A novel mixed shell finite element (FE) is presented. The element is obtained from the Hellinger–Reissner variational principle and it is based on an elastic solution of the generalized stress field, which is ruled by the minimum number of variables. As such, the new FE is isostatic because the number of stress parameters is equal to the number of kinematical parameters minus the number of rigid body motions. We name this new FE MISS‐8. MISS‐8 has generalized displacements and rotations interpolated along its contour and drilling rotation is also considered as degree of freedom. The element is integrated exactly on its contour, it does not suffer from rank defectiveness and it is locking‐free. Furthermore, it is efficient for recovering both stress and displacement fields when coarse meshes are used. The numerical investigation on its performance confirms the suitability, accuracy, and efficiency to recover elastic solutions of thick‐ and thin‐walled beam‐like structures. Numerical results obtained with the proposed FE are also compared with those obtained with isogeometric high‐performance solutions. Finally, numerical results show a rate of convergence between h² and h⁴.

中文翻译：

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用于粗网格解决方案的高效等静混合壳单元

提出了一种新颖的混合壳有限元（FE）。该元素是根据Hellinger-Reissner变分原理获得的，它基于广义应力场的弹性解，该解由最小变量数决定。这样，由于应力参数的数量等于运动参数的数量减去刚体运动的数量，因此新的有限元函数是等静的。我们将其命名为新的FE MISS-8。MISS-8具有沿其轮廓插补的广义位移和旋转，并且钻孔旋转也被视为自由度。该元件完全集成在其轮廓上，没有等级缺陷，并且没有锁定。此外，当使用粗网格时，它对于恢复应力场和位移场都是有效的。对其性能进行的数值研究证实了恢复厚壁和薄壁梁状结构弹性解的适用性，准确性和效率。拟议的有限元获得的数值结果也与等几何高性能解决方案获得的数值结果进行了比较。最后，数值结果表明h ²和h ⁴。