Elasticity Solutions for Sandwich Arches considering Permeation Effect of Adhesive

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.