Four New Methods for Finding Structural Critical Points

Abstract

Four systematic approaches are developed in the context of the indirect methods for<br><br>analyzing the nonlinear prebuckling behavior. In this study, an appropriate test function<br><br>to monitor bypassing of the critical points is utilized. The main idea of the article<br><br>is to find the critical loads by using the perturbation of the eigenvalue. Both linear<br><br>and quadratic variations of the eigenvalue and also parabolic changes of the structural<br><br>stiffness are considered. Moreover, other available techniques to find the critical points<br><br>are briefly reviewed. Finally, the accuracy and robustness of the presented procedures<br><br>are investigated by solving some well-known benchmark problems