Stochastic Methods for Seismic Engineering Applications

本项目的目标是：(1)将地震分析的变异性方法扩展到土壤边界速度矩阵与无界区域相关联的情况下；(2)建立一套土壤的非线性本构方程。这将有可能评估土壤本构性质的变化对地震地面运动的影响，从而对土壤（嵌入式）结构系统在这种地面运动下的反应。这些结果将通过蒙特卡罗模拟进行验证。描述高阶统计近似的公式的代数复杂性将通过与人工智能程序相关的符号操作语言在数字计算机中处理。将探讨统计相关性最终结果的自动顺序改进。为了实现这一目标，将作出重大努力开发一种计算机代码，在有限元素分析的框架内执行适当的随机等效线性化方法。还将努力拟订如何将变率分析和非线性反应分析结合起来的分析纲要。本项目将寻求充分扩展随机方法在地震工程中的适用性，从而合理处理这些问题中固有的随机性和不确定性。

The objectives of this project are (1) to extend the variability methods of seismic analysis to situations where the soil boundary swiftness matrix is associated with an unbounded region, and (2) to develop a set of nonlinear constitutive equations for the soil. This will make it possible to evaluate the effects of variation in the soil constitutive properties on the seismic ground motions and hence on the response of soil-(embedded) structure systems subjected to such ground motions. These results will be verified against Monte Carlo simulations. The algebraic complexities of the formulae depicting the higher-order statistical approximations will be handled in a digital computer by symbolic manipulation languages germane to artificial intelligence procedures. Automated sequential refinements of the final results of the statistical correlations will be explored. A major effort will be expended to develop a computer code which implements an appropriate stochastic equivalent linearization method within the framework of a finite element analysis to achieve this objective. Efforts will also be made to develop analytical outlines as to how the variability and nonlinear response analyses can be combined. This project will seek to fully extend the applicability of stochastic methods in earthquake engineering so that the inherent randomness and uncertainty existing in these problems can be rationally dealt with.