Boundary-domain element method for free vibration of moderately thick laminated orthotropic shallow shells

In this paper an integral equation formulation of free vibration of moderately thick laminated orthotropic shallow shells has been established by using the method of weighted residuals and taking the static fundamental solution as the weighted function. In the present formulation there are not only boundary unknowns but also domain unknowns. The integral equations presented are reduced to a standard algebraic eigenvalue problem by means of the boundary-domain element. In the numerical implementation, two kinds of different matrix formulation are presented by using two kinds of different domain elements. Some numerical results are presented and compared with the exact solutions in order to demonstrate the correctness and the accuracy of the present method.