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.

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SUMMARYThis study is concerned with the Stokes flow of an incompressible fluid of constant density and viscosity with circular boundaries. To fully capture the circular boundary, the boundary densities in the direct and indirect boundary integral equations (BIEs) are expanded in terms of Fourier series. The kernel functions in either the direct BIE or the indirect BIE are expanded to degenerate kernels by using the separation of field and source points. Consequently, the improper integrals are transformed to series sum and are easily calculated. The linear algebraic system can be established by matching the boundary conditions at the collocation points. Then, the unknown Fourier coefficients can be easily determined. Finally, several examples including circular and eccentric domains are presented to demonstrate the validity of the present method. Five gains were obtained: (1) meshless approach; (2) free of boundary-layer effect; (3) singularity free; (4) exponential convergence; and (5) well-posed model.

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