An Analytical Approach for the Green's Functions of Biharmonic Problems with Circular and Annular Domains

Abstract

In this paper, an analytical approach for deriving the Green's function of circular and annular plate was presented. Null-field integral equations were employed to solve the plate problems while kernel functions were expanded to degenerate kernels. The unknown boundary data of the displacement, slope, normal moment and effective shear force were expressed in terms of Fourier series. It was noticed that all the improper integrals were avoided when the degenerate kernels were used. After determining the unknown Fourier coefficients, the displacement, slope, normal moment and effective shear force of the plate could be obtained by using the boundary integral equations. The present approach was seen as an “analytical” approach for a series solution. Finally, several analytical solutions were obtained. To see the validity of the present method, FEM solutions using ABAQUS were compared well with our analytical solutions. The displacement, radial moment and shear variations of radial and angular positions were presented.