Linear dynamic analysis of revolutional shells using finite elements and modal expansion

Abstract

Doubly-curved, axisymmetric shell finite elements are used to perform the dynamic analysis of shells of revolution. The modal expansion method is used since it is more efficient than the direct integration method when the axisymmetric shell structures are subjected to certain specific loadings. For the case of complicated loadings such as travelling loads, the modal participation factors are obtained in the form of convolution integrals which can be solved either by Laplace transformation or by numerical integration. Orthogonality conditions between displacement functions and the Fourier expansions of loadings have been used to simplify the consistent loads. It thus becomes possible to perform response calculations, like impulse response, step response, frequency response, travelling loading response, and also static deflections. The effectiveness of the present method is demonstrated through its performance in a series of examples with results compared to alternative solutions with excellent agreements.