ABSTRACT Adhesively bonded joints are often addressed through Finite Element (FE). However, analyses based on FE models are computationally expensive, especially when the number of adherends increases. Simplified approaches are suitable for intensive parametric studies. Firstly, a resolution approach for a 1D-beam simplified model of bonded joint stress analysis under linear elastic material is presented. This approach, named the macro-element (ME) technique, is presented and solved through two different methodologies. Secondly, a new methodology for the formulation of ME stiffness matrices is presented. This methodology offers the ability to easily take into account for the modification of simplifying hypotheses while providing the shape of solutions, which reduced then the computational time. It is illustrated with the 1D-beam ME resolution and compared with the previous ones. Perfect agreement is shown. Thirdly, a 1D-beam multi-layered ME formulation involving various local equilibrium equations and constitutive equations is described. It is able to address the stress analysis of multi-layered structures. It is illustrated on a double lap joint (DLJ) with the presented method.

中文翻译：

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用于模拟多层键合结构的宏观元素的一般公式

摘要 粘接接头通常通过有限元 (FE) 来解决。然而，基于有限元模型的分析在计算上是昂贵的，尤其是当被粘附者的数量增加时。简化的方法适用于密集的参数研究。首先，提出了一种求解线弹性材料下粘结接头应力分析的一维梁简化模型的方法。这种称为宏元素 (ME) 技术的方法是通过两种不同的方法提出和解决的。其次，提出了一种新的 ME 刚度矩阵公式化方法。这种方法提供了在提供解决方案形状的同时轻松考虑修改简化假设的能力，从而减少了计算时间。它以 1D 光束 ME 分辨率进行说明，并与之前的分辨率进行了比较。显示完全一致。第三，描述了涉及各种局部平衡方程和本构方程的一维梁多层 ME 公式。它能够解决多层结构的应力分析。使用所提出的方法在双搭接接头 (DLJ) 上对其进行了说明。