Stability analysis of plates using cut Bogner-Fox-Schmit elements

Abstract

In this paper, the classical C1-continuous Bogner-Fox-Schmit (BFS) elements are employed to study the buckling behavior of rectangular plates with multiple cutouts. BFS elements are constructed by taking the tensor product of cubic Hermitian polynomials, and thus, arguably constitute one of the simplest approaches to deriving plate/shell elements. The simplicity, however, comes at the cost of requiring regular/structured discretizations, which significantly restricts their use for applications featuring complex geometrical details. To circumvent this shortcoming, a combination of a fictitious domain approach, in particular the finite cell method (FCM), with BFS elements is proposed. Consequently, a typically geometry-conforming discretization is replaced by a structured Cartesian background mesh in conjunction with a more involved numerical integration of the system matrices. This opens the path to analyzing geometrically more complex structures such as plates with one ore more cutouts. Here, the main focus is on the stability (buckling) analysis of such plates. By means of two numerical examples featuring only one circular cutout, it is shown that the critical load can be obtained with high accuracy using the proposed approach. In this context, the attained numerical results are compared with high-fidelity solutions computed using isogeometric analysis (IGA). Moreover, the position of a circular cutout is optimized to maximize the critical buckling load, before the last example demonstrates the applicability of Cut BFS elements to more complex cutout geometries.