Static response of double-layered pipes via a perturbation approach

A double-layered pipe under the effect of static transverse loads is considered here. The mechanical model, taken from the literature and constituted by a nonlinear beam-like structure, is constituted by an underlying Timoshenko beam, enriched with further kinematic descriptors which account for local effects, namely, ovalization of the cross-section, warping and possible relative sliding of the layers under bending. The nonlinear equilibrium equations are addressed via a perturbation method, with the aim of obtaining a closed-form solution. The perturbation scheme, tailored for the specific load conditions, requires different scaling of the variables and proceeds up to the fourth order. For two load cases, namely, distributed and tip forces, the solution is compared to that obtained via a pure numeric approach and the finite element method.