Scaled boundary polygon formula for Cosserat continuum and its verification

Abstract

Cosserat continuum method can be used to solve stress concentration of holes. However, with the shape limitation of its elements, it is worthwhile to improve the element quality so that this method can be universal and feasible to complex situations. In this paper, a flexible polygonal Cosserat continuum analysis method is firstly deduced and numerically developed based on the theory of Scaled Boundary FEM. Stress concentration on the holes embedded in different structures is then investigated using the proposed method and verified against theoretical solution, which not only shows good agreement, but also reasonably weakens the stress concentration. The proposed method can closely replicate the theoretical solution for the case when the material is nearly incompressible (Poisson's ratio close to 0.5), also indicating the robustness of this method. Additionally, complex polygonal elements can be solved directly, coupling the quadtree and polygon discretization techniques seamlessly, wherein the efficiency and convenience are improved for processing complex geometries. The proposed method can provide important technical support for stress concentration analysis of structures with complex holes, and contribute to facilitating shape optimization of holes design.