Composite structures are convenient structural solutions for many engineering fields, but their design is challenging and may lead to oversizing due to the significant amount of uncertainties concerning the current modeling capabilities. From a structural analysis standpoint, the finite element method is the most used approach and shell elements are of primary importance in the case of thin structures. Current research efforts aim at improving the accuracy of such elements with limited computational overheads to improve the predictive capabilities and widen the applicability to complex structures and nonlinear cases. The present paper presents shell elements with the minimum number of nodal degrees of freedom and maximum accuracy. Such elements compose the best theory diagram stemming from the combined use of the Carrera Unified Formulation and the Axiomatic/Asymptotic Method. Moreover, this paper provides guidelines on the choice of the proper higher-order terms via the introduction of relevance factor diagrams. The numerical cases consider various sets of design parameters such as the thickness, curvature, stacking sequence, and boundary conditions. The results show that the most relevant set of higher-order terms are third-order and that the thickness plays the primary role in their choice. Moreover, certain terms have very high influence, and their neglect may affect the accuracy of the model significantly.

中文翻译：

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通过壳有限元的多层结构的最佳理论图

复合结构是许多工程领域的便捷结构解决方案，但其设计具有挑战性，并且由于有关当前建模功能的大量不确定性，可能会导致尺寸过大。从结构分析的角度来看，有限元法是最常用的方法，而壳单元在薄结构的情况下最重要。当前的研究工作旨在以有限的计算开销来提高此类元素的准确性，以提高预测能力并扩大对复杂结构和非线性情况的适用性。本文提出了具有最少节点自由度和最大精度的壳单元。这些元素构成了Carrera统一公式和公理/渐近方法的组合使用的最佳理论图。此外，本文通过引入相关因子图，为选择合适的高阶术语提供了指导。数值案例考虑了各种设计参数集，例如厚度，曲率，堆叠顺序和边界条件。结果表明，最相关的一组高阶项是三阶，并且厚度在它们的选择中起主要作用。此外，某些术语的影响非常大，而忽略它们可能会严重影响模型的准确性。本文通过引入相关因子图，为选择合适的高阶术语提供了指导。数值案例考虑了各种设计参数集，例如厚度，曲率，堆叠顺序和边界条件。结果表明，最相关的一组高阶项是三阶，并且厚度在它们的选择中起主要作用。此外，某些术语具有很高的影响力，其忽略可能会严重影响模型的准确性。本文通过引入相关因子图，为选择合适的高阶术语提供了指导。数值案例考虑了各种设计参数集，例如厚度，曲率，堆叠顺序和边界条件。结果表明，最相关的一组高阶项是三阶，并且厚度在它们的选择中起主要作用。此外，某些术语的影响非常大，而忽略它们可能会严重影响模型的准确性。