In this paper,a new formulation is proposed to evaluate the origin intensity factors(OIFs)in the singular boundary method(SBM)for solving 3D potential problems with Dirichlet boundary condition.The SBM is a strong-form boundary discretization collocation technique and is mathematically simple,easy-to-program,and free of mesh.The crucial step in the implementation of the SBM is to determine the OIFs which isolate the singularities of the fundamental solutions.Traditionally,the inverse interpolation technique(IIT)is adopted to calculate the OIFs on Dirichlet boundary,which is time consuming for large-scale simulation.In recent years,the new methodology has been developed to efficiently calculate the OIFs on Neumann boundary,but the Dirichlet problem remains an open issue.This study employs the subtracting and adding-back technique based on the integration of the fundamental solution over the whole boundary to develop a new formulation of the OIFs on 3D Dirichlet boundary.Several problems with varied domain shapes and boundary conditions are carried out to validate the effectiveness and feasibility of the proposed scheme in comparison with the SBM based on inverse interpolation technique,the method of fundamental solutions,and the boundary element method.
The embedded water pipe system is often used as a standard cooling technique during the construction of large-scale mass concrete hydrostructures. The prediction of the temperature distribution considering the cooling effects of embedded pipes plays an essential role in the design of the structure and its cooling system. In this study, the singular boundary method, a semi-analytical meshless technique, was employed to analyze the temperature distribution. A numerical algorithm solved the transient temperature field with consideration of the effects of cooling pipe specification, isolation of heat of hydration, and ambient temperature. Numerical results are verified through comparison with those of the finite element method, demonstrating that the proposed approach is accurate in the simulation of the thermal field in concrete structures with a water cooling pipe.
