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.

中文翻译：

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双层管的静摄动响应

这里考虑在静态横向载荷作用下的双层管。力学模型取自文献，由非线性的梁状结构构成，由下层的Timoshenko梁构成，并富含进一步的运动学描述符，这些描述符描述了局部效应，即横截面的椭圆化，翘曲和可能的相对应力。弯曲下各层的滑动。非线性平衡方程是通过摄动法解决的，目的是获得封闭形式的解。为特定的负载条件量身定制的摄动方案需要对变量进行不同的缩放，并升至第四级。对于两种载荷情况，即分布力和尖端力，将解与通过纯数值方法和有限元方法获得的解进行比较。