A component mode synthesis method using retransformed physical coordinates. (2nd report A method in the case where some of the phisical coordinates become insignificant in the unconstrained mode method)

Abstract

An improved substructure synthesis method is proposed for analysing complex mechanical structures. In this method, since each component can be treated as one of the finite elements in FEM analysis, it is easy for them to connect with each other or with nonlinear elements obtained by FEM. In the first report, theoretical analysis and error estimation of the dummy mass technique in the unconstrained mode method were described. The proposed method in the first report, in which lower modal coordinates are retransformed to the physical coordinates, showed that numerical problems are often caused in the cases where the subordinate relation exists between the physical coordinates and that the lower modes of employed modal coordinates are not valid for representing the physical coordinates. In this paper, a new technique is proposed for solving these problems by eliminating the subordinate and insignificant degrees of freedom from the employed physical coordinates and by making optimum exployed modes to correspond with the physical coordinates using pivot selection in Gaussian forward elimination. The usefulness of this method is made clear by numerical examples.