In this work, analytical solution of simply supported sandwich arches considering permeation effect of adhesives is presented. The permeation layer is described by the functionally graded material, exponentially graded in the radial direction. The stresses and deformations of each layer are based on the two-dimensional (2D) elasticity theory in the polar coordinate. The governing equations of the arch are solved by the layer-wise method, which turns the differential equations with variable coefficients into constant coefficients. The solution can be obtained efficiently by means of the recursive matrix method, especially for the arch with many layers. The present solution agrees well with the finite element solution with a fine mesh, while the finite element method is time consuming in mesh division and calculation. The one-dimensional (1D) solution based on the Euler–Bernoulli theory is close to the present one; however, the error increases as the arch becomes thick. The effect of permeation layer thickness on the stresses is studied. It is indicated that the stress distributions tend to be smooth along the radial direction as the permeation layer thickness increases.

中文翻译：

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考虑粘合剂渗透效应的夹心拱门弹性解法

在这项工作中，提出了考虑粘合剂渗透效应的简支夹层拱的解析解。渗透层由功能梯度材料描述，在径向方向上呈指数梯度。每层的应力和变形均基于极坐标中的二维 (2D) 弹性理论。采用分层法求解拱形控制方程，将变系数微分方程转化为常系数。递归矩阵法可以有效地求解，特别是对于多层拱。目前的解法与细网格的有限元解法吻合较好，而有限元法在网格划分和计算上比较耗时。基于 Euler-Bernoulli 理论的一维 (1D) 解与目前的解很接近；但是，随着拱形变厚，误差会增加。研究了渗透层厚度对应力的影响。表明随着渗透层厚度的增加，应力分布沿径向趋于平滑。