An Introduction to Meshfree Methods and Their Programming

ISBN-13: 9789048168194 / Angielski / Miękka / 2011 / 480 str.

G. R. Liu; Y. T. Gu

Opis

This book aims to present meshfree methods in a friendly and straightforward manner, so that beginners can very easily understand, comprehend, program, implement, apply and extend these methods. It provides first the fundamentals of numerical analysis that are particularly important to meshfree methods. Typical meshfree methods, such as EFG, RPIM, MLPG, LRPIM, MWS and collocation methods are then introduced systematically detailing the formulation, numerical implementation and programming. Many well-tested computer source codes developed by the authors are attached with useful descriptions. The application of the codes can be readily performed using the examples with input and output files given in table form. These codes consist of most of the basic meshfree techniques, and can be easily extended to other variations of more complex procedures of meshfree methods. Readers can easily practice with the codes provided to effective learn and comprehend the basics of meshfree methods.

Spis treści

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 MFree2DÓ ; 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.