Four New Methods for Finding Structural Critical Points^#

Abstract

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

Keywords:

• Critical point
• Eigenvalue
• Equilibrium path
• Perturbation
• Structural stability
• Tangent stiffness matrix

Notes

^#Communicated by I. Elishakoff.