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Zusatztext "The book begins with an introduction to the hybrid-Tretz (HT) FEM that covers basic concepts and general element formulations of the method. It then concentrates on both the essentials and subroutines of MATLAB and C programming. The next few chapters present applications of T-elements to potential problems and linear plane elasticity! discuss how to solve body force in elasticity through radial basis functions! and examine how special purpose functions can be constructed. The final chapter explores advanced topics! such as the construction of Tretz p-elements! dimensionless transformation! and an alternative formulation to HT FEM. Unifying the computer programming aspects of the Tretz FEM! this book will stimulate the development and application of this novel method in many facets of practical engineering."-Zentralblatt MATH Informationen zum Autor Hui Wang, Qing-Hua Qin Zusammenfassung Offers the MATLAB[registered] and C programming processes in applications of the Trefftz FEM to potential and elastic problems. This book presents MATLAB and C subroutines for inputting data and outputting results, Gaussian integration, generating shape functions, assembling an elemental stiffness matrix, and introducing boundary conditions. Inhaltsverzeichnis 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 Vari...
