Fracture analysis of a piezoelectric elliptical tube subject to internal pressure and thermal loadings

In this article, a quadtree element-free Galerkin method (QEFGM) is proposed for automatically configuring background cells. The QEFGM is then employed in the fracture analysis of a piezoelectric elliptical tube subjected to internal pressure and thermal loading. The stress intensity factor (SIF) is calculated by the QEFGM and the traditional element-free Galerkin method (EFGM). By investigating an internally cracked piezoelectric plate subjected to lateral tension, the error of SIF for the EFGM is 5.17%, and the QEFGM is 1.28% at the crack-to-length ratio ( $$c/W = 0.25$$ ). The results show that the error of QEFGM is one-fourth of EFGM, which demonstrates the correctness and superiority of the approach. The QEFGM was then employed in an examination of the system geometry on the SIF in a fractured piezoelectric tube. Fracture analysis was carried out for four ellipses with different axial ratios and three super-ellipses of different powers. The SIF increased with the axial ratio for the ellipses, and increased with the powers for the super-ellipses. In this paper, various physical characteristics analyses of fracture piezoelectric material were carried out under different structure geometries. The presented result is beneficial to the prediction of material life.