It is realized that, for many practical problems, the localized vibration pattern usually has a very little contribution to the overall response behavior of the system. From this point, a new dynamic reduction procedure is proposed and applied to the seismic analysis of complex engineering structures. By introducing a set of virtual master degrees of freedom (VMDOF) which represent the mean value of displacements at the substructural interface. The compatibility is conducted to those VMDOF only while all other real nodes at interfaces are considered as secondary slavers and then can be eliminated by the conventional Guyan reduction procedure. Numerical example shows that this method is quite efficient for the seismic analysis of high-rise building structures.

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.

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.

利用模糊有限元方法研究了文克尔地基上的梁和桩在确定性荷载作用下的反应，其中梁和桩身材料的物性参数及地基参数均模拟成模糊变量。在上述模糊变量为小变量的前提下，利用一种基于普通摄动法原理的模糊摄动展开方法求解模糊有限元平衡方程组得到结构反应量的模糊集。导出了用模糊摄动展开方法求解弹性地基上梁和桩的计算公式，并研究了结构中各模糊参变量对结构反应量模糊集的影响。经与数值模拟的结果比较后表明，方法在精度和实用性方面可较好的满足要求。

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.