Simulation of static thermoelastic fracture problems by a novel meshless Galerkin method

In this paper, a linear gradient smoothed meshless Galerkin method (LGSM) is presented to solve the static thermoelastic fracture problems. To accurately represent the discontinuity of temperature and displacement fields across the crack surface as well as the singularity of heat flux and stress fields near the crack tip, the diffraction method is combined with intrinsic enrichment basis to construct meshless approximation. Meanwhile, to effectively save computational cost, the smoothed temperature gradient and the smoothed strain fields are expressed as the linear forms with respect to the center point in each smoothing domain by using the recently proposed linear-gradient smoothed integral (LGSI) scheme, respectively. This leads to substantial reduction of the number of Gaussian integration points without lowing the accuracy of meshless method. The thermal stress intensity factor is evaluated using interaction integrals that considering thermal effects. The novelty of the current work is the extension of LGSI scheme to solve thermoelastic fracture problems, which further verifies that the LGSI scheme is accurate, efficiency, and stable for the integration computation in meshless Galerkin method based on polynomial basis as well as intrinsic enrichment basis. Several numerical examples have been performed to validate the accuracy, efficiency, and robustness of the presented LGSM.