A novel node-based smoothed polygonal finite element method with reconstructed strain fields for solving heat conduction problems

Abstract

This paper presents a novel node-based smoothed polygonal finite element method (NS-PFEM) with reconstructed strain fields for solving heat conduction problems. In order to approximate the thermal strain field in Wachspress coordinates, the high-order smoothed thermal strain field is constructed using pick-out theory. Two high-order S-FEM models have been developed: NS-PFEM-1 for linear thermal strain and NS-PFEM-2 for second-order thermal strain. By employing the gradient smoothing technique, the shape function values on the boundaries of node-based smoothing domains are required rather than the derivatives of the shape function, which reduces the continuity requirements for shape functions. It also eliminates the isoparametric mapping in polygonal finite element methods, which can significantly enhance computational efficiency. The performance of the high-order NS-PFEMs is rigorously examined against the standard NS-PFEM, PFEM, FEM-T3, ES-FEM-T3 and the finite element software COMSOL. Numerical examples demonstrate that our high-order NS-PFEMs produce super convergent and nearly exact solutions in both temperature and energy at low computational costs.