Efficient generation of geodesic random fields in finite elements with application to shell buckling

Abstract

Structures contain inherent deviations from idealized geometry and material properties. Quantifying the effects of such random variations is of interest when determining the reliability and robustness of a structure. Generating fields that follow complex shapes is not trivial. Generating random fields on simple shapes such as a cylinder can be done using series-expansion methods or analytically computed distances as input for a decomposition approach. Generating geodesic random fields on a mesh representing complex geometric shapes using these approaches is very complex or not possible. This paper presents a generalized approach to generating geodesic random fields representing variations in a finite element setting. Geodesic distances represent the shortest path between points within a volume or surface. Computing geodesic distances of structural points is achieved by solving the heat equation using normalized heat gradients originating from every node within the structure. Any element (bar, beam, shell, or solid) can be used as long as it can solve potential flow problems in the finite element program. Variations of the approach are discussed to generate fields with defined similarities or fields that show asymmetric behavior. A numerical example of a gyroid structure demonstrates the effect of using geodesic distances in field generation compared to Euclidean distances. An anisotropic cylinder with varying Young’s modulus and thickness is taken from literature to verify the implementation. Variations of the approach are analyzed using a composite cylinder in which fiber angles are varied. Although the focus of this paper is thin-walled structures, the approach works for all types of finite element structures and elements.