2D analytical solution of a multilayered hollow cylinder subjected to non-uniform loads

Abstract

International audienceIn this paper, a new analytical solution has been developed using the recursive method to assess stresses,strains and displacements in the cross-section of an elastic multilayered hollow cylinder subjected to nonuniforminternal and external loads. Using Michell's analysis of the stress function and Hooke's law, wederived the analytical solution and compared it to the numerical results obtained using FDM software. Theanalytical and numerical results are in perfect agreement and lead to the conclusion that the nonuniformityof the loading significantly influences the amplitudes of the orthoradial stresses. Theseorthoradial stresses may not always be equal to the maximum principal stress, depending on the positionwithin the layer. This result suggests that it is not possible to find an analytical solution in the elastoplasticframework where the fracture criterion is expressed in terms of principal stresses, σ1 = σrr or σθθ, depending on the position considered. The present study makes it possible to deduce the non-uniform loading at theinterface of 2 layers by minimizing the deviations with stress and / or strain measurements in one of thelayers of the hollow cylinder. This study should also help to understand the influence of a low stiffnessmaterial interspersed between rigid materials