An accurate and efficient boundary element procedure is developed for the analysis of dynamic response of rigid surface footings. The footings are assumed to be resting on an elastic half-space. The problem is formulated in the frequency domain by adopting the half-space Green's function for surface points loads. Therefore, only discretization is required for the soil-footing interface. Two types of element, linear and quadratic isoparametric elements, are employed for the discretization. Examples of the single-footing as well as two-footing system are presented to demonstrate the application of the method. The results are compared with other published results. It is demonstrated that the present results are in good agreement with the approximate solution proposed by Tajimi at low frequency range. However, the approximate solution may lead to an over-estimation of the amplitude and decaying rate as the frequency increases.

A boundary element methodology is developed for studying the response of a system of two rigid, massless or massive, surface foundations of arbitrary planforms to various harmonic waves under three-dimensional conditions. The method employs the frequency domain Green's function for the surface of the elastic half-space, thereby restricting the discretization only to the soil-foundation interfaces, and isoparametric quadratic quadrilateral boundary elements for increased accuracy. Extensive comparison studies with other known numerical solutions confirm the high accuracy of the proposed method. Detailed parametric studies are conducted in order to study the harmonic wave response of two square foundations as a function of the kind of incident wave, the angles of wave incidence, the wave frequency, the separation distance between the foundations and the amount of mass in each foundation and compare it against that of a single foundation for assessing the through the soil coupling effect.

A mathematical programming method for the analysis of the cable-stayed bridge with unilateral supports is presented. A detailed comparative study of the nonlinear phenomenon arising from the unilateral restriction at intermediate piers of the bridge is carried out. The characteristics of the unilateral supports can be described by a set of control variables which are of multi-folded constitutive relations with piecewise linearity. By using the parametric variational principle, it leads to the solution of a quadratic programming problem or to a linear complementary problem. The distinguished figures of the cable-stayed bridge with this kind of support are illustrated' by numerical examples.