Stochastic Finite Element Methods

本研究的目的是开发通用有限元（FE）代码的不确定性传播程序。扩展代码将包含几个选项，用户可以：指定哪些几何参数、材料特性、载荷和其他相关环境条件是不确定的；为每个随机变量或随机函数选择一个概率模型；选择响应变量（位移、变形、内力等），计算其概率分布；控制不确定性传播的方法。对于响应不确定性的表示也将具有灵活性，例如，第二矩与全分布以及完全不确定性与将不确定性分离为不同来源（负载，几何变量等）的贡献。随机分析选项将在NONSAP-C规范中实施，并通过一个问题的详细研究来说明：预应力节段桥的蠕变和收缩变形作为时间的函数。

The objective of this research is to develop uncertainty-propagation procedures for general-purpose finite-element (FE) codes. The extended codes will contain several options, with the user being able to: specify which geometrical parameters, material properties, loads, and other relevant environmental conditions are uncertain; choose a probabilistic model for each random variable or random function; select the response variables (displacements, deformation, internal forces, etc.), the probability distribution of which is to be calculated; and control the method of uncertainty propagation. There will be also flexibility as to the representation of response uncertainty, e.g., second-moment versus full-distribution and total-uncertainty versus separation of uncertainty into contributions from different sources (loads, geometrical variables, etc.). Stochastic-analysis options will be implemented on the NONSAP-C code and illustrated through detailed study of one problem: creep and shrinkage deformation of prestressed segmental bridges as a function of time.