A major challenge with modern aircraft design is the occurrence of structural features of varied length scales. Structural stiffness can be accurately represented using homogenisation, however aspects such as the onset of failure may require information on more refined length scale for both metallic and composite components. This work considers the errors encountered in the coarse global models due to the mesh size and how these are propagated into detailed local sub-models. The error is calculated by a goal oriented error estimator, formulated by solving dual problems and Zienkiewicz-Zhu smooth field recovery. Specifically, the novel concept of this work is applying the goal oriented error estimator to shell elements and propagating this error field into the continuum sub-model. This methodology is tested on a simplified aluminium beam section with four different local feature designs, thereby illustrating the sensitivity to various local features with a common global setting. The simulations show that when the feature models only contained holes on the flange section, there was little sensitivity of the von Mises stress to the design modifications. However, when holes were added to the webbing section, there were large stress concentrations that predicted yielding. Despite this increase in nominal stress, the maximum error does not significantly change. However, the error field does change near the holes. A Monte Carlo simulation utilising marginal distributions is performed to show the robustness of the multi-scale analysis to uncertainty in the global error estimation as would be expected in experimental measurements. This shows a trade-off between Saint-Venant’s principle of the applied loading and stress concentrations on the feature model when investigating the response variance.

中文翻译：

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多尺度壳单元有限元问题中的面向目标误差估计

现代飞机设计的主要挑战是出现各种长度尺度的结构特征。使用均质化可以准确地表示结构刚度，但是，诸如失效的开始等方面可能需要有关金属和复合材料构件的更精确长度范围的信息。这项工作考虑了由于网格大小而在粗略全局模型中遇到的错误，以及这些错误如何传播到详细的局部子模型中。该误差由面向目标的误差估计器计算，该误差估计器通过解决对偶问题和Zienkiewicz-Zhu平滑场恢复公式化。具体而言，这项工作的新颖概念是将面向目标的误差估计器应用于壳元素，并将该误差字段传播到连续子模型中。此方法在具有四个不同局部特征设计的简化铝梁截面上进行了测试，从而说明了使用通用全局设置对各种局部特征的敏感性。仿真显示，当特征模型仅在法兰部分上包含孔时，冯·米塞斯应力对设计修改的敏感性很小。但是，将孔添加到织带部分时，会出现很大的应力集中，从而预测屈服。尽管公称应力有所增加，但最大误差并没有明显改变。但是，误差区域在孔附近确实会改变。进行了利用边际分布的蒙特卡罗模拟，以显示多尺度分析对全局误差估计中不确定性的鲁棒性，这将在实验测量中得到预期。