Abstract
This paper describes a novel computational algorithm of a hybrid method composed of the thin-layered-element and the finite-element methods to obtain the vibrational responses of foundations embedded in soil. The modified-displacement method, which can efficiently solve a modified system of linear equations, is incorporated into the conventional hybrid method in order to avoid inverting a free-field flexibility matrix. Since the floating-point operations of the inverting operation, which is needed to acquire the soil stiffness matrix explicitly, dominates the whole calculating work of the conventional method, the proposed method may extremely reduce computational time. It is concluded that the floating-point operation counts of the proposed method is less than that of the conventional method, and the ratio of these two numbers is proportional to the cubes of the ratio of the number of degrees of freedom of embedded foundations and substructures to that of the whole system. The computational accuracy and efficiency of the proposed method are demonstrated through numerical examples.
