论文标题
增强平面杆非线性弯曲的模型：本地化现象和多稳定性
Enhanced models for the nonlinear bending of planar rods: localization phenomena and multistability
论文作者
论文摘要
我们从Föppl-von-vonkármán薄壳模型开始推断出弹性平面杆的一维模型。此类模型通过其他运动学描述符增强，这些运动描述符可在2D父连续体中保持明确跟踪兼容性条件，即在尺寸降低后，标准杆模型在标准杆模型中得到了相同的满足。还提出了不可扩展的模型，从不可延迟的壳的非线性Koiter模型开始。这些增强的模型描述了杆的非线性平面弯曲，即使在一维体中，例如奇异和定位（D-Cones）（d-cones），也可以考虑到某些显着重要性的现象，否则经典的1D模型无法访问。此外，兼容性的影响转化为获得多个稳定平衡构型的可能性。
We deduce a 1D model of elastic planar rods starting from the Föppl--von Kármán model of thin shells. Such model is enhanced by additional kinematical descriptors that keep explicit track of the compatibility condition requested in the 2D parent continuum, that in the standard rods models are identically satisfied after the dimensional reduction. An inextensible model is also proposed, starting from the nonlinear Koiter model of inextensible shells. These enhanced models describe the nonlinear planar bending of rods and allow to account for some phenomena of preeminent importance even in 1D bodies, such as formation of singularities and localization (d-cones), otherwise inaccessible by the classical 1D models. Moreover, the effects of the compatibility translate into the possibility to obtain multiple stable equilibrium configurations.
