# MATLAB and C Programming for Trefftz Finite Element Methods

#### By **Qing-Hua Qin**, **Hui Wang**

CRC Press – 2008 – 464 pages

CRC Press – 2008 – 464 pages

Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson’s equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the subject. Collecting results scattered in the literature, **MATLAB ^{®} and C Programming for Trefftz Finite Element Methods **provides the detailed MATLAB

The book begins with an introduction to the hybrid-Trefftz (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 Trefftz *p*-elements, dimensionless transformation, and an alternative formulation to HT FEM.

Unifying the computer programming aspects of the Trefftz FEM, this book will stimulate the development and application of this novel method in many facets of practical engineering.

** 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.*

Name: MATLAB and C Programming for Trefftz Finite Element Methods (Hardback) – CRC Press

Description: By Qing-Hua Qin, Hui Wang. Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson’s equation, heat conduction, and piezoelectric materials, there are few books...

Categories: Mathematics & Statistics for Engineers, Mechanics, Computational Physics