In this paper, a numerical solution strategy is proposed for studying the large deformations of rectangular plates made of hyperelastic materials in the compressible and nearly incompressible regimes. The plate is considered to be Mindlin-type, and material nonlinearities are captured based on the Neo-Hookean model. Based on the Euler–Lagrange description, the governing equations are derived using the minimum total potential energy principle. The tensor form of equations is replaced by a novel matrix–vector format for the computational aims. In the solution strategy, based on the variational differential quadrature technique, a new numerical approach is proposed by which the discretized governing equations are directly obtained through introducing differential and integral matrix operators. Fast convergence rate, computational efficiency and simple implementation are advantages of this approach. The results are first validated with available data in the literature. Selected numerical results are then presented to investigate the nonlinear bending behavior of hyperelastic plates under various types of boundary conditions in the compressible and nearly incompressible regimes. The results reveal that the developed approach has a good performance to address the large deformation problem of hyperelastic plates in both regimes.

中文翻译：

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超弹性 Mindlin 板的非线性弯曲分析：数值方法

在本文中，提出了一种数值求解策略，用于研究由超弹性材料制成的矩形板在可压缩和几乎不可压缩状态下的大变形。该板被认为是 Mindlin 类型的，并且基于 Neo-Hookean 模型捕获了材料非线性。基于欧拉-拉格朗日描述，使用最小总势能原理推导出控制方程。为了计算目的，方程的张量形式被一种新的矩阵向量格式所取代。在求解策略上，基于变分求积技术，提出了一种新的数值方法，通过引入微分矩阵算子和积分矩阵算子，直接得到离散化的控制方程。收敛速度快，计算效率和简单的实现是这种方法的优点。结果首先用文献中的可用数据进行验证。然后提供选定的数值结果，以研究超弹性板在可压缩和几乎不可压缩状态下在各种类型的边界条件下的非线性弯曲行为。结果表明，所开发的方法在解决两种状态下超弹性板的大变形问题方面具有良好的性能。