Extended finite element homework

Miloslav Okrouhlík

Miloslav Okrouhlík Institute of Thermomechanics, Academy of Sciences of the Czech Republic

Abstract

Today the solution of mechanical problems in engineering practice is often routinely carried out by means of finite element packages. These packages are powerful and efficient and are able to solve many complicated problems of technical practice on a routine basis. The packages are more and more automated. In some cases, the user is even "deprived" of solving meshing problems - the so called meshless finite element approach is being advocated. In other cases the packages take care of the correct determination of time step in transient problems. These packages offer a lot of options to choose from; the options themselves are described in particular manuals to a variable extent of details. As the Murphy law states, however, the manuals are as a rule read only if nothing else helps. It is thus worthwhile to recall some of the essentials from the finite element theory, show pitfalls which should be avoided and to present modern programming tools which help a lot in the derivation of necessary relations and in subsequent understanding of the matter. The behaviour of a rectangular membrane element and that of some finite element packages when solving simple problems will be shown in this paper with the intention to answer the question whether a modern engineer is supposed to know the theoretical details of the finite element theory and the essentials of programming.

Keywords

References

[1] K.J. Bathe. Finite element procedures in engineering analysis. Prentice-Hall, Englewood Cliffs, 1982. 71
[2] G. Beer, J.O. Watson. Introduction to finite and boundary element methods for engineers. John Wiley & Sons, Chichester, 1992
[3] T. Belytschko, W.E. Bachrach. Efficient implementation of quadrilaterals with high coarse-mesh accuracy. Comput. Methods in Appl. Mech. and Engng., 54: 279-301, 1986.
[4] T. Belytschko, L.P. Bindeman. Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems, Comput. Methods in Appl. Mech. and Engng., 88: 311-340, 1991.
[5] T. Belytschko, W.K. Liu, J.S.J. Ong. Nine node Lagrange shell elements with spurious mode control. AIAA/ ASME Str. Dyn. Conf. , Palm Springs, May, 1984.