NAFEMS - Introduction to FEA

This manual is part of a set of training material for finite element analysis software packages, developed by the Manchester Computer Centre UMIST Support Unit under the Universities Funding Council, Information Systems Committee (UFC,ISC) Information Technology Training Initiative (ITTI), during 1993 -1995.

This module was developed and written by Dr Geoffrey Modlen, Department of Manufacturing, Loughborough University on behalf of the project holders at the Manchester Computer Centre UMIST Support Unit.

The illustrations for this document were prepared by Mrs Mary McDerby of the Manchester Computer Centre Graphics Unit and Dr Rae S. Gordon of the Manchester Computer Centre UMIST Support Unit.

The material was updated in 2007 under the supervision of Dr Jim Wood, Department of Mechanical Engineering, University of Strathclyde, who was also a member of the Steering Committee for the original ITTI project. The updating involved conversion of all text documents to pdf; conversion of all associated overheads to Powerpoint and conversion of all figures to jpeg format. Colour was also added to figures.

This updating was funded by the Higher Education Academy Engineering Subject Centre.

Contents	ii
Acknowledgements	iv
Notation	v
1 Introduction	1
1.1 What is finite element analysis (FEA)?	1
1.2 The User's View	1
1.2.1 Pre-processing	3
1.2.2 Analysis	4
1.2.3 Post-processing	4
1.3 The FE Developer's View	5
2 The Ideas of FEA	6
2.1 The Engineering Approach	6
2.2 The Principles of Virtual Displacement and Minimum Potential Energy	11
2.3 Shape Functions	13
2.4 Relationship between displacement and strain	16
2.5 Use of the principle of virtual displacements	18
2.6 Use of the Principle of Minimum Potential Energy	20
3 Variational and Weighted Residual Methods	22
3.1 Introduction	22
3.2 Governing equations for physical problems	22
3.3 Variational Methods	24
3.3.1 Numerical Solution of Variational Problems: the Rayleigh-Ritz Method	27
3.3.2 The Finite-Element Modification of the Rayleigh-Ritz Method	31
3.3.3 Natural coordinates and quadratic shape functions	38
3.4 The Weighted Residual Method	41
3.5 Extension to Two and Three Dimensions	46
3.5.1 Three-noded element for thermal conduction	48
4 References	52
Appendix 1: Review of Matrix Algebra	53
Appendix 2: Isotropic Elasticity	59
Appendix 3: Shape Functions	68
Appendix 4: Rotation of axes & Isoparametric elements	78

Document Details

Reference	itti-1
Author	Modlen. G
Language	English
Audiences	Analyst Student
Type	Publication
Date	1st January 2008
Organisation	Loughborough University
Region	Global

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Introduction to FEA - ITTI

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