FINITE ELEMENT ANALYSIS USING MIXED FORCE-DISPLACEMENT METHOD VIA SINGULAR VALUE DECOMPOSITION

Abstract

The present approach is a combination of the force method and displacement approachto achieve the analysis using the substructuring technique. In this method, the inverse of thestiffness matrices of the substructures are constructed for the formation of the flexibility matrices.This part of the solution is equivalent to the stiffness approach. In the subsequent stage, the resultsof the analysis are assembled using the singular value decomposition (SVD) and the solution forthe entire structure is obtained. In fact, for assembling the structure, we need the flexibilitymatrices of the substructures which are obtained by the stiffness method.In this paper, a mixed force-displacement method is applied to finite element models forincreasing the speed of their solution. Each substructure is analyzed independently by singularvalue decomposition of the corresponding equilibrium matrix. Methods are then utilized fortransforming the substructures into regular forms whenever it is possible. The application of thismethod in finite element models with different substructures improves the process of analysis, andmakes the use of the existing solution techniques possible for regular systems.