Development and Application of the Finite Element Method based on MatLab

✍ Scribed by Herbert Baaser

• Publisher: Springer
• Year: 2010
• Tongue: English
• Leaves: 70
• Category: Library

✦ Synopsis

The intention of this booklet is a brief but general introduction into the treatment of the Finite Element Method (FEM). The FEM has become the leading method in computer–oriented mechanics, so that many scienti?c brancheshavegrownup besides overthelastdecades. Nevertheless,theFEM today is a question of economy. On the one hand its industrial application is forced to reduce product development costs and time, on the other hand a large number of commercial FEM codes and a still growing number of software for e?ective pre– and postprocessors are available in the meantime. Due to that, today it is a quite challenging task to operate with all these di?erent tools at the same time and to understand all handling and so- tion techniques developed over the last years. So, we want to help in getting a deeper insight into the main “interfaces” between the “customers of the FEM” and the codes itself by providing a totally open structured FE–code based on Matlab, which is a very powerful tool in operating with matrix based formulations. That idea and conditions forced us some years ago to initiateDAEdalon as a tool for general FE developments in research appli- tions. In spite of still existing high sophisticated – mostly commercial – FE codes, the success and the acceptance of such a structured tool justify that decision afterwards more and more.

✦ Table of Contents

Title Page
Preface
Contents
A Quick Start into DAEdalon
Download and Installation
Elastomechanical Example
Principle of Virtual Displacements
Discretization of Basic Equations
Run DAEdalon
Fundamentals of Solid (Continuum) Mechanics
Vector–, Matrix– and Tensor–Notation
Kinematics and Deformation Gradient F
Definitions
Properties and Derivatives of F
Implementation
Strain– and Stress–Tensors
A Selection
Invariants and Derivatives of Strain Tensors
Stress Representation — Voigt Notation
Rate of Strain Energy — Stress Power, Internal Energy Turn Over
Variational Principle and Weak Form
Discretization in Space
Preparation and Rearrangement of Equations
Linear Shape Functions
Derivatives of the Shape Functions
Volume Integration
General Treatment of Nonlinearities — Solution by Newton–Procedure
Linearization
Iteration
Constitutive Behavior
The Materials Point of View
Stress Response
The Material Modulus ID
Selected Constitutive Models
Hyperelasticity
Parameter Calibration
Inelastic Behavior
FEM Implementation within {\sc Matlab}
{\sc Matlab} Basics
Structure of DAEdalon
Preprocessing
Structure of Input-Files and Processing
Numerical Solution
Assembly Procedure — The Global System
{\sc Newton}–Iteration
Postprocessing
Mesh Representation, Loads and Boundary Conditions
Contour-Plots
GUI — Realization of a Graphical Environment
Writing Extensions for DAEdalon
Continuum Element elem4.m with 4–Nodes in Plane Strain
Formulation for Rotational Symmetry of elem4.m
EAS Expansion of elem4.m
General Truss Element elem10.m with 2 Nodes
Material Models
Applications and Examples
Crane Modeled by 2D–Trusses
Axisymmetric Applications
Crack Tip Simulation
K_I–Field
Analysis of Plastic Zone within K_I–Field
What Does DAEdalon Mean ?— Background for Computational System — and Greek Mythology
References
Index