Meshless fracture analysis of 3D planar cracks with generalized thermo-mechanical stress intensity factors

Abstract

This paper implements three dimensional meshless local Petrov–Galerkin method in the linear elastic fracture mechanics analyses of isotropic functionally graded and homogeneous materials under different thermo-mechanical loads. Energy equation based on Lord–Shulman non-Fourier heat conduction law coupled with equation of motion is applied to evaluate the effect of theoretical and realistic relaxation times on transient thermal stress intensity factors along 3D thorough or semielliptical cracks under thermo-mechanical shock. A new coordinate transform method with linear weight function is introduced to evaluate stress intensity factors by generalized interaction integral method based on incompatibility formulation. Simple linear test function is introduced, which is approximated via compatible radial basis functions and leads in eliminating internal boundary integrals of meshless method and reducing computational time. Shape functions are constructed in every Gauss point by determining the closest domain point method in preprocessing. Parametric studies are carried out in order to determine suitable radial basis functions shape parameters and penalty method parameter. Reasonable accuracy and the small number of used points are the main advantages of this method over finite element method.