A natural stress boundary integral equation for calculating the near boundary stress field

The stress computational accuracy of internal points by conventional boundary element method becomes more and more deteriorate as the points approach to the boundary due to the nearly singular integrals including nearly strong singularity and hyper-singularity. For calculating the boundary stress, a natural boundary integral equation in which the boundary variables are the displacements, tractions and natural boundary variables was established in the authors’ previous work. Herein, a natural stress boundary integral equation (NSBIE) is further proposed by introducing the natural variables to analyze the stress field of interior points. There are only nearly strong singular integrals in the NSBIE, i.e., the singularity is reduced by one order. The regularization algorithm proposed by the authors is taken over to deal with these singular integrals. Consequently, the NSBIE can analyze the stress field closer to the boundary. Numerical examples demonstrated that two orders of magnitude improvement in reducing the approaching degree can be achieved by NSBIE compared to the conventional one when the near boundary stress field is evaluated. Furthermore, this new way is extended to the multi-domain elasticity problem to calculate the stress field near the boundary and interface.