A cell-based smoothed point interpolation method (CS-PIM) for 2D thermoelastic problems

Abstract

Purpose

Due to the strong reliance on element quality, there exist some inherent shortcomings of the traditional finite element method (FEM). The model of FEM behaves overly stiff, and the solutions of automated generated linear elements are generally of poor accuracy about especially gradient results. The proposed cell-based smoothed point interpolation method (CS-PIM) aims to improve the results accuracy of the thermoelastic problems via properly softening the overly-stiff stiffness.

Design/methodology/approach

This novel approach is based on the newly developed G space and weakened weak (w²) formulation, and of which shape functions are created using the point interpolation method and the cell-based gradient smoothing operation is conducted based on the linear triangular background cells.

Findings

Owing to the property of softened stiffness, the present method can generally achieve better accuracy and higher convergence results (especially for the temperature gradient and thermal stress solutions) than the FEM does by using the simplest linear triangular background cells, which has been examined by extensive numerical studies.

Practical implications

The CS-PIM is capable of producing more accurate results of temperature gradients as well as thermal stresses with the automated generated and unstructured background cells, which make it a better candidate for solving practical thermoelastic problems.

Originality/value

It is the first time that the novel CS-PIM was further developed for solving thermoelastic problems, which shows its tremendous potential for practical implications.

Citation

Liu, Y., Zhang, G., Lu, H. and Zong, Z. (2017), "A cell-based smoothed point interpolation method (CS-PIM) for 2D thermoelastic problems", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 6, pp. 1249-1265. https://doi.org/10.1108/HFF-02-2016-0042