THE THEOREMS OF STRUCTURAL VARIATION FOR SOLID CUBIC FINITE-ELEMENTS

The theorems of structural variation predict the forces and displaceme nts throughout a structure without need of fresh analysis when the phy sical properties of one or more of its elements are altered. It has be en shown, that by means of these theorems, the elastic, non-linear ela stic and elastic-plastic analysis of number of related frame structure s can be obtained from the simple elastic analysis of a parent structu re. They are later extended to cover the triangular and quadrilateral finite element structures. In this paper, it is shown that these theor ems can also be applied to three-dimensional finite element structures . For this purpose, eight noded solid cubic element structures are con sidered. The unit loading cases required to study the modification of a single element are derived. They are later used to obtain the variat ion factors. These factors are utilized to predict the behavior of a c ubic element structure when one or more of its element are modified or totally removed. It is verified that the accuracy of the results is t he same as the original finite element discritization of the parent st ructure. (C) 1998 Elsevier Science Ltd and Civil-Comp Ltd. All rights reserved.