Two-dimensional fractal-like finite element method for thermoelastic crack analysis

Abstract

The fractal-like finite element method has been proved to be very efficient and accurate in two-dimensional static and dynamic crack problems. In this paper, we extend our previous study to include the thermal effect for two-dimensional isotropic thermal crack problems. Both the temperature intensity factor and thermal stress intensity factor can be calculated directly. The temperature distribution is first found, which is imposed thereafter as a thermal load in the elastic problem. The transformation function used in the study has been found analytically. The effects of different thermal loading on the thermal stress intensity factor are presented. The numerical examples are compared with the results from other methods and find to be in good agreement.

Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method

“…The present results computed by the singular ES-FEM (GSM) using a coarse mesh with 20 Â 40 Â 2 elements are compared with those computed by other methods in Table 1. The present results agree well with values reported in the literatures, and the absolute value of relative difference with respect to the extended finite element method (XFEM) varies between 0.09% and 0.73% [9], with respect to the extended element free Galerkin method (XEFG) varies between 0.20% and 0.83% [37], and with respect to the fractal-like finite element method (FFEM) varies between 0.07% and 0.20% [40].…”

Analytical stress intensity factors for edge-cracked cylinder

“…He et al [18] derived a three-dimensional crack opening displacement correlation formula to calculate stress intensity factors for 20-node collapsed isoparametric quarter-point elements. Tsang et al [19] developed a fractal-like finite element mesh for thermoelastic crack analysis using SIF as the primary unknowns using conventional finite elements and no singular element is required. Coupling with FEM is simple.…”

Super singular element method for two-dimensional crack analysis

“…The SSEM is an improved version of the fractallike finite-element method (Leung et al 2000;Tsang et al 2004Tsang et al , 2007. The SSEM is designed to be easy to use for engineering purposes such that crack analysis can be done by a normal stress analyst.…”

“…The super singular element method (SSEM) is a semi-analytical method, which combines the efficiency and accuracy of analytical solutions and the agility of standard finite-element method. The SSEM is an improved version of the fractallike finite-element method (Leung et al 2000;Tsang et al 2004Tsang et al , 2007. The SSEM is designed to be easy to use for engineering purposes such that crack analysis can be done by a normal stress analyst.…”