Dynamic Response of Rigid Foundations of Arbitrary Shape Using Half-Space Green’s Function

Abstract

This paper deals with the dynamic steady-state force-displacement relationships (impedance) for rigid foundations of arbitrary shape resting on a semi-infinite medium consisting of homogeneous, isotropic, linear elastic materials using the boundary element method (BEM). An elaborate numerical technique is used to calculate Green’s function, yielding a highly accurate numeric approximation in an explicit form. By using a BEM formulation for triangular elements (linear and infinite shape function) compliance of rigid massless surface foundations was obtained. The use of triangular elements causes stress continuity between elements to be satisfied. Meanwhile, the tendency for foundation edge stresses toward infinity can be modeled by using these triangular infinite stress elements. As a result of this, computations are more accurate but less time-consuming. This procedure is used to evaluate the vertical rocking compliance functions for rigid rectangular, circular, and square foundations with internal holes. Finally, comparisons are made between the results obtained from the proposed approach and those from other methods.