Meshless Methods and Their Numerical Properties

ISBN: 9781138072312 出版年：2013 页码：429 Li, Hua Mulay, Shantanu S CRC Press

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 PHI(Z) Appendix B: Definition of Reduced Polynomial PHI1(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