Buckling Modes of Large-Scale Shell Structures Automatically Detected from Linearized Stiffness by Iterative Solvers

This study presents a novel method to automatically detect bifurcation buckling modes of large scale shell structures during solving a set of linearized stiffness equations in geometrically nonlinear problems by iterative solvers, such as the CG method or the Lanczos method. The proposed method is based on the LDLT decomposition method for direct solvers proposed by the authors [

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] and is extended for the iterative solvers in order to handle large-scale problems. First, the proposed method detects the approximate buckling mode during the simultaneous process of tri-diagonalization and the LDLT decomposition of the stiffness matrix, utilizing the fact that the Lanczos algorithm still preserves the eigenvalue properties of original matrix during the tri-diagonalization. Second, it is also shown that the correction vector in the direction of solution in the CG method can approximate the buckling mode. The proposed method can avoid a time-consuming eigenanalysis, which is usually necessary for detecting bifurcation modes at critical points, and can compute the approximate bifurcation modes closed to the critical points very efficiently and accurately. Several numerical examples of bifurcation buckling of shells demonstrate the potential of the proposed method