Revisit of Two Classical Elasticity Problems by using the Null-Field Boundary Integral Equations

Abstract

In this paper, the two classical elasticity problems, Lamé problem and stress concentration factor, are revisited by using the null-field boundary integral equation (BIE). The null-field boundary integral formulation is utilized in conjunction with degenerate kernels 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 at the same time. In a similar way, Lamé problem is solved without any difficulty.

Revisit of degenerate scales in the BIEM/BEM for 2D elasticity problems

“…From the above results, the degenerate form of the Kelvin solution ( , ) ij U sx can be obtained in [23]. The results were also summarized by using the Table of Mathematics [24].…”

Torsional rigidity of an elliptic bar with multiple elliptic inclusions using a null-field integral approach

“…Adaptive observer system is chosen to fully employ the property of degenerate kernels. More detail can be found in [13][14][15][16][17][18][19] 3.4 Linear algebraic system…”

“…Recently, Chen et al [12][13][14][15][16][17][18][19][20][21][22] applied the null-field boundary integral method in conjunction with the degenerate kernel and Fourier series to solve many problems with circular boundaries. Basic and classical problems, e.g.…”

“…Basic and classical problems, e.g. two classical elasticity problems, Lamé problem and the problem of stress concentration factor, were also revisited by using the approach [17]. Also, torsion problems containing circular holes and/or inclusions [13,19] have been solved.…”