Null-field integral equation approach using degenerate kernels and its engineering applications

Abstract

In this paper, a systematic approach is developed to deal with the problems including multiple circular boundaries. The null-field integral formulation is utilized in conjunction with degenerate kernel and Fourier series. To fully utilize the circular geometry, the fundamental solutions and the boundary densities are expanded by using degenerate kernels and Fourier series, respectively. This approach is seen as one kind of semi-analytical methods, since the error stems from the truncation of Fourier series in the implementation. The unknown Fourier coefficients are easily determined by solving a linear algebraic system after using the collocation method and matching the boundary conditions. Four goals: (1) free of calculating principal value, (2) exponential convergence, (3) well-posed algebraic system and (4) meshless, of the formulation are achieved. The proposed approach is extended to deal with the problems including multiple circular inclusions. Finally, the general-purpose program in a unified manner is developed for BVPs with circular boundaries. Several examples including the torsion bar, water wave and elasticity problems are given to demonstrate the validity of the present approach.