An advanced boundary element method for axisymmetric elastodynamic analysis Original Research Article

An advanced boundary element method is appropriately combined with the fast Fourier transform (FFT) to analyze general axisymmetric problems in frequency domain elastodynamics. The problems are characterized by axisymmetric geometry and non-axisymmetric boundary conditions. Boundary quantities are expanded in complex Fourier series in the circumferential direction and the problem is efficiently decomposed into a series of problems, which are solved by the BEM for the Fourier coefficients of the boundary quantities, discretizing only the surface generator of the axisymmetric body. Quadratic boundary elements are used and BEM integrations are done by FFT algorithm in the circumferential direction and by Gauss quadrature in the generator direction. Singular integrals are evaluated directly in a highly accurate way. The Fourier transformed solution is then numerically inverted by the FFT to provide the final solution. The method combines high accuracy and efficiency and this is demonstrated by illustrative numerical examples.