Abstract In the present study, the ability of the classical solid-shell element to satisfy the membrane patch test is examined. Theoretical and numerical investigations showed that the classical solid-shell element fails to satisfy the membrane patch test when the elements' referential covariant base vectors in the thickness directions are coordinate-dependent. This deficiency has motivated the development of a new solid-shell formulation in the present study for modeling elastic thin structures and shell-like applications. Within the new solid-shell element, a modified Green-Lagrange strain tensor is constructed by adopting both the assumed natural inhomogeneous strain ( ANIS ) and the enhanced assumed strain ( EAS ) methods. The developed formulation is implemented in the commercial finite element software Abaqus for numerical simulations. An extensive numerical study is carried out for testing the accuracy of the developed finite element. To this end, the accuracy of the ANIS solid-shell element incorporating the proposed set of 21 EAS parameters is compared to the classical ANS solid-shell element with the same set of the EAS parameters. It is shown that the ANIS solid-shell element combined with the set of 21 EAS parameters is of great accuracy and excellent performance considering both the linear and the non-linear regimes.

中文翻译：

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具有假定自然应变方法的经典实体壳单元是否满足任意几何体的三维补丁测试？

摘要 在本研究中，研究了经典的实体壳单元满足膜贴片测试的能力。理论和数值研究表明，当单元在厚度方向的参考协变基向量与坐标相关时，经典的实体壳单元不能满足膜补丁测试。这种缺陷促使在本研究中开发了一种新的固体-壳公式，用于对弹性薄结构和壳状应用进行建模。在新的实体壳单元中，采用假设自然非均匀应变（ANIS）和增强假设应变（EAS）方法构建了一个修正的格林-拉格朗日应变张量。开发的公式在商业有限元软件 Abaqus 中实现，用于数值模拟。进行了广泛的数值研究以测试开发的有限元的准确性。为此，将包含建议的 21 个 EAS 参数集的 ANIS 实体壳单元的精度与具有相同 EAS 参数集的经典 ANS 实体壳单元进行比较。结果表明，ANIS 实体壳单元结合 21 个 EAS 参数集具有很高的精度和优异的性能，同时考虑到线性和非线性状态。