A Node-based Smoothed Point Interpolation Method (NS-PIM) for Three-dimensional Thermoelastic Problems

Abstract

A node-based smoothed point interpolation method (NS-PIM) is formulated to analyze 3-D steady-state thermoelastic problems subjected to complicated thermal and mechanical loads. Gradient smoothing technique with node-based smoothing domains is utilized to modify the gradient fields and to perform the numerical integration required in the weak form formulation. Numerical results show that NS-PIM can achieve more accurate solutions even when the 4-node tetrahedral mesh is used compared to the finite-element method (FEM) using the same mesh, especially for strains and hence stresses. Most importantly, it can produce an upper bound solution of the exact solution in energy norm for both temperature and stress fields when a reasonably fine mesh is used. Together with FEM, we now for the first time have a simple means to obtain both upper and lower bounds of the exact solution to complex thermoelastic problems.