Buckling analysis of structures under combined loading with acceleration forces

The structures of concern in this study are subject to two types of forces: dead loads from the acceleration imposed on the structures as well as the installed operation machines and the additional adjustable forces. We wish to determine the critical values of the adjustable forces when buckling of the structures occurs. The mathematical statement of such a problem gives rise to a constrained eigenvalue problem (CEVP) in which the dominant eigenvalue is subject to an equality constraint. A numerical algorithm for solving the CEVP is proposed in which an iterative method is employed to identify an interval embracing the target eigenvalue. The algorithm is applied to four engineering application examples finding the critical loads of a fixed-free beam subject to its own body force, two plane structures and one wide-flange beam using shell elements when acceleration force is present. The accuracy is demonstrated using the first example whose classical solution exists. The significance of the equality constraint in the EVP is shown by comparing the solutions without the constraint on the eigenvalue. Effectiveness and accuracy of the numerical algorithm are presented.