A HYBRID TIME-FREQUENCY DOMAIN FORMULATION FOR NONLINEAR SOIL-STRUCTURE INTERACTION

Methods that combine frequency and time domain techniques offer an att ractive alternative for solving Soil-Structure-interaction problems wh ere the structure exhibits non-linear behaviour. In the hybrid-frequen cy-time-domain procedure a reference linear system is solved in the fr equency domain and the difference between the actual restoring forces and those in the linear model are treated as pseudo-forces. In the sol ution scheme explored in this paper, designated as the hybrid-time-fre quency-domain (HTFD) procedure, the equations of motion are solved in the time domain with due consideration for non-linearities and with th e unbounded medium represented by frequency-independent springs and da mpers. The frequency dependency of the impedance coefficients is intro duced by means of pseudo-forces evaluated in the frequency domain at t he end of each iteration. A criterion of stability for the HTFD approa ch is derived analytically and its validity is sustained numerically. As is often the case, the criterion takes the form of a limit of unity on the spectral radius of an appropriately defined matrix. Inspection of the terms in this matrix shows that convergence can be guaranteed by suitable selection of the reference impedance. The CPU times requir ed to obtain converged solutions with the HTFD are found, in a number of numerical simulations, to be up to one order of magnitude less than those required by the alternative hybrid-frequency-time-domain approa ch. (C) 1998 John Wiley & Sons, Ltd.