Uncertainty in Boundary Conditions---An Interval Finite Element Approach
Uncertainty in Boundary Conditions---An Interval Finite Element Approach
复制标题
边界条件的不确定性——区间有限元法
DOI：
10.1007/978-3-030-40814-5_20
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Shahi, Shahrokh
中科院分区：
文献类型：
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作者：
Muhanna, Rafi;Shahi, Shahrokh
在这项工作中，我们引入了一个区间制定，占支撑条件的结构系统的不确定性。结构系统的不确定性一直是广泛研究的焦点。不同的模型的不确定参数已被使用。不确定性的传统处理涉及概率论，其中不确定参数被建模为随机变量。由于概率方法的特定限制，例如需要关于分布的先验知识，缺乏完整的信息，以及除了其密集的计算成本之外，其结果背后的理由正在争论中。替代方法，如模糊集，证据理论，和区间已经开发。在这项工作中，它是假设只有不确定参数的界限是可用的，区间被用来建模的不确定性。在这里，我们提出了一种新的方法来处理支持条件的不确定性。在区间有限元法（IFEM）的背景下，所有的不确定性参数建模为区间。然而，支持条件被认为是在理想化的类型和描述的确定性值，而不考虑任何形式的不确定性。在当前开发的方法中，支撑条件中的不确定性被建模为有界值范围，即，区间值，用于捕获给定区间内支撑条件任何可能的变化。通过分析所考虑的系统在特定支撑条件存在和不存在的情况下，可以得到极值区间界。一组数值例子来说明和验证所提出的方法的准确性。
In this work, we introduce an interval formulation that accounts for uncertainty in supporting conditions of structural systems. Uncertainty in structural systems has been the focus of a wide range of research. Different models of uncertain parameters have been used. Conventional treatment of uncertainty involves probability theory, in which uncertain parameters are modeled as random variables. Due to specific limitation of probabilistic approaches, such as the need of a prior knowledge on the distributions, lack of complete information, and in addition to their intensive computational cost, the rationale behind their results is under debate. Alternative approaches such as fuzzy sets, evidence theory, and intervals have been developed. In this work, it is assumed that only bounds on uncertain parameters are available and intervals are used to model uncertainty. Here, we present a new approach to treat uncertainty in supporting conditions. Within the context of Interval Finite Element Method (IFEM), all uncertain parameters are modeled as intervals. However, supporting conditions are considered in idealized types and described by deterministic values without accounting for any form of uncertainty. In the current developed approach, uncertainty in supporting conditions is modeled as bounded range of values, i.e., interval value that capture any possible variation in supporting condition within a given interval. Extreme interval bounds can be obtained by analyzing the considered system under the conditions of the presence and absence of the specific supporting condition. A set of numerical examples is presented to illustrate and verify the accuracy of the proposed approach.