Thermal stress singularity analysis for V-notches by natural boundary element method

The accuracy of thermal stresses at internal points by the conventional boundary element method becomes deteriorate when the points are approaching to the boundary due to the inaccuracy of the calculation of nearly singular integrals by the Gaussian integration. Herein, a thermal stress natural boundary integral equation is proposed, in which the nearly hyper-strongly singular integral is reduced to a nearly strongly singular one and then dealt by the regularization method. Thus, it can be applied to model the high stress gradient in the vicinity very close to the V-notch vertex. The stress method is subsequently introduced to calculate the stress singularity orders and thermal stress intensity factors once the thermal stresses along the bisector and very close to the notch tip are yielded. The mathematical and physical singularity difficulties, i.e., the evaluation of nearly singular integrals and singular stress fields, are both overcome in this paper. After a benchmark model being given out to verify the efficiency of the present method, the thermal stress singularities for a symmetrical V-notch and an inclined one are respectively analyzed. The benchmark example manifests that the thermal stress nature boundary integral equation can be successfully used to calculate the thermal stresses much closer to the boundary by the comparison with the conventional thermal stress boundary integral equation. The accuracy of the stress singularity orders and thermal stress intensity factors by the present method is confirmed and the computational effort is dramatically decreased by comparing with the finite element method.