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 approach to achieve the analysis using the substructuring technique. In this method, the inverse of the stiffness 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 results of the analysis are assembled using the singular value decomposition (SVD) and the solution for the entire structure is obtained. In fact, for assembling the structure, we need the flexibility matrices of the substructures which are obtained by the stiffness method. In this paper, a mixed force-displacement method is applied to finite element models for increasing the speed of their solution. Each substructure is analyzed independently by singular value decomposition of the corresponding equilibrium matrix. Methods are then utilized for transforming the substructures into regular forms whenever it is possible. The application of this method in finite element models with different substructures improves the process of analysis, and makes the use of the existing solution techniques possible for regular systems.