FINITE-ELEMENT APPLICATIONS OF THE THEOREMS OF STRUCTURAL VARIATION

The theorems of structural variation predict the forces and displacements throughout a structure without need of fresh analysis when the physical properties of one or more of its elements are altered. It is possible to show by means of these theorems that the simple elastic analysis of a structure is sufficient to obtain the elastic, nonlinear-elastic and elastic-plastic analysis of number of related structures. In this paper, these theorems are extended to cover the triangular and rectangular finite element structures. The unit loading cases required to study the modification of a single element are given. They are later used to obtain the variation factors. Number of examples are presented to demonstrate the application of the theorems. It is verified that the theorems yield to the exact response of modified structure. In the case where the original structure is subjected to minor and sequential alterations, they are proven to be effective and cheaper to be used. They provide an efficient alternative for the engineering problems which requires reanalysis.