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The BEM for buckling analysis of viscoelastic plates modelled with fractional derivatives

机译：分数衍生物模拟粘弹性板屈曲分析的BEM

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In this paper the buckling of viscoelastic plates is studied. The constitutive equations of the viscoelastic material are expressed in differential form using fractional derivatives. The proposed analysis is illustrated with the fractional Kelvin-Voigt and fractional Standard solid models. Plates of arbitrary shape with any type of boundary conditions under interior and edge conservative membrane loads are considered. The principle of the analog equation is applied to convert the original equation into a plate equation (biharmonic) under a fictitious load. Subsequent application of the BEM enables the spatial discretization resulting thus an initial value problem for the values of the fictitious load, which is a system of linear Fractional Differential Equations (FDEs) with respect to time. Using a property of the Mittag-Leffler function a dynamic criterion is established and the eigenvalue problem for the evolution equations is converted into an eigenvalue problem of linear algebra, which permits the evaluation of the buckling loads of the viscoelastic plate. Several plate problems are studied and interesting conclusions on the effect of viscoelasticity on bucking of thin plates are drawn.
机译：在本文中，研究了粘弹板的屈曲。粘弹性材料的组成方程以使用分数衍生物以差异形式表示。所提出的分析用分数kelvin-voigt和分数标准固体模型说明。考虑具有内部和边缘保守膜负载下的任何类型的边界条件的任意形状的板。应用模拟方程的原理在虚拟载荷下将原始方程转换为板式方程（BiHarmonic）。后续应用BEM使得空间离散化能够产生用于虚拟负载的值的初始值问题，这是关于时间的线性分数差分方程（FDE）的系统。使用Mittag-Leffler函数的属性建立动态标准，并且演化方程的特征值问题被转换为线性代数的特征值问题，这允许评估粘弹性板的屈曲负载。研究了几个板问题，并对粘弹性对薄板折叠的影响进行了有趣的结论。

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