论文标题
Howell等人的非线性光束理论的批判性研究
A Critical Study of Howell et al.'s Nonlinear Beam Theory
论文作者
论文摘要
在我们的分析中，我们表明Howell等人的非线性束理论并未描述Euler-Bernoulli光束方程的表示，非线性或其他方式。作者的非线性光束理论意味着，可以将光束弯曲到变形的恒定半径上，并以零力保持变形的恒定半径。因此，通过证明变形的曲率是恒定的，而即使是线性的Euler-Bernoulli梁方程在此类变形下也完全有效时，该模型被证明是无效的。总而言之，我们使用Ciarlet的非线性板方程得出了非线性束方程，并表明我们的模型对于恒定的变形半径有效。
In our analysis, we show that Howell et al.'s nonlinear beam theory does not depict a representation of the Euler-Bernoulli beam equation, nonlinear or otherwise. The authors' nonlinear beam theory implies that one can bend a beam in to a constant radius of deformation and maintain that constant radius of deformation with zero force. Thus, the model is disproven by showing that it is invalid when the curvature of deformation is constant, while even the linear Euler-Bernoulli beam equation stays perfectly valid under such deformations. To conclude, we derive a nonlinear beam equation by using Ciarlet's nonlinear plate equations and show that our model is valid for constant radius of deformations.
