NAFEMS - Two Dimensional Analysis

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 Rae S. Gordon, FE Project Officer, MCC 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	Plane Analysis	1
1.1	Plane Stress Analysis	2
1.2	Plane Strain Analysis	4
2	Two Dimensional Finite Element Analysis	6
3	Axisymmetric Analysis	15
3.1	Axisymmetric Relationships	15
3.2	Axisymmetric Finite Element Analysis	17
4	Linear Triangular Element	25
4.1	Introduction	25
4.2	Area Coordinates Approach	25
4.3	Element Shape Functions	28
4.4	Intrinsic Shape Functions	33
5	Four Node Quadrilateral Element	37
5.1	Element Shape Functions	37
5.2	Standard Element Shape Functions	39
5.3	Intrinsic Element Shape Functions	41
6	Higher Order Elements	44
6.1	Introduction	44
6.2	Triangular Elements	44
6.3	Rectangular Elements	52
6.3.1	Lagrangian Elements	52
6.3.2	Serendipity Element Family	55
7	Numerical Integration	61
7.1	Gaussian Integration	61
7.2	Integration of a Rectangular Element	64
7.3	Integration of Triangular Elements	65
7.4	Singularities Due to Numerical Integration	65
8	Solver Appreciation	67
8.1	Introduction	67
8.2	Gaussian Elimination and Backsubstitution	67
8.3	Banded Solvers	72
8.4	Frontal Solvers	77
9	Constraints	84
10	Pressure Loading	88
10.1	Introduction	88
10.2	Equivalent Work	88
11	Stress Results	94
11.1	Introduction	94
11.2	Optimal Stress Positions	94
12	Sources of Errors	99
12.1	Introduction	99
12.2	Numerical Errors	100
12.2.1	Truncation Error	100
12.2.2	Round-Off Error	101
12.2.3	Ill-Conditioning	101
12.3	Discretisation Errors	102
12.4	Incompatible Element Types	103
12.5	Element Distortion	105
12.6	Interpretation of Results	108
13	References	110

Document Details

Reference	itti-3
Author	Gordon. R
Language	English
Audiences	Analyst Student
Type	Publication
Date	1st January 2008
Organisation	UMIST
Region	Global

Download

NAFEMS Member Download

Back to Previous Page

Two Dimensional Analysis - ITTI

Contents

Document Details

Download

NAFEMS Membership