Revisit of two classical elasticity problems by using the null-field BIE

Abstract

In this paper, the two classical elasticity problems, Lamé problem and stress concentration factor, are revisited by using the null-field integral equation. 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. In the two classical problems of elasticity, the null-field BIE is employed to derive the exact solutions.The Kelvin solution is first separated to degenerate kernel in this paper. After employing the null-field BIE, not only the stress but also the displacement field are obtained. In a similar way, Lamé problem is solved without any difficulty.