Finite element and Ritz vector techniques for the solution to three‐dimensional soil — structure interaction problems in the time domain

Abstract

A general time domain finite element formulation and several efficient numerical techniques are combined to form a new method of analysis for the solution of three‐dimensional soil‐structure interaction problems in the time domain. For elastic systems the method is a very cost effective alternative to the frequency domain approach. However, the major advantage of the new method is its ability to be extended to non‐linear behaviour such as separation of foundation and soil or non‐linear material. The general equations of motion for the linear cases are expressed in terms of the relative displacements of the soil‐structure system with respect to the displacements of the buried part of the structure (volume methods). This formulation allows the load vector to be an exclusive function of the free field accelerations at the foundation level. The non‐linear case requires that the equation of motion be established in terms of the total interaction displacements. The soil is modelled with three‐dimensional solid elements in the near field and axisymmetric elements in the far field. Coupling between the two systems is enforced by expanding the displacements of the solid elements in terms of the axisymmetric ones. Reduction in the number of degrees of freedom is achieved by the use of orthogonal sets of Ritz functions. The reduced system of equations is uncoupled and solved very efficiently using the complex eigenvectors. A numerical example consisting of the response of a structure resting on a homogeneous half‐space is solved using the new method and one of the approaches in the frequency domain. Results given by both methods are remarkably similar.

Citation

Bayo, E. and Wilson, E.L. (1984), "Finite element and Ritz vector techniques for the solution to three‐dimensional soil — structure interaction problems in the time domain", Engineering Computations, Vol. 1 No. 4, pp. 298-311. https://doi.org/10.1108/eb023584