A SMOOTHED FEM (S-FEM) FOR HEAT TRANSFER PROBLEMS

Abstract

By smoothing, via various ways, the compatible strain fields of the standard finite element method (FEM) using the gradient smoothing technique, a family of smoothed FEMs (S-FEMs) has been developed recently. The S-FEM possesses the advantages of both mesh-free methods and the standard FEM and works well with triangular and tetrahedral background cells and elements. Intensive theoretical investigations have shown that the S-FEM models can achieve numerical solutions for many important properties, such as the upper bound solution in strain energy, free from volumetric locking, insensitive to the distortion of the background cells, super-accuracy and super-convergence in displacement or stress solutions or both. Engineering problems, including complex heat transfer problems, have also been analyzed with better accuracy and efficiency. This paper presents the general formulation of the S-FEM for thermal problems in one, two and three dimensions. To examine our formulation, some computational results are compared with those obtained using other established means.