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Reissner's mixed variational theorem toward MITC finite elements for multilayered plates

机译：多层板的MITC有限元的Reissner混合变分定理

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摘要

In this paper, we analyze a two dimensional model of multilayered plates for which the main interest is to study the mechanical and physical properties, that may change in the thickness direction. The finite element method showed successful performances to approximate the solutions of the advanced structures. In this regard, two variational formulations are available to reach the stiffness matrices, the principle of virtual displacement (PVD) and the Reissner mixed variational theorem (RMVT). Here we introduce a strategy similar to Mixed Interpolated of Tensorial Components (MITC) approach, in the RMVT formulation, in order to construct an advanced locking-free finite element. Assuming the transverse stresses as independent variables, the continuity at the interfaces between layers is easily imposed. It is known that unless the combination of finite element spaces for displacement and stresses is chosen carefully, the problem of locking is likely to occur. Following this suggestion, we propose a finite element scheme that it is known to be robust with respect to the locking phenomenon in the classical PVD approach. We show that in the RMVT context, the element exhibits both properties of convergence and robustness when comparing the numerical results with benchmark solutions from literature.
机译：在本文中，我们分析了多层板的二维模型，其主要目的是研究可能在厚度方向上发生变化的机械和物理性能。有限元方法显示出成功的性能，可以近似高级结构的解。在这方面，有两种变式公式可用于获得刚度矩阵，即虚拟位移原理（PVD）和Reissner混合变分定理（RMVT）。在这里，我们介绍一种在RMVT公式中类似于张量分量的混合插值（MITC）方法的策略，以构造高级的免锁定有限元。假设横向应力为自变量，则可以轻松施加层之间界面的连续性。众所周知，除非仔细选择用于位移和应力的有限元空间的组合，否则很可能会发生锁定问题。根据这一建议，我们提出了一种有限元方案，该方案对于经典的PVD方法中的锁定现象是可靠的。我们显示，在RMVT上下文中，当将数值结果与文献中的基准解决方案进行比较时，该元素展现出收敛性和鲁棒性。

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