Analysis of static and dynamic structural problems by a combined finite element-transfer matrix method

Abstract

The combined use of the finite element and transfer matrix techniques (FETM) for the study of dynamic problems was proposed a few years ago, in order to overcome the large amount of computer storage and long computation time that the finite element technique often requires. In this paper some interesting applications are emphasized for both static and dynamic problems of structures. A great deal of attention has been paid to the use of shell isoparametric elements for very thin structures, where the usual numerical integration by a two-by-two Gaussian quadrature of the stiffness matrix leads to an ineffective increase of stiffness in the structure. Particularly appealing seems to be the use of quadratic shell elements in the FETM method, because even with a reduction in the total number of elements of the structure it is possible to increase the accuracy of results. Computation time is appreciably reduced by this method, because of the notable lowering of the final matrix order, the manipulation of which gives the solution of the problem. Some results for natural frequencies of a thin plate are finally presented, showing a favourable agreement with those obtained by other proposed methods.