Null-field integral equation approach for plate problems with circular boundaries

Abstract

In this paper, a semi-analytical approach for circular plate problems with multiple circular holes is presented. Null-field integral equation is employed to solve the plate problems while the kernel functions in the null-field integral equation are expanded to degenerate kernels based on the separation of field and source points in the fundamental solution. The unknown boundary densities of the circular plates are expressed in terms of Fourier series. It is noted that all the improper integrals are transformed to series sum and are easily calculated when the degenerate kernels and Fourier series are used. By matching the boundary conditions at the collocation points, a linear algebraic system is obtained. After determining the unknown Fourier coefficients, the displacement, slope, normal moment, and effective shear force of the plate can be obtained by using the boundary integral equations. Finally, two numerical examples are proposed to demonstrate the validity of the present method and the results are compared with the available exact solution, the finite element solution using ABAQUS software and the data of Bird and Steele.