DEVELOPMENT AND APPLICATIONS OF QUASI-3D METHODS OF FINITE ELEMENT ANALYSIS

Abstract

High-speed electronic digital computers have enabled engineers to employ various numerical discretization techniques, especially the finite element method, for approximate solution of complex problems. Strictly speaking any continuum problem is three dimensional in space and hence standard three-dimen-sional formulation for finite element analysis have been deve-loped. A three dimensional analysis, however, requires consi-derable manual and computational effort, time and cost. Hence approximate solution of many practical problems it carried out using simplified formulations applicable for plane stress, plane strain,axisymmetriz solids etc. But for many problems such an approximation is either not possible or, if done, gives unacCe-ptably erroneous results. This has led to the development of Quasi-three dimensional (413D) methods of finite element analysis wherein the three dimensional effect of the continuum is taken into account while keeping the element geometry as two dimensional. The need and importance of quasi three dimensional methods calls for a systematic study of their development. Basically two approadhes have been attempted for Quasi-three dimensional analysis. According to the first type of formulations, analysis is carried out in a two dimensional reference plane and a pres-cribed variation of displacements is used along the third dimension.,1 to incorporate three dimensional effect. Depending upon the number ( vi) of reference planes, in terms of which the displacement variation is expressed, this can further be classified as single layer, double layer or multi layer method. Such formulations have been applied for the analysis of geological problems, concrete gravity dams and strip footings supported on piles. The other approach is based on the sub-structure method of matrix structural analysis and uses a perturbation displacement analysis4 to incorporate three dimensional effect. Such a for-mulation has been applied for the approximate analysis of structural configurations having almost axisymmetric geometry but for pronounced geometrical changes in circumferential direction,.......