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# How To Plan A Finite Element Analysis

This book is intended to **introduce new users to the practical
aspects of finite element Modelling**. There are many texts available
which present the theory at different levels of complexity.
Although some of these present examples to illustrate aspects of
the theory, most do not provide a step by step guide to the
application of the method to real problems.

Since it is dealt with in great depth elsewhere, theory has been avoided as far as possible in this book. This is not intended as an invitation to the new user to treat finite element software as a black box. The user friendliness of commercial software has been greatly improved over the past decade, by automating parts of the modelling process, improving diagnostics, and obviating some of the pitfalls. This has improved the chances of obtaining meaningful results when the method is used as a black box , but some knowledge of the theory is essential if the fitness for use is not to be left to chance. More importantly, this knowledge will equip the user to judge whether the results obtained are reliable. The booklet ‘How to get started with finite elements’ offers advice on training in the theory.

Some aspects of creating a reliable finite element model are lonked almost inextricably with the theory, and this has been addressed here from a practical point of view, with little reference to the mathematics.

The general process of creating a finite element model is described in chapters 2 to 8. Many of the topics discussed are then illustrated in example analyses in chapter 9 to 12. The results from the same examples are used in the booklet ‘How to interpret Finite Element Results’ .

The finite element method can be used to solve many types of field problem and some of these described in ‘Why do Finite Element Analysis ?. By far the most common application is to static linear analysis and this booklet concentrates mainly on this type of analysis. Some references are made to steady state heat transfer and normal modes (natural frequency) analyses, since these can be tackled relatively easily by the novice.

It is assumed that the reader understands a little Finite Element jargon, including the terms node, element and mesh. Some jargon will be explained as it is used. A glossary of other terms is included in the booklet ‘How to understand Finite Element Jargon’ .

Once the fundamentals of finite element theory are understood, it is necessary for the user to learn how to prepare numerical data in a form suitable for the finite element software to be used. Data preparation is not part of the idealization process, but merely a way of feeding a description of the model to the software. Certain types of data are common to all programs, but since the details of formats vary greatly from one to another, the technicalities of data preparation are not addressed in this booklet. Most software vendors provide informative instruction manuals and training in program specific requirements, including the use of graphic-based pre-processors for model creation.

## Contents

**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
- True Supports
- Symmetry Constraints
- Constraint Equations
- Rigid Elements
- Summary

**Loading**

- Mechanical Loads
- Initial Strain
- Component Load Cased
- 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 Examples**

- Analysis Type
- Units
- Extent of Model
- Material data
- Co-ordinate System
- 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 Example**

- Analysis Type
- 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
- Results

**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

# About

D. Baguley and D. R. Hose

First Published - January 1994

Softback, 23 Pages