Novel Continuous Limit Analysis Modeling with Deformable Polygon Discretization

Limit analysis with continuous modeling is a quite suitable framework for analyzing the failure of soil-like material. Standard formulation comes up from the idea of finite element analysis. Usually, in this approach, the freedom of the degrees is assigned at the nodes. However, such a theory will limit the shape of the elements, which is only applicable to solving triangular mesh. In this paper, we propose a novel approach based on the idea of continuous modeling limit analysis. Here, all the variables are assigned at the centroid of the element, through which the approach can be easily extended to consider arbitrary polygon discretization. Assuming constant strain distribution, we first derive the geometric compatibility for arbitrary polygon deformable elements. Then, the flow rule for the plasticity in the elements is investigated. Implementing the proposed theory, the classical strip footing problem is solved as a benchmark study, with consideration of one triangular mesh and two polygon mesh. The results show that the load predicted by polygon mesh is overestimated, indicating the occurrence of the locking in the elements. However, the strain rate distribution predicted by the polygon mesh is more uniform.