2-D infinite element modeling for elastostatic problems with geometric singularity and unbounded domain

In this paper, we propose a two-dimensional infinite element method (IEM) for modeling elastostatic problems with imbedded geometric singularities (e.g. re-entrant corners and cracks) in an unbounded domain. In this method, the primary problem domain is subdivided into several sub-domains which are modeled using a large number of layer-wise elements. The method is formulated based on the conventional finite element method (FEM) and uses the similarity partition concept and certain matrix condensation operations. All degrees of freedom related to the sub-domain are condensed and transformed to form an infinite element (IE) with the master nodes on the boundary only. Each IE is regarded as a regular finite element, and the IE stiffness matrix is assembled into the system stiffness matrix. The corresponding time in the modeling stage, the number of degrees of freedom, and the required PC memory storage are significantly reduced for these computations. Numerical examples are presented in this paper to show the performance of the proposed method, compared with the corresponding analytical or FEM numerical solutions.