Abstract This paper presents a comprehensive numerical finite element implementation of the nonlocal strain gradient theory applied to thin laminated composite nanoplates using Kirchhoff theory (known as Classical Laminated Plate Theory or CLPT). Hermite interpolation functions are used to approximate membrane and bending degrees of freedom according to the conforming and nonconforming approaches. To the best of the authors’ knowledge, there is no finite element formulation in the literature able to deal with laminated Kirchhoff plates including the strain gradient theory, which allows to consider general stacking sequences and boundary conditions. A simple and effective matrix notation is employed to facilitate the computer implementation. Benchmarks reported prove the accuracy of the implementation. Novel applications are provided for further developments in the subject.

中文翻译：

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使用应变梯度理论在弯曲中一致和非一致的层压有限元基尔霍夫纳米板

摘要 本文使用基尔霍夫理论（称为经典层压板理论或 CLPT）提出了非局部应变梯度理论的综合数值有限元实现，该理论应用于薄层压复合纳米板。Hermite 插值函数用于根据符合和不符合方法来近似膜和弯曲自由度。据作者所知，文献中没有能够处理层压基尔霍夫板的有限元公式，包括应变梯度理论，它允许考虑一般的堆叠序列和边界条件。一个简单而有效的矩阵符号被用来促进计算机的实现。报告的基准证明了实施的准确性。