Thermoelastic fracture analysis in orthotropic media using optimized element free Galerkin algorithm

Abstract

In this work the effectuality of element free Galerkin method (EFGM) have been enhanced by proposing a novel algorithm for modeling discrete cracks in two-dimensional orthotropic media that are subjected to thermoelastic loading. The standard element-free Galerkin method (EFGM) is amended at the approximation level in conjunction with parametric optimization at computational level. The proposed algorithm not only extends the capability of element free Galerkin method for simulating thermoelastic fracture in orthotropic media but additionally it demonstrates a higher degree of computational efficiency and solution accuracy. The proposed algorithm utilizes variable quadrature points from the problem domain for the purpose of numerical integration. A parametric optimization has also been incorporated in the proposed algorithm for minimizing the computational time of simulation. The proposed algorithm is proficient to simulate near tip stress field in both convex and non-convex problem domains. A modified conservative M-integral technique has been used in order to extract the thermal stress intensity factors (SIFs) for the simulated problems. Few static and quasi-static crack problems have been modeled and simulated to illustrate and establish the accuracy and effectiveness of the proposed algorithm. Moreover, two component level problems, having non-convex domains, have also been modeled in order to establish the versatility of proposed algorithm. A good agreement between the obtained results with those of the available reference results establishes the capability and robustness of proposed algorithm for simulating fracture in orthotropic media subjected to thermoelastic loads. Moreover, the proposed EFGM algorithm significantly reduces the computational time which further enhances and augments its modeling prowess.