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Finite Element Model for Linear Elastic Thick Shells Using Gradient Recovery Method

机译：线性弹性厚壁壳的梯度恢复有限元模型

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摘要

This research purposed a new family of finite elements for spherical thick shell based on Nzengwa-Tagne's model proposed in 1999. The model referred to hereafter as N-T model contains the classical Kirchhoff-Love (K-L) kinematic with additional terms related to the third fundamental form governing strain energy. Transverse shear stresses are computed and..C-0 finite element is proposed for numerical implementation. However, using straight line triangular elements does not guarantee a correct computation of stress across common edges of adjacent elements because of gradient jumps. Thegradient recovery method known as Polynomial Preserving Recovery (PPR) is used for local interpolation and applied on a hemisphere under diametrically opposite charges. A good agreement of convergence results is observed; numerical results are compared to other results obtained with the classical K-L thin shell theory. Moreover, simulation on increasing values of the ratio of the shell shows impact of the N-T model especially on transverse stresses because of the significant energy contribution due to the third fundamental formtensor present in the kinematics of this model. The analysis of the thickness ratio shows difference between the classical K-L theory and N-T model when the ratio is greater than 0.099.
机译：这项研究的目的是基于1999年Nzengwa-Tagne模型提出的球形厚壳的新有限元族。此后模型称为NT模型，其中包含经典的Kirchhoff-Love（KL）运动学以及与第三基本形式有关的附加术语控制应变能。计算了横向剪应力，并提出了C-0有限元进行数值计算的方法。但是，由于斜率跳跃，使用直线三角形单元不能保证在相邻单元的公共边缘上正确计算应力。被称为多项式保留恢复（PPR）的梯度恢复方法用于局部插值，并在完全相反的电荷下应用于半球。观察到收敛结果的良好一致性；将数值结果与经典K-L薄壳理论获得的其他结果进行比较。此外，由于壳层比率的增加值的模拟显示了N-T模型的影响，特别是对横向应力的影响，这是由于该模型的运动学中存在第三基本形式的张量，因此产生了巨大的能量贡献。厚度比的分析表明，当厚度比大于0.099时，经典K-L理论与N-T模型之间存在差异。

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