SENSITIVITY ANALYSIS OF BIFURCATION LOAD OF FINITE-DIMENSIONAL SYMMETRIC SYSTEMS

Three methods are presented for sensitivity analysis of bifurcation load factor of finite-dimensional conservative symmetric systems subjected to a set of symmetric proportional loads. In the first method, a conventional method with diagonalization is utilized to derive an explicit formula of sensitivity coefficients corresponding to a minor ʹmperfection. Next, a new concept is introduced to find the sensitivity coefficients of the load factor, displacc ments and the eigenmodes under fixed lowest eigenvalue of the tangent stiffness matrix. Based on this concept, a method is presented for finding approximate sensitivity coefficients of the buckling load factor. Finally, a direct method is presented to find the accurate sensitivity coefficients of the bifurcation load factor, displacements at buckling and the buckling mode of a symmetric system. Note that different formula should be used for sensitivity analysis of a limit point load factor. In the examples, the proposed three methods are compared in view of accuracy of the results and simplicity in coding