A boundary element method for axisymmetric elastodynamic analysis

Abstract

A new numerical method is proposed for the boundary element analysis of axisymmetric bodies. The method is based on complex Fourier series expansion of boundary quantities in circumferential direction, which reduced the boundary element equation to an integral equation in (r-z) plane involving the Fourier coefficients of boundary quantities, where r and z are the coordinates of the r theta z cylindrical coordinate system. The kernels appearing in these integral equations can be computed effectively by discrete Fourier transform formulas together with the fast Fourier transform (FFT) algorithm, and the integral equations (r-z) plane can be solved by Gaussian quadrature, which establishes the Fourier coefficients associated with boundary quantities. The Fourier transform solution can then be inverted into r theta z space by using again discrete Fourier transform formulas together with FFT algorithm. In this paper, we present the formulation of the proposed method which is outlined above. A comparison is given between the existent methods in literature and our method, which shows that the use of FFT algorithm for the integrations in circumferential direction provides considerable saving in computer time.