Recursive Evaluation of Interaction Forces of Unbounded Soil in Frequency Domain

The interaction forces of the linear unbounded soil needed in a non-linear soil-structure-interaction analysis can be calculated recursively in the frequency domain. To evaluate the displacement amplitudes in the frequency domain at a specific time, only the corresponding amplitudes at the previous time station and the displacements at these two time stations are needed. The computational procedures working with stiffness and flexibility formulations in conjunction with explicit and implicit time integration schemes are derived. The recursive evaluation is, in principle, rigorous, with the exception of the stiffness formulation with an explicit time integration working with the total dynamic-stiffness coefficients, where decay functions have to be introduced to suppress the unrealistic high-frequency content. In contrast to the calculation of the interaction forces in the time domain as convolution integrals, only the familiar dynamicstiffness or (-flexibility) coefficients in the frequency domain are needed. No FFTs are required in the algorithm to calculate a transient as a recursive evaluation is used. The recursive evaluation in the frequency domain leads to the following advantages (a) significant reduction of the number of operations of up to one order of magnitude resulting from the avoidance of FFTs and the possibility of using a larger frequency increment, (b) drastic decrease of the storage requirements, as no time histories of the displacements or (interaction forces) have to be stored.