Meshless Methods and Their Numerical Properties (Hardcover)

Introduction

Formulation of Classical Meshless Methods
Introduction
Fundamentals of Meshless Methods
Common Steps of Meshless Method
Classical Meshless Methods
Summary

Recent Development of Meshless Methods
Introduction
Hermite-Cloud Method
Point Weighted Least-Squares Method
Local Kriging (LoKriging) Method
Variation of Local Point Interpolation Method (vLPIM)
Random Differential Quadrature (RDQ) Method
Summary

Convergence and Consistency Analyses
Introduction to Convergence Analysis
Development of Superconvergence Condition
Convergence Analysis
Application of RDQ Method for Solving Fixed-Fixed and Cantilever Microswitches under Nonlinear Electrostatic Loading
Introduction to Consistency Analysis of RDQ Method
Consistency Analysis of Locally Applied DQ Method
Effect of Uniform and Cosine Distributions of Virtual Nodes on Convergence of RDQ Method
Summary

Stability Analyses
Introduction
Stability Analysis of First Order Wave Equation by RDQ Method
Stability Analysis of Transient Heat Conduction Equation
Stability Analysis of the Transverse Beam Deflection Equation
Summary

Adaptive Analysis
Introduction
Error Recovery Technique in ARDQ Method
Adaptive RDQ Method
Convergence Analysis in ARDQ Method
Summary

Engineering Applications
Introduction
Application of Meshless Methods to Microelectromechanical System Problems
Application of Meshless Method in Submarine Engineering
Application of RDQ Method for 2-D Simulation of pH-Sensitive Hydrogel
Summary

Appendix A: Derivation of Characteristic Polynomial Φ(Z)
Appendix B: Definition of Reduced Polynomial Φ1(Z)
Appendix C: Derivation of Discretization Equation by Taylor Series
Appendix D: Derivation of Ratio of Successive Amplitude Reduction Values for Fixed-Fixed Beam using Explicit and Implicit Approaches
Appendix E: Source Code Development

Index