The authors proposed a quadrilateral shell element enriched with degrees of freedom to represent thickness‐stretch. The quadrilateral shell element can be utilized to consider large deformations for nearly incompressible materials, and its performance is demonstrated in small and large deformation analyses of hyperelastic materials in this study. Formulation of the proposed shell element is based on extension of the MITC4 shell element. A displacement variation in the thickness direction is introduced to evaluate the change in thickness. In the proposed approach, the thickness direction is defined using the director vectors at each midsurface node. The thickness‐stretch is approximated by the movements of additional nodes, which are placed along the thickness direction from the bottom to the top surface. The transverse normal strain is calculated using these additional nodes without assuming the plane stress condition; hence, a three‐dimensional constitutive equation can be employed without any modification. In this work, the authors apply an assumed strain technique to the special shell element to alleviate volumetric locking for nearly incompressible materials. Several numerical examples are presented to examine the effectiveness of the proposed element.

中文翻译：

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四边形壳单元结合了厚度拉伸功能，几乎具有不可压缩的超弹性

作者提出了一个四边形的壳单元，该单元具有丰富的自由度来表示厚度拉伸。四边形壳单元可用于考虑几乎不可压缩的材料的大变形，并且在本研究的超弹性材料的小和大变形分析中证明了其性能。拟议的外壳元素的制定是基于MITC4外壳元素的扩展。引入厚度方向上的位移变化以评估厚度的变化。在提出的方法中，使用每个中表面节点处的指向矢矢量定义厚度方向。通过其他节点的运动来近似厚度拉伸，这些节点沿着厚度方向从底部到顶部表面放置。使用这些附加节点可计算出横向法向应变，而无需假设平面应力条件；因此，可以直接使用三维本构方程。在这项工作中，作者将一种假定的应变技术应用于特殊的壳单元，以减轻几乎不可压缩的材料的体积锁定。提出了几个数值示例来检查所提出元素的有效性。