Analysis of transient thermo-elastic problems using edge-based smoothed finite element method

An edge-based smoothed finite element method (ES-FEM) is extended to deal with the transient thermo-elastic problems. For this edge-based smoothed finite element method, the problem domain is first discretized into a set of triangular elements, and the edge-based smoothing domains are further formed along the edges of the triangular meshes. In order to improve the accuracy, the ES-FEM utilizes the smoothed Galerkin weak form to obtain the discretized system equations in smoothing domains, in which the gradient field is obtained using a gradient smoothing operation. After applying these approaches, the numerical integration becomes a simple summation over each edge-based smoothing domain. The transient thermo-elastic problem is decoupled into two separate parts. At first, the temperature field is acquired by solving the transient heat transfer problem and it is then employed as an input for the mechanical problem to calculate the displacement and stress fields. Several numerical examples with different kinds of boundary conditions are investigated. It has been found that ES-FEM can achieve better accuracy and higher convergence in energy norm than the finite element method (FEM) when using the same triangular mesh.