Large deflections of inextensible cantilevers: modeling, theory, and simulation
Large deflections of inextensible cantilevers: modeling, theory, and simulation
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DOI：
10.1051/mmnp/2020033
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发表时间：
2019-10
影响因子：
2.2
通讯作者：
Maria Deliyianni;Varun M. Gudibanda;J. Howell;J. Webster
中科院分区：
文献类型：
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作者：
Maria Deliyianni;Varun M. Gudibanda;J. Howell;J. Webster
考虑了一个新近提出的大挠度悬臂梁模型。主要的非线性效应来自梁的不可扩展性-局部弧长保持-而不是传统的可扩展效应归因于完全限制的边界条件。强制不可扩展性导致：非线性刚度项，表现为准线性和半线性效应，以及非线性惯性效应，表现为非局部项，使梁隐含在加速度中。在本文中，我们讨论的运动方程的推导，通过汉密尔顿的原则与拉格朗日乘子，以加强有效的不可扩展性约束。然后，我们提供的功能框架弱和强的解决方案，然后提出新的结果强解的存在性和唯一性。一个显着的特点是，这两种类型的非线性项提出了独立的挑战：准线性性质的刚度力更高的拓扑结构的解决方案，而非局部惯性需要考虑开尔文-沃伊特型阻尼关闭估计。最后，模态方法是用来产生面向几何的数值模拟，提供洞察的功能和局限性的不可扩展的模型。
A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam’s inextensibility – local arc length preservation – rather than traditional extensible effects attributed to fully restricted boundary conditions. Enforcing inextensibility leads to: nonlinear stiffness terms, which appear as quasilinear and semilinear effects, as well as nonlinear inertia effects, appearing as nonlocal terms that make the beam implicit in the acceleration. In this paper we discuss the derivation of the equations of motion via Hamilton’s principle with a Lagrange multiplier to enforce the effective inextensibility constraint. We then provide the functional framework for weak and strong solutions before presenting novel results on the existence and uniqueness of strong solutions. A distinguishing feature is that the two types of nonlinear terms present independent challenges: the quasilinear nature of the stiffness forces higher topologies for solutions, while the nonlocal inertia requires the consideration of Kelvin-Voigt type damping to close estimates. Finally, a modal approach is used to produce mathematically-oriented numerical simulations that provide insight into the features and limitations of the inextensible model.