An adaptive pseudo-lower bound limit analysis for fracture structures

Abstract

In this study, we present a new approach to determine the limit loads of fracture structures by using the pseudo-lower bound method with adaptive quadtree meshes. A significant advantage of the pseudo-lower bound method is that calculations done with the stress field immediately solve the volumetric locking problem. Additionally, by defining quadtree meshes in the context of polygonal elements, it is possible to handle the technique of adaptive quadtree meshes, which poses a significant challenge in traditional finite elements due to the presence of hanging nodes during the refinement procedure. The von Mises yield criterion is employed, and structures containing cracks are assumed to have plane stress or plane strain conditions. The static form of the limit analysis is changed into second-order cone programming (SOCP), and the Mosek tool is then used to solve it. Numerical validation is used to illustrate the reliability and effectiveness of the proposed approach.