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An Introduction to Meshfree Methods and Their Programming

G. R. Liu,Y. T. Gu|2011.02.03

1 Fundamentals: 1.1 Numerical simulation; 1.2 Basics of mechanics for solids; 1.3 Strong-forms and weak-forms; 1.4 Weighted residual method; 1.5 Global weak-form for solids; 1.6 Local weak-form for solids ;1.7 Discussions and remarks. 2 Overview of meshfree methods: 2.1 Why MeshFree methods; 2.2 Definition of MeshFree methods; 2.3 Solution procedure of MFree methods; 2.4 Categories of Meshfree methods; 2.5 Future development. 3 Meshfree shape function construction: 3.1 Introduction; 3.2 Point interpolation methods; 3.3 Moving least squares shape functions; 3.5 Remarks; Appendix; Computer programs. 4 MFree methods based on global weak-forms: 4.1 Introduction; 4.2 Meshfree radial point interpolation method ; 4.3 Element Free Galerkin method; 4.4 Source code; 4.5 Example for two-dimensional solids - a cantilever beam; 4.6 Example for 3D solids; 4.7 Examples for geometrically nonlinear problems; 4.8 MFree2DO ; 4.9 Remarks; Appendix; Computer programs. 5. MFree methods based on local weak-forms: 5.1 Introduction; 5.2 Local radial point interpolation method; 5.3 Meshless Local Petrov-Galerkin method ; 5.4 Source code; 5.5 Examples for two dimensional solids - a cantilever beam; 5.6 Remarks ; Appendix; Computer programs. 6 Meshfree collocation methods: 6.1 Introduction; 6.2 Techniques for handling derivative boundary conditions; 6.3 Polynomial point collocation method for 1D problems; 6.4 Stabilization in convection-diffusion problems using MFree methods; 6.5 Polynomial point collocation method for 2D problems; 6.6 Radial point collocation method for 2D problems; 6.7 RPCM for 2D solids; 6.8 Remarks. 7 MFree methods based on local weak form and collocation : 7.1 Introduction; 7.2 Meshfree collocation and local weak-form methods; 7.3 Formulation for 2-D statics; 7.4 Source code; 7.5 Examples for testing the code; 7.6 Numerical examples for 2D elastostatics; 7.7 Dynamic analysis for 2-D solids; 7.8 Analysis for incompressible flow problems; 7.9 Remarks;Appendix; Computer programs.Reference. Index.