One of the most successful mixed finite element methods in solid mechanics is the enhanced assumed strain (EAS) method developed by Simo and Rifai in 1990. However, one major drawback of EAS elements is the highly mesh dependent accuracy. In fact, it can be shown that not only EAS elements, but every finite element with a symmetric stiffness matrix must either fail the patch test or be sensitive to mesh distortion in bending problems (higher order displacement modes) if the shape of the element is arbitrary. This theorem was established by MacNeal in 1992. In the present work we propose a novel Petrov–Galerkin approach for the EAS method, which is equivalent to the standard EAS method in case of regular meshes. However, in case of distorted meshes, it allows to overcome the mesh-distortion sensitivity without loosing other advantages of the EAS method. Three design conditions established in this work facilitate the construction of the element which does not only fulfill the patch test but is also exact in many bending problems regardless of mesh distortion and has an exceptionally high coarse mesh accuracy. Consequently, high quality demands on mesh topology might be relaxed.

中文翻译：

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用于线性弹性的网格变形不敏感且无锁定的 Petrov-Galerkin 低阶 EAS 单元

固体力学中最成功的混合有限元方法之一是由 Simo 和 Rifai 在 1990 年开发的增强假定应变 (EAS) 方法。然而，EAS 单元的一个主要缺点是高度依赖于网格的精度。事实上，可以证明不仅是 EAS 单元，而且每个具有对称刚度矩阵的有限单元必须要么无法通过补丁测试，要么对弯曲问题（高阶位移模式）中的网格变形敏感，如果单元的形状是随意的。该定理由 MacNeal 于 1992 年建立。在目前的工作中，我们为 EAS 方法提出了一种新的 Petrov-Galerkin 方法，该方法等效于规则网格情况下的标准 EAS 方法。然而，在扭曲的网格的情况下，它允许在不失去 EAS 方法的其他优点的情况下克服网格失真敏感性。在这项工作中建立的三个设计条件促进了单元的构建，该单元不仅满足补丁测试，而且在许多弯曲问题中也很精确，无论网格变形如何，并且具有异常高的粗网格精度。因此，可能会放宽对网状拓扑的高质量要求。