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

In 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 non-uniform internal and external loads. Using Michell's analysis of the stress function and Hooke's law, we derived the analytical solution and compared it to the numerical results obtained using FDM software. The analytical and numerical results are in perfect agreement and lead to the conclusion that the non-uniformity of the loading significantly influences the amplitudes of the orthoradial stresses. These orthoradial stresses may not always be equal to the maximum principal stress, depending on the position within the layer. This result suggests that it is not possible to find an analytical solution in the elastoplastic framework where the fracture criterion is expressed in terms of principal stresses, σ 1 = σ rr or σ θθ, depending on the position considered. The present study makes it possible to deduce the non-uniform loading at the interface of 2 layers by minimizing the deviations with stress and / or strain measurements in one of the layers of the hollow cylinder. This study should also help to understand the influence of a low stiffness material interspersed between rigid materials. • New analytical model for multilayered hollow cylinders under load • Captures non-uniform internal and external radial and tangential stresses • Validated against FDM simulations with excellent agreement • Enables fast stress/displacement initialization in numerical models • Useful for tunnel linings and composite cylindrical structures