The focus of this paper is on the introduction of uncertainty on structural properties, including the thermal expansion coefficient, on linear finite element models of heated structures. A "mesoscale" approach is adopted here in which the uncertainty is introduced directly on the elemental matrices and vectors of each element by randomizing those corresponding to the mean model following the maximum entropy approach and recent work by the authors. As such, the approach is applicable to finite element models developed in commercial software in which the elemental matrices can be exported. In this approach, the elemental stiffness matrix and the thermal force vectors are regrouped into an extended, positive definite matrix which is randomized. However, the uncertainty can be introduced either separately or jointly on the stiffness matrix and the thermal force vectors. The parameters of this uncertainty modeling include the overall levels of uncertainty on the stiffness matrix and the thermal force vectors and the correlation lengths of these properties. It is noted that the proposed approach is also applicable to structures with piezoelectric components when the piezoelectric effect is modeled using the thermal analogy.

中文翻译：

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加热结构有限元级的最大熵不确定性建模

本文的重点是在加热结构的线性有限元模型中引入结构特性的不确定性，包括热膨胀系数。这里采用“中尺度”方法，其中通过按照最大熵方法和作者最近的工作随机化与平均模型相对应的那些，直接在每个元素的元素矩阵和向量上引入不确定性。因此，该方法适用于在商业软件中开发的可以导出元素矩阵的有限元模型。在这种方法中，单元刚度矩阵和热力矢量被重新组合成一个扩展的正定矩阵，该矩阵是随机的。然而，不确定性可以单独或联合引入刚度矩阵和热力矢量。这种不确定性建模的参数包括刚度矩阵和热力矢量的总体不确定性水平以及这些属性的相关长度。值得注意的是，当使用热类比对压电效应进行建模时，所提出的方法也适用于具有压电元件的结构。