Computational Methods in Mechanics II
Aim of the course
The course ‘Computational Methods in Mechanics II’ is a part of MSc study program
‘Applied Mechanics’. Its aim is to give basic information about selected numerical methods in
mechanics like the Finite Difference Method or Boundary Element Method, and their relation
to Finite Element Method, which is the central theme of the course. The theory, algorithms
and practical usage of FEM are presented, with application to the area of linear elasticity,
dynamics, thermal conduction and thermal stress analysis. All the mentioned topics are later
enhanced in the following course ‘Nonlinear Mechanics’ by material, geometrical and contact
nonlinearity.
Pre-requisite
Undergraduate level of mathematics, strength of materials, dynamics and thermomechanics is
supposed for full understanding of the course.
Lectures
1. Discretization of continuum in selected numerical methods
2. Variational formulation of FEM, historical notes, elements, nodes, shape functions etc.
3. Illustration of the FE algorithm – one dimensional problem of linear elasticity
4. Line elements in 2D and 3D – bars, beams, frame structures
5. Plane and axisymmetrical elements, mesh topology and structure of stress stiffness matrix
6. Isoparametric formulation, 3D elements
7. Band solver and frontal solver, sub-domains and macroelements
8. Convergence, compatibility, hierarchic and adaptive algorithms
9. Plate and shell elements, thin walled structures in 3D
10. FEM in dynamics, consistent and diagonal mass matrix
11. FEM in thermal conduction, stationary and transient problems
12. Weakly coupled thermo-mechanical problem
13. Introduction to solution of nonlinear problems by FEM
Seminars
Most of the seminar work is done by ANSYS, each student should gain the ability to prepare
individually the computational model, run the computation and interpret results of a simple
problem of solid mechanics. The sequence of seminar work follows this schedule:
1. Algorithm of finite difference method – illustration on selected problem of elasticity
2. Application of Ritz method on the previously selected problem
3. Overview of commercial FE systems
4. Introduction to ANSYS environment and commands
5. Frame structures in 2D, 3D
6. 2D problem of linear elasticity
7. 3D problem, advanced functions of pre- and post-processing
8. – 12. Individual work on seminar projects
13. Presentation of seminar projects
Books
More than 470 books about FEM have already been published, many of them helpful for
individual study. Large and actualized bibliography can be found at
http://www.solid.ikp.liu.se/fe/index.html. Some of the most reputable titles are:
Bathe, K. J., Finite Element Procedures, Prentice-Hall, Englewood Cliffs,1995,
1037 pp.
ISBN 0-13-301458-4
Bathe, K. J. and Wilson, E. L., Numerical Methods in Finite Element Analysis,
Prentice-Hall, Englewood Cliffs, 1976, 524 pp.
ISBN 0-13-627190-1
Belytschko, T. et al., Nonlinear Finite Elements for Continua and Structures, J. Wiley
& Sons, New York, 2000, 600 pp.
ISBN 0-471-98773-5
Cook, R. D., Concepts and Applications of Finite Element Analysis, J. Wiley & Sons,
New York, 1974, 1981, 1989, 2001, 537 pp.
ISBN 0471-84788-7
Hinton, E. and Owen, D. R. J., An introduction to Finite Element Computations,
Pineridge Press, Swansea, 1979, 385 pp.
ISBN 0-906674-06-9
Hinton, E. and Owen, D. R. J., Finite Element Programming, Academic Press,
London, 1977, 305 pp.
ISBN 0-12-349350-1
Owen, D. R. J. and Hinton, E., Finite Elements in Plasticity- Theory and Practice,
Pineridge Press, Swansea, 1980, 594 pp.
ISBN 0-906674-05-2
Zienkiewicz, O. C. and Taylor, R. L., Finite Element Method, Vol. 1, The Basis,
Butterworth Heinemann, London, 2000, 712 pp.
ISBN 0750650494
Zienkiewicz, O. C. and Taylor, R. L., Finite Element Method, Vol. 2, Solid Mechanics,
Butterworth Heinemann, London, 2000, 480 pp.
ISBN 0750650559
Other sources
Following links to a number of commercial FE systems represent a valuable source of
information:
Year
1965
1966
1967
1969
1970
1971
1972
1973
1975
Program name
ASKA (PERMAS)
STRUDL
NASTRAN
BERSAFE
SAMCEF
ASAS
MARC
PAFEC
SESAM
ANSYS
SAP
STARDYNE
TITUS (SYSTUS)
DIANA
WECAN
GIFTS
ADINA
CASTEM
FEAP
1976
1978
1979
NISA
DYNA2D, DYNA3D
ABAQUS
1980
1982
1984
LUSAS
COSMOS/M
ALGOR
Developer
IKOSS GmbH, (INTES),Germany
MCAUTO, USA
MacNeal-Schwendler Corp., USA
CEGB, UK (restructured in 1990)
Univer. of Liege, Belgium
Atkins Res.&Devel., UK
MARC Anal. Corp., USA
PAFEC Ltd, UK now SER Systems
DNV, Norway
Swanson Anal. Syst., USA
NISEE, Univ. of California,
Berkeley, USA
Mech. Res. Inc., USA
CITRA, France; ESI Group
TNO, The Netherlands
Westinghouse R&D, USA
CASA/GIFTS Inc., USA
ADINA R&D, Inc., USA
CEA, France
URL address
www.intes.de
www.gtstrudl.gatech.edu
www.macsch.com
NISEE, Univ. of California,
Berkeley, USA
Eng. Mech. Res. Corp., USA
Livermore Softw. Tech. Corp., USA
Hibbit, Karlsson & Sorensen,
Inc., USA
FEA Ltd., UK
Structural Res. & Anal. Corp., USA
Algor Inc., USA
www.eerc.berkeley.edu/sof
tware_and_data
www.emrc.com
www.lstc.com
www.abaqus.com
www.samcef.com
www.wsasoft.com
www.marc.com
www.dnv.no
www.ansys.com
www.eerc.berkeley.edu/sof
tware_and_data
www.reiusa.com
www.systus.com
www.diana.nl
www.adina.com
www.castem.org:8001/
HomePage.html
www.lusas.com
www.cosmosm.com
www.algor.com