Modares, M. and Bergerson, J., "Buckling Analysis of Uncertain Structures Using Imprecise Probability," SAE Int. J. Passeng. Cars - Mech. Syst. 8(2):421-425, 2015, doi:10.4271/2015-01-0485.
In order to ensure the safety of a structure, adequate strength for structural elements must be provided. Moreover, catastrophic deformations such as buckling must be prevented. Using the linear finite element method, deterministic buckling analysis is completed in two main steps. First, a static analysis is performed using an arbitrary ordinate applied loading pattern. Using the obtained element axial forces, the geometric stiffness of the structure is assembled. Second, an eigenvalue problem is performed between structure's elastic and geometric stiffness matrices, yielding the structure's critical buckling loads. However, these deterministic approaches do not consider uncertainty the structure's material and geometric properties.In this work, a new method for finite element based buckling analysis of a structure with uncertainty is developed. An imprecise probability formulation is used to quantify the uncertainty present in the mechanical characteristics of the structure. For each element, independent variations are considered. Using the developed method, entitled Imprecise Monte-Carlo Buckling Analysis (IMBA), sharp bounds on critical buckling loads at different probability levels are obtained. This method establishes a framework for handling uncertainty in structural stability. A numerical example problem is presented that illustrates the capabilities of the new method along with discussions on their computational efficiency.