We present in this study a new approach for predicting the plastic and shakedown limits of structures composed of orthotropic materials. In this approach, the Hill yield criterion is introduced to Melan’s theorem. By formulating the problem by means of the finite element method and solving the resulting large-scale nonlinear optimization problem we successfully predict the plastic and shakedown limits of structures having complex geometries made from multi-orthotropic materials. Several numerical examples are elaborated in this study for evaluating the accuracy, general applicability, as well as the efficiency of the established numerical scheme. Overall, the study confirms that the direct method can be extended and adopted as a viable means for design and analysis of structures made of orthotropic materials.

中文翻译：

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正交各向异性材料的下限和安定分析

我们在这项研究中提出了一种预测由正交各向异性材料组成的结构的塑性和安定极限的新方法。在这种方法中，希尔屈服准则被引入到梅兰定理中。通过利用有限元方法制定问题并解决由此产生的大规模非线性优化问题，我们成功地预测了由多正交各向异性材料制成的具有复杂几何形状的结构的塑性和安定极限。本研究详细阐述了几个数值例子，以评估所建立数值方案的准确性、普遍适用性以及效率。总体而言，该研究证实，直接方法可以扩展并用作设计和分析正交各向异性材料结构的可行方法。