This paper proposes a new finite-element modelling of a recent layerwise model for multilayered plates. This layerwise model is built from a specific 3D stress-field expansion along the thickness direction and involves, in particular, interlaminar transverse shear and out-of-plane stresses as generalized stresses. Its main feature is that 3D equilibrium equations and free-edge boundary conditions are directly taken into account into the stress-based construction of the model. A dual displacement-based finite-element discretization is implemented using the FEniCS software package and a remeshing strategy is proposed based on a novel error indicator. The error indicator is built based on the 3D stress field directly deduced from the layerwise generalized stresses and compared to a reconstructed stress field based on the model generalized displacements. The proposed error indicator is shown to identify the most critical parts of a laminate structure associated with complex 3D stress fields such as boundaries or stress concentration/singularity regions (near free-edges or delamination fronts). Through the combination of thickness discretization and in-plane mesh refinement in regions of interest, the proposed framework therefore offers an attractive alternative to 3D solid finite elements for an accurate prediction of stress states in composite laminates.

中文翻译：

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使用分层模型的多层板的网格自适应应力分析

本文为多层板的最新分层模型提出了一种新的有限元建模。该分层模型是通过沿厚度方向的特定3D应力场扩展建立的，尤其涉及层间横向剪切和平面外应力作为广义应力。其主要特征是在基于应力的模型构建中直接考虑了3D平衡方程和自由边缘边界条件。使用FEniCS软件包实现了基于双位移的有限元离散化，并基于一种新型的误差指示器提出了一种重新网格化策略。误差指示器基于直接从分层广义应力导出的3D应力场构建，并与基于模型广义位移的重构应力场进行比较。显示的拟议错误指示器可以识别与复杂3D应力场（例如边界或应力集中/奇异区域（靠近自由边缘或分层前沿））相关的层压结构的最关键部分。通过在感兴趣的区域中将厚度离散化和平面内网格细化相结合，所提出的框架可以为3D实体有限元提供有吸引力的替代方案，以准确预测复合材料层压板中的应力状态。显示的拟议错误指示器可以识别与复杂3D应力场（例如边界或应力集中/奇异区域（靠近自由边缘或分层前沿））相关的层压结构的最关键部分。通过在感兴趣的区域中将厚度离散化和平面内网格细化相结合，所提出的框架可以为3D实体有限元提供有吸引力的替代方案，以准确预测复合材料层压板中的应力状态。显示的拟议错误指示器可以识别与复杂3D应力场（例如边界或应力集中/奇异区域（靠近自由边缘或分层前沿））相关的层压结构的最关键部分。通过在感兴趣的区域中将厚度离散化和平面内网格细化相结合，所提出的框架可以为3D实体有限元提供有吸引力的替代方案，以准确预测复合材料层压板中的应力状态。