A model reduction technique of transfer matrix in the stability analysis of beam structures

To analyze the stability of beam structures accurately and reduce the order of the system stiffness matrix, a model reduction technique based on transfer matrix method and exact finite element method is presented. The noncollinear branch chain substructure with elastic supports is modeled as a super element. In combination of exact stiffness matrix of beams, the force-displacement relation between both ends is developed by the transfer matrix method. The symmetrical stiffness matrix of the super element in the global coordinate system is derived, which has the same order as the classic beam element and can be assembled into the system stiffness matrix directly. The Euler critical force of the structure can be obtained from the determination of the reduced system stiffness matrix. The internal DOFs of the substructure are not used in the model, so the order of the model is greatly reduced and the accuracy of the computation is guaranteed. The validity and efficiency of the proposed method are shown by solving various numerical examples found in the literature.