Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method

Abstract

This paper presents a singular edge-based smoothed finite element method (ES-FEM) for solving two-dimensional thermoelastic crack problems. The physical domain is first discretized using linear triangular elements which can be generated easily for complicated geometries, and then the smoothing domains are constructed based on edges of these elements. Each smoothing domain is bounded by a set of enclosed line segments. The finite element equations are obtained utilizing the smoothed Galerkin weak form with edge-based smoothing domains. One needs only values of assumed temperature/displacement on each segment of the smoothing domains to form thermal stiffness matrix/stiffness matrix of the system. To produce the proper stress singularity, a layer of five-node crack-tip elements is designed around a crack tip. The stress intensity factors are evaluated using interaction integral with the domain form. Several numerical examples with different boundary conditions are investigated and the numerical results are in excellent agreement with the reference solutions. The thermal and mechanical influence on the crack growth is explored with different thermal and mechanical conditions. It has been found that the present method is more accurate than standard finite element method (FEM) using the same mesh.