P- refinements.- Meshless Analysis of Elastostatics: Background Theories of Applications of Elastostatics.- Meshless Solution of Elastostatics.- Numerical Examples.- Meshless Analysis of Elastodynamics: Wave Propagation Problems and Structural Dynamics Problems.- Natural Frequencies and Modal Shapes.- Transient Analysis: Direct Integration Methods.- Meshless Solution of Elastodynamics.- Numerical Examples.- Meshless Analysis of Nonlocal Continua: .- Introduction to Nonlocal Theory.- The Framework of Nonlocal Theory.- Material Instability and Intrinsic Length.- Nonlocal Constitutive Relations.- Formulation of Nonlocal Meshless Method.- Numerical Examples.- Discussions.- Meshless Analysis of Plasticity: Formulation of Plasticity.- Return Mapping Algorithm.- J(2) Flow Theory.- Numerical Procedures.- Slow Crack Growth Problem.- Numerical Results.- Appendix A Vector and Tensor.- Appendix B Representations of Isotropic Scalar, Vector and Tensor Functions.- Appendix C Classification of Partial Differential Equations.- Appendix D Summary of the Procedures of Direct Integration Methods.- Appendix E User’s Manual of Meshless Programs.- Bibliography.- Index