Stochastic Seismic Response Analysis of Nonlinear Soil-Structural Systems

讨论了非线性土-结构体系随机地震反应分析的基本概念和方法。首先，基于传统的塑性理论，推导了滞回结构构件的多轴本构方程及其在多轴状态下的震害度量的微分形式，得到了控制滞回空间结构地震反应的随机微分方程组。利用等效应力应变本构关系的微分形式和关联塑性流动法则，导出了滞回介质的二次多轴本构方程，并以时间和空间变量的一阶偏微分方程组的形式得到了滞回介质的非线性波动方程。另一方面，提出了一种基于随机微分方程组的滞回结构体系抗震可靠性分析方法，通过求解指定最高阶的闭合弯矩方程组来确定结构构件乃至整个结构体系的抗震可靠度函数。其次，给出了控制滞回不规则表面层中非线性波传播的随机微分方程组的有限元方法，以及确定滞回表面层与粘弹性无限空间界面上的矩阵刚度函数输入运动的边界元方法。最后，提出了一种分析随机地震激励下滞回土-结构体系非线性随机反应的有限元-边界元混合方法。

Basic concepts and a method of stochastic seismic response analysis of nonlinear soil-structural systems are discussed. First, based on the conventional theory of plasticity, the differential forms of multi-axial constitutive equations of hysteretic structural components and their measures of seismic damages under multi-axial state are derived to obtain stochastic differential equations governing seismic responses of hystertic space structures. Secondary, multi-axial constitutive equations of hysteretic media are derived by making use of the differential forms of hysteretic constitutive laws in terms of equivalent stress and strain and the associative plastic flow rule, and the nonlinear wave equations of hysteretic media are obtained in the form of the simultaneous first order partial differential equations both in time and special variables. On the other hand, a method for seismic reliability analysis of hysteretic structural systems based on stochastic differential equations is presented to determine the seismic reliability functions of structural components as well as the whole structural system through solving a closed set of moment equations up to a specified highest order. Next, the finite element method for obtaining stochastic differential equations which govern the nonlinear wave propagation, in hysteretic irregular surface layer is presented, whereas the boundary element method for determining the matrix-valued stiffness function input motion associated with the interface between the hysteretic surface layer and viscoelastic infinite space is discussed. Finally, a hybrid finite and boundary element method for analyzing nonlinear stochastic responses of hysteretic soil-structural systems subjected to random seismic excitations is proposed.