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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.

In order to ensure the safety of a structure, adequate strength for structural elements must be provided. In addition, the catastrophic deformations such as buckling must be prevented. In most buckling analyses, structural properties and applied loads are considered certain. Using the linear finite element method, the deterministic buckling analysis is done in two main steps. First, a static analysis is performed using an arbitrary ordinate of applied load. Using the obtained element axial forces, the geometric stiffness of the structure is assembled. Second, performing an eigenvalue problem between the structure's elastic and geometric stiffness matrices yields the structure's critical buckling loads. However, these deterministic approaches disregard uncertainty in the structure's material and geometric properties. In this work, an interval formulation is used to represent the uncertainty in the structure's parameters such as material characteristics.