Edge-buckling in stretched thin films under in-plane bending
Edge-buckling in stretched thin films under in-plane bending
复制标题
面内弯曲下拉伸薄膜的边缘屈曲
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
C. Coman
中科院分区：
文献类型：
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作者：
C. Coman
摘要。在薄板线性化Donnell-von Kármán分岔方程的框架下，研究了受面内弯曲作用的拉伸矩形薄膜的起皱不稳定性。我们的主要目标之一是评估薄膜的有限弯曲刚度在线性起皱机制中所起的作用。为此，我们采用非齐次线性预分叉解，并将相应的特征值问题转化为变系数奇摄动微分方程。对该问题的数值模拟表明存在两种不同的最低特征值状态。在此基础上，进行了WKB分析，以捕获临界起皱载荷对局部振荡屈曲模式波长和弹性膜刚度的依赖关系。利用复合矩阵法对特征值进行独立数值计算，验证了分析结果的有效性。
Abstract.The wrinkling instabilities of a stretched rectangular thin film subjected to in-plane bending are investigated within the framework of the linearised Donnell-von Kármán bifurcation equation for thin plates. One of our principal objectives is to assess the role played by the finite bending stiffness of the film on the linear wrinkling mechanism. To this end, we employ a non-homogeneous linear pre-bifurcation solution and cast the corresponding eigenvalue problem as a singularly-perturbed differential equation with variable coefficients. Numerical simulations of this problem reveal the existence of two different regimes for the behaviour of the lowest eigenvalue. Based on this observation, a WKB analysis is carried out in order to capture the dependence of the critical wrinkling load on the wavelength of the localised oscillatory buckling pattern and the stiffness of the elastic film. The validity of the analytical results is corroborated by independent numerical computations of the eigenvalues using the method of compound matrices.