Abstract:

An adaptive and efficient element subdivision method for accurate evaluation of nearly singular domain integrals is presented, which is mainly applied to address the difficulties involved with thin-structure mechanics, crack propagation, etc, in the boundary integral formulations. Based on the binary-tree data structure, the reasonable integration result of different types of volume elements can be achieved by the adaptive subdivision algorithm. Combined with the cavity construction and projection algorithms, high-quality regenerated patches around the source point can be obtained for evaluation of nearly singular integrals with discontinuous kernels. Compared to other methods, the proposed element subdivision method can obtain the accurate results with fewer integration nodes. Numerical results have been given to verify the effectiveness, feasibility and robustness of the illustrated integration schemes. For the stress analysis on arbitrary thin structures, accurate evaluation of the nearly singular integrals is restricted by the difficulties, such as the singularity of the integrals in the boundary integral formulations. An adaptive and efficient volume element subdivision method for evaluation of nearly singular domain integrals with continuous or discontinuous kernels is presented. For nearly singular domain integrals with continuous kernel, a reasonable result can be achieved by the binary-tree subdivision algorithm for different types of elements. By using the techniques of the binary-tree subdivision scheme, construction of the projection cavities and the cavity projection algorithm, well-shaped patches can be obtained for nearly singular domain integrals with discontinuous kernels. Numerical results for volume elements of arbitrary type with various relative locations of the source point demonstrate robustness and accuracy of the proposed method.

Key words: boundary element method, nearly singular integral, continuous or discontinuous kernels, adaptive element subdivision