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SENSITIVITY ANALYSIS OF BIFURCATION LOAD OF FINITE‐DIMENSIONAL SYMMETRIC SYSTEMS
Author(s) -
OHSAKI M.,
UETANI K.
Publication year - 1996
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19960530)39:10<1707::aid-nme923>3.0.co;2-k
Subject(s) - sensitivity (control systems) , mathematics , tangent , bifurcation , eigenvalues and eigenvectors , buckling , tangent stiffness matrix , mathematical analysis , limit point , bifurcation theory , stiffness , stiffness matrix , control theory (sociology) , geometry , structural engineering , nonlinear system , physics , engineering , computer science , control (management) , quantum mechanics , electronic engineering , artificial intelligence
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 imperfection. Next, a new concept is introduced to find the sensitivity coefficients of the load factor, displacements 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.