ABSTRACT
A high-order local transmitting boundary condition is developed to model an unbounded domain of arbitrary geometry as occurring in a dynamic soil-structure interaction analysis. A continued-fraction solution of the dynamic stiffness matrix of an unbounded domain is constructed by using the scaled boundary finite-element method. After formulating the force-displacement relationship on the boundary by introducing auxiliary variables, a system of first order ordinary differential equations [A]{Z(t)} + [B]{Ż(f)} = {F(t)} is obtained. The coefficient matrices, corresponding to the static stiffness and damping matrices, are symmetric. This transmitting boundary condition can be coupled seamlessly with standard finite elements. Transient responses are evaluated directly in the time domain by using a standard time-integration scheme. Only the response at the previous time step is required. The expensive task of evaluating convolution integrals is circumvented. The accuracy of this novel transmitting boundary is demonstrated by numerical examples.
