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首页> 美国卫生研究院文献>Proceedings. Mathematical Physical and Engineering Sciences >Nonlinear bending models for beams and plates
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Nonlinear bending models for beams and plates

机译：梁和板的非线性弯曲模型

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A new nonlinear model for large deflections of a beam is proposed. It comprises the Euler–Bernoulli boundary value problem for the deflection and a nonlinear integral condition. When bending does not alter the beam length, this condition guarantees that the deflected beam has the original length and fixes the horizontal displacement of the free end. The numerical results are in good agreement with the ones provided by the elastica model. Dynamic and two-dimensional generalizations of this nonlinear one-dimensional static model are also discussed. The model problem for an inextensible rectangular Kirchhoff plate, when one side is clamped, the opposite one is subjected to a shear force, and the others are free of moments and forces, is reduced to a singular integral equation with two fixed singularities. The singularities of the unknown function are examined, and a series-form solution is derived by the collocation method in terms of the associated Jacobi polynomials. The procedure requires solving an infinite system of linear algebraic equations for the expansion coefficients subject to the inextensibility condition.
机译：提出了一种新的梁大挠度非线性模型。它包括关于挠度的Euler-Bernoulli边值问题和非线性积分条件。当弯曲不改变梁的长度时，此条件可确保偏转的梁具有原始长度并固定自由端的水平位移。数值结果与elastica模型提供的结果非常吻合。还讨论了该非线性一维静态模型的动态和二维概括。对于不可扩展的矩形Kirchhoff板，当一侧被夹紧时，相对的一侧受到剪切力，而另一侧没有力矩和力，则该模型的问题被简化为具有两个固定奇点的奇异积分方程。检查未知函数的奇异性，并根据搭配的Jacobi多项式通过搭配方法导出级数解。该过程需要求解一个线性代数方程的无限系统，以解决受不可扩展性条件影响的膨胀系数。

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