NAFEMS - Energy Methods

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 Costas Soutis, Department of Engineering, University of Leicester on behalf of the project holders at the Manchester Computer Centre (MCC) UMIST Support Unit.

The illustrations for this document were prepared by Dr Rae S. Gordon, of the MCC 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 format; 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	iii
Notation	iv
1 Analytical Methods	1
1.1 Introduction	1
2 Energy Based Approximate Methods	5
2.1 Introduction	5
2.2 Derivation	5
2.3 Principle of Virtual Displacements (PVD)	8
2.4 Principle of Virtual Forces (PVF)	8
2.5 Illustration of Using PVD to Set Up Equilibrium Equations	9
2.5.1 Worked Example 2	10
2.5.2 Tutorial Problem	13
3 Approximate Methods Based on PVD	14
3.1 Rayleigh-Ritz Approximate Method	14
3.2 Rayleigh-Ritz Worked Example	15
3.2.1 Single Assumed Shape (n=1)	15
3.2.2 Two Assumed Shapes (n=2)	17
3.3 Tutorial Problems	18
4 Displacement Finite Elements the Basic Approach	20
4.1 Illustrations of using PVD to Derive the Element Stiffness Matrix [k]	22
4.1.1 Two Node Bar Element	22
4.2 Kinematically Equivalent Nodal Forces	29
4.2.1 Surface Loading	29
4.2.2 Body Loading	31
4.3 Tutorial Problems	33
5 References	35

Document Details

Reference	itti-5
Author	Soutis. C
Language	English
Audiences	Analyst Student
Type	Publication
Date	1st January 2008
Organisation	University of Leicester
Region	Global

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Energy Methods - ITTI

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