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Mesh Free Methods: Moving Beyond the Finite Element Method

Mesh Free Methods: Moving Beyond the Finite Element Method


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About the Book

As we attempt to solve engineering problems of ever increasing complexity, so must we develop and learn new methods for doing so. The Finite Difference Method used for centuries eventually gave way to Finite Element Methods (FEM), which better met the demands for flexibility, effectiveness, and accuracy in problems involving complex geometry. Now, however, the limitations of FEM are becoming increasingly evident, and a new and more powerful class of techniques is emerging. For the first time in book form, Mesh Free Methods: Moving Beyond the Finite Element Method provides full, step-by-step details of techniques that can handle very effectively a variety of mechanics problems. The author systematically explores and establishes the theories, principles, and procedures that lead to mesh free methods. He shows that meshless methods not only accommodate complex problems in the mechanics of solids, structures, and fluids, but they do so with a significant reduction in pre-processing time. While they are not yet fully mature, mesh free methods promise to revolutionize engineering analysis. Filled with the new and unpublished results of the author's award-winning research team, this book is your key to unlocking the potential of these techniques, implementing them to solve real-world problems, and contributing to further advancements.

Table of Contents:
INTRODUCTION What is Mesh Free Method Why MFree Method The Idea of MFree Method Outline of the Book MESH FREE METHODS FOR ENGINEERING PROBLEMS Physical Phenomena in Engineering Solution Procedure Modeling of the Geometry Node Generation Shape Function Creation Property of Material or Media Boundary, Initial and Loading Conditions Simulation Visualization MFree Method Procedure Remarks BRIEFING ON MECHANICS Briefing on Mechanics for Solids and Structures Equations for Three-Dimensional Solids Equations for Two-Dimensional Solids Equations for Truss Members Equations for Beams Equations for Plates Remarks Captions of Figures PRINCIPLES FOR WEAK FORMS Strong and Weak Forms Hamilton's Principle Constrained Hamilton's Principle Galerkin Weak Form Constrained Galerkin Weak Form Minimum Total Potential Energy Principle Weighted Residual Method Weighted Residual Method with Constraints Points to Note Remarks MFREE SHAPE FUNCTION CONSTRUCTION Overview Smoothed Particle Hydrodynamics Approach Reproducing Kernel Particle Method Moving Least Squares Approximation Point Interpolation Method Radial PIM Radial PIM with Polynomial Reproduction Polynomial PIM with Coordinate Transformation Matrix regularization Algorithm Comparison Study via Examples Compatibility of MFree Function Approximation Features of MFree Shape Functions Other Methods Remarks ELEMENT FREE GALERKIN METHOD EFG Formulation with Lagrange Multipliers EFG with Penalty Method Constrained Moving Least Square Method for EFG EFG for Nonlinear Elastic Problems Summary MESHLESS LOCAL PETROV-GALERKIN METHOD MLPG Formulation MLPG for Dynamic Problems Remarks POINT INTERPOLATION METHODS Point Interpolation Method (PIM) Application of PIM to Foundation Consolidation Problem Radial Point Interpolation Method (RPIM) Local Point Interpolation Method (LPIM) Examples of Static Problems Application of LRPIM to Diffusion Equations Comparison Study Summary MESH FREE METHODS FOR FLUID DYNAMIC PROBLEMS Introduction Smoothed Particle Hydrodynamics Method Local Petrov-Galerkin Method Local Radial Point Interpolation Method MESH FREE METHODS FOR BEAMS PIM Shape Function for Thin Beams Elastostatic Analysis of Thin Beams Buckling Analysis of Thin Beam (Eigenvalue Problem) Free Vibration Analysis of Thin Beams (Eigenvalue Problem) Forced Vibration Analysis of Thin Beams (Time Dependent Problem) Timoshenko Beams Remarks MESH FREE METHODS FOR PLATES EFG Method for Thin Plates EFG Method for Thin Composite Laminates EFG Method for Thick Plates RPIM for Thick Plates MLPG for Thin Plates Remarks MESH FREE METHODS FOR SHELLS EFG Method for Spatial Thin Shells EFG Method for Thick Shells RPIM for Thick Shells Summary BOUNDARY MESH FREE METHODS BPIM Using Polynomial Basis BPIM Using Radial Function Basis Remarks MESH FREE METHODS COUPLED WITH OTHER METHODS Coupled EFG/BE Method Coupled EFG and Hybrid BEM Coupled MLPG/FE/BE Methods Remarks IMPLEMENTATION ISSUES Definition of the Support Domain or Influence Domain Triangular Mesh and Size of Influence Domain Node Numbering and Bandwidth of the Stiffness Matrix **Bucket Algorithm for Node Searching Relay Model for Domains with Irregular Boundaries Adaptive Procedure Based on Background Cells Strategy for Local Adaptive Refinement Remarks MFREE2D© Overview Techniques used in MFree2D© Pre-processing in MFree2D© Post-processing in MFree2D©

Review :
"This book addresses some of the current important issues, both positive and negative, related to MFree methods, which should prove beneficial to researchers, engineers, and students who are interested in venturing into this area of research. This book provides systematic steps that lead the reader to understand mesh free methods; how they work; how to use and develop a mesh free method, as well as the problems associated with element free methods. This is the first book published that comprehensively covers MFree methods." - Zentralblatt MATH, Vol. 1031 (2004/06)


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Product Details
  • ISBN-13: 9780849312380
  • Publisher: Taylor & Francis Inc
  • Publisher Imprint: CRC Press Inc
  • Height: 254 mm
  • No of Pages: 712
  • Returnable: N
  • Weight: 1397 gr
  • ISBN-10: 0849312388
  • Publisher Date: 29 Jul 2002
  • Binding: Hardback
  • Language: English
  • No of Pages: 712
  • Sub Title: Moving Beyond the Finite Element Method
  • Width: 178 mm


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