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Approximation of anisotropic multilayered plates through RMVT and MITC elements

机译：通过RMVT和MITC元素逼近各向异性多层板

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This paper presents a mixed two dimensional model for the analysis of mechanical response in anisotropic multilayered plates, with particular attention to the behavior along the thickness of the plate. It is well known that the study of anisotropic material structures requires to take into account cross-elasticity effects that make the solution converge very slowly. The finite element method showed successful performances to approximate the solutions of these structures. In this regard, two variational formulations are available to calculate the stiffness matrix, the Principle of Virtual Displacement (PVD) and the Reissner Mixed Variational Theorem (RMVT). Here, a strategy similar to MITC (Mixed Interpolated of Tensorial Components) approach, in the RMVT formulation, is adopted to formulate advanced locking-free finite elements. Then, assuming the transverse stresses as independent variables, the continuity at the interfaces between layers is easily imposed. The displacement field is defined according to the Reissner-Mindlin theory and the shear stresses are assumed parabolic along the thickness by means of RMVT. The normal strain epsilon(zz) and the normal stress sigma(zz) are discarded. The shear stresses sigma(xz) and sigma(yz) are interpolated in each element according to the MITC. By comparing the results with benchmark solutions from literature, it is shown that the element exhibits both properties of convergence and robustness and provides very accurate results in terms of transverse shear stresses of the anisotropic multilayered plate. (C) 2016 Elsevier Ltd. All rights reserved.
机译：本文提出了一个混合二维模型，用于分析各向异性多层板的机械响应，尤其要注意沿板厚度方向的行为。众所周知，各向异性材料结构的研究需要考虑使解决方案收敛非常缓慢的交叉弹性效应。有限元方法显示出成功的性能，可以近似这些结构的解。在这方面，有两种变式公式可用来计算刚度矩阵，即虚拟位移原理（PVD）和Reissner混合变分定理（RMVT）。在此，在RMVT公式中采用了类似于MITC（张量分量的混合插值）方法的策略来公式化高级的无锁定有限元。然后，假定横向应力为自变量，则可以容易地施加层之间的界面处的连续性。根据Reissner-Mindlin理论定义位移场，并通过RMVT假定剪切应力沿厚度呈抛物线形。丢弃法向应变ε（zz）和法向应力σ（zz）。剪切应力sigma（xz）和sigma（yz）根据MITC插值到每个元素中。通过将结果与文献中的基准解决方案进行比较，可以看出该单元同时具有收敛性和鲁棒性，并且在各向异性多层板的横向剪切应力方面提供了非常准确的结果。 （C）2016 Elsevier Ltd.保留所有权利。

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