MATLAB and C Programming for Trefftz Finite Element Methods

ISBN: 9781420072754 出版年：2008 页码：464 Qin, Qing-Hua Wang, Hui CRC Press

Introduction to Trefftz Finite Element Method Historical background Trefftz FE procedure Variational principles Concept of the T-complete solution Comparison of Trefftz FEM and conventional FEM Comparison of T-elements with boundary elements Foundation of MATLAB Programming Introduction Basic data types in MATLAB Matrix manipulations Control structures M-file functions I/O file manipulation Vectorization programming with MATLAB Common built-in MATLAB functions C Programming Data types, variable declaration, and operators Control structures Advanced array and pointer action Functions and parameter transfer File manipulation Create and execute C codes in visual C++ platform Common library functions and related head files Commonly Used Subroutines Introduction Input and output Numerical integration over element edges Shape functions along element edge Assembly of elements Introduction of essential boundary conditions Solution of global stiffness equation Potential Problems Introduction Basic equations of potential problems Trefftz FE formulation T-complete functions Computation of H and G matrix Computation of equivalent nodal load Program structure for HT FEM MATLAB programming for potential problems C computer programming Numerical examples Plane Stress/Strain Problems Introduction Linear theory of elasticity Trefftz FE formulation T-complete functions Computation of H and G matrix Evaluation of equivalent nodal loads MATLAB functions for plane elastic problems C computer programming Numerical examples Treatment of Inhomogeneous Terms Using RBF Approximation Introduction Radial basis functions (RBFs) Non-homogeneous problems Solution procedure of HT FEM for non-homogeneous problems Particular solutions in terms of RBFs Modification of the program structure MATLAB functions for particular solutions C programming Numerical examples Special Purpose T-Elements Introduction Basic concept of special Trefftz functions Special purpose elements for potential problems Special purpose elements for linear elastic problems Programming implementation MATLAB functions for special T-elements C programming for special T-elements Test examples Advanced Topics for Further Programming Development Introduction Construction of Trefftz elements Dimensionless transformation Nodal stress evaluation-smooth techniques Generating intra-element points for outputting field results Sparse matrix generation and solving procedure An alternative formulation to HT FEM Appendix A: Format of Input Data Appendix B: Glossary of Variables Appendix C: Glossary of Subroutines Appendix D: Plane Displacement and Stress Transformations Index References appear at the end of each chapter.