A survey of non-probabilistic uncertainty treatment in finite element analysis
A survey of non-probabilistic uncertainty treatment in finite element analysis
复制标题
DOI：
10.1016/j.cma.2004.03.019
复制
发表时间：
2005-04
影响因子：
7.2
通讯作者：
D. Moens;D. Vandepitte
中科院分区：
文献类型：
--
作者：
D. Moens;D. Vandepitte
本文的目的是严格审查新兴的非概率方法的不确定性处理有限元分析。本文讨论了一般的理论和实践方面的区间和模糊有限元分析。首先，从理论的角度讨论了数值不确定性分析的非概率概念的适用性。确定了非概率概念的有用应用的必要条件，并被证明是互补的，而不是竞争的经典概率方法。本文的第二部分着重于区间有限元法的数值方面。它描述了实施的两个主要策略，即，反优化和区间算术方法，并给出了一个国家的最先进的区间有限元算法，从文献中。它示出了如何应用的区间算术方法的经典有限元程序可以导致严重高估的输出上的不确定性，并确定这种保守性的主要来源。在本文的最后一部分的数值例子说明了不同的策略的能力上的特征频率分析的一个建成的基准结构。
The objective of this paper is to critically review the emerging non-probabilistic approaches for uncertainty treatment in finite element analysis. The paper discusses general theoretical and practical aspects of both the interval and fuzzy finite element analysis. First, the applicability of the non-probabilistic concepts for numerical uncertainty analysis is discussed from a theoretical viewpoint. The necessary conditions for a useful application of the non-probabilistic concepts are determined, and are proven to be complementary rather than competitive to the classical probabilistic approach. The second part of the paper focuses on numerical aspects of the interval finite element method. It describes two principal strategies for the implementation, i.e., the anti-optimisation and the interval arithmetic approach, and gives a state-of-the-art of the interval finite element algorithms available from literature. It is shown how the application of the interval arithmetic approach to the classical finite element procedure can result in a severe overestimation of the uncertainty on the output, and the main sources of this conservatism are identified. A numerical example in the final part of the paper illustrates the capabilities of the different strategies on an eigenfrequency analysis of a built-up benchmark structure.