An Introduction to Meshfree Methods and Their Programming

By: G.R. Liu, Y.T. Gu

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Hardcover | 8 June 2005

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500 Pages

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24.13 x 16.51 x 2.54

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The finite difference method (FDM) hasbeen used tosolve differential equation systems for centuries. The FDM works well for problems of simple geometry and was widely used before the invention of the much more efficient, robust finite element method (FEM). FEM is now widely used in handling problems with complex geometry. Currently, we are using and developing even more powerful numerical techniques aiming to obtain more accurate approximate solutions in a more convenient manner for even more complex systems. The meshfree or meshless method is one such phenomenal development in the past decade, and is the subject of this book. There are many MFree methods proposed so far for different applications. Currently, three monographs on MFree methods have been published. Mesh Free Methods, Moving Beyond the Finite Element Method d by GR Liu (2002) provides a systematic discussion on basic theories, fundamentals for MFree methods, especially on MFree weak-form methods. It provides a comprehensive record of well-known MFree methods and the wide coverage of applications of MFree methods to problems of solids mechanics (solids, beams, plates, shells, etc.) as well as fluid mechanics. The Meshless Local Petrov-Galerkin (MLPG) Method d by Atluri and Shen (2002) provides detailed discussions of the meshfree local Petrov-Galerkin (MLPG) method and itsvariations. Formulations and applications of MLPG are well addressed in their book.

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Fundamentals
Numerical simulation
Basics of mechanics for solids
Strong-forms and weak-forms
Weighted residual method
Global weak-form for solids
Local weak-form for solids
Discussions and remarks
Overview of meshfree methods
Why MeshFree methods
Definition of MeshFree methods
Solution procedure of MFree methods
Categories of Meshfree methods
Future development
Meshfree shape function construction
Introduction
Point interpolation methods
Moving least squares shape functions
Remarks; Appendix; Computer programs
MFree methods based on global weak-forms
Introduction
Meshfree radial point interpolation method
Element Free Galerkin method
Source code
Example for two-dimensional solids - a cantilever beam
Example for 3D solids
Examples for geometrically nonlinear problems
MFree2DA
Remarks
Appendix
Computer programs
MFree methods based on local weak-forms
Introduction
Local radial point interpolation method
Meshless Local Petrov-Galerkin method
Source code
Examples for two dimensional solids - a cantilever beam
Remarks
Appendix
Computer programs
Meshfree collocation methods
Introduction
Techniques for handling derivative boundary conditions
Polynomial point collocation method for 1D problems
Stabilization in convection-diffusion problems using MFree methods
Polynomial point collocation method for 2D problems
Radial point collocation method for 2D problems
RPCM for 2D solids
Remarks
MFree methods based on local weak form and collocation
Introduction
Meshfree collocation and local weak-form methods
Formulation for 2-D statics
Source code
Examples for testing the code
Numerical examples for 2D elastostatics
Dynamic analysis for 2-D solids
Analysis for incompressible flow problems
Remarks
Appendix
Computer programs
Reference
Index
Table of Contents provided by Publisher. All Rights Reserved.

An Introduction to Meshfree Methods and Their Programming

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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