How To Model With Finite Elements

Baguley, D, and Hose, D R

First Published - July 1997
Softback, 147 Pages

In these ‘How to….’ books, theory and jargon are kept to a minimum. The authors have endeavoured to ensure the correctness of statements presented as fact, although simplicity has often required that exceptions to rules be omitted. In the application of the finite element method there are many grey areas where the opinions of experienced practitioners vary. The opinions of software vendors are naturally coloured by their commercial interests. While the authors have aspired to be impartial, some of the booklets contents reflect their opinions as users of commercial software. For ease of reading the border between fact and opinion is not clearly delineated, but it is hoped that the context will distinguish between the two.

The last two decades have seen major changes in the application of the finite element method. During the seventies the range of elements and their performance was inproved. Application of the method was still fairly new and the learning curve was steep. Much of the change, particularly in the functionality of programs, was influenced by response from the growing number of users. The advances in the eighties were greatly influenced by the increasing power and reducing cost of computers, and the development of computer graphics. Development of solution techniques slowed, but powerful graphics based techniques for the modeling of complex structures were developed. Computer power hungry techniques for the solution of nonlinear problems became a practical reality. Development in the nineties has been dominated by the automation of the modeling process, involving adaptive mesh refinement and design optimization. These have let to a return to the theory to establish error estimating techniques and the development pf p-type elements.

This set of books is mainly a snapshot in time, although there is some reference to the development of the method where it influences current practice, and some prediction of future trends.

Contents

Preface

Introduction

Idealisation

• • Empathy
  • Balancing Approximations
  • Stages of Model Creation
  • Summary

Analysis Type

• • Linear Stress
  • Steady State Heat Transfer
  • Normal Modes
  • Summary

Materials

• Units
• Modulus of Elasticity
• Poisson’s Ratio
• Shear Modulus
• Density
• Coefficient of Thermal Expansion
• Conductivity
• Orthotropic Materials
• Summary

Geometry

• • Extent of Model
  • Element Type
    • 3D Solids
    • 2D Solids
    • 3D Shells and membranes
    • 2D Plates
    • 3D Line Elements
    • 2D Line Elements
    • Miscellaneous Elements
    • Mixing Elements

• • Mesh Density
  • Mesh Design
  • Adaptive Refinement
  • Sub-structuring and Super-elements
  • Summary

Supports

• • Rigid Body Motion and Mechanisms
  • True Supports
  • Symmetry Constraints
  • Constraint Equations
  • Rigid Elements
  • Summary

Loading

• • Mechanical Loads
  • Initial Strain
  • Component Load Cases
  • Benchmark Load Cases
  • Summary

Solution Optimisation

• • Numerical Accuracy
  • Solution Cost
  • Summary

Frame Example

• • Analysis Type
  • Units
  • Extent of Model
  • Material Data
  • Co-ordinate Systems
  • Major Dimensions
  • Element Type and Options
  • Real Constants or Geometric Properties
  • Mesh Density
  • Element Plots
  • Element Shapes and Internal Edges
  • Elements Missing and Elements Duplicated
  • Consistent Normals
  • Constraint Equations
  • Symmetry Constraints
  • Supports
  • Rigid Body Motion and Mechanisms
  • Load Cases
  • Summed Mass
  • Master Freedoms
  • Frontwidth/Bandwidth
  • Output Options
  • Results

Axi-symmetric Example

• • Analysis Type
  • Units
  • Extent of Model
  • Material Data
  • Co-ordinate Systems
  • Major Dimensions
  • Element Types and Options
  • Real Constants or Geometric Properties
  • Mesh Density
  • Element Plots and Element Shapes
  • Internal Edges
  • Elements Missing and Elements Duplicated
  • Consistent Normals
  • Constraint Equations
  • Symmetry Constraints
  • Supports, Rigid Body Motion and Mechanisms
  • Load Cases
  • Frontwidth/Bandwidth
  • Output Options
  • Results

3D Shell Examples

• Analysis Types
• Extent of Model
• Material Data
• Co-ordinate Systems
• Element Types and Options
• Real Constants
• Mesh Density, Element Plots and Element Shapes
• Consistent Normals
• Constraint Equations
• Symmetry Constraints
• Supports
• 1Results

3D Solid Examples

• • Analysis Type
  • Extent of Model
  • Material Data
  • Co-ordinate Systems
  • Element Types and Options
  • Real Constants
  • Mesh Density, Element Plots and Element Shapes
  • Constraint Equations
  • Symmetry Constraints
  • Supports
  • Loading
  • Results

References

Appendix A