基于非线性梯度单元的石墨烯功能梯度悬臂板力学特性

Mechanical properties of graphene functionally graded cantilever plate based on nonlinear gradient element

针对石墨烯功能梯度材料提出了一种基于20节点非线性梯度单元的有限元建模方法,该方法克服了传统有限元分层法无法精确拟合功能材料梯度变化和无法进行应力分析的缺点。以U形、X形和O形3种梯度分布形式的悬臂板为研究对象,分析了悬臂板静载荷下的弯曲变形、应力分布和模态特性,并与有限元分层法模型进行了对比分析和验证。研究结果表明:与非线性梯度单元法相比,传统分层法模型会导致X形悬臂板弯曲刚度和对应各阶固有频率大于实际值,而导致O形悬臂板的弯曲刚度和对应各阶固有频率小于实际值;与U形分布形式相比,X形梯度分布可以提高悬臂板弯曲刚度,提高悬臂板各阶固有频率,而O形分布形式会降低悬臂板弯曲刚度,降低各阶固有频率;非线性梯度单元法能够实现对功能梯度板厚度方向的应力求解,为功能梯度板的疲劳寿命分析提供了理论基础。

Aiming at the complex gradient changes of graphene-reinforced composite materials,a finite element method based on 20-node nonlinear gradient element is proposed to satisfy the analysis of the mechanical properties of complex gradient materials.In this paper,the finite element models of U-shaped,X-shaped and O-shaped gradient distribution cantilever plates are established,and the static displacement,stress and mode of the cantilever plates under the three gradient distribution forms are compared and analyzed.The method in this paper is compared and verified with the finite element layered method.The results show that compared with the nonlinear gradient element method,the traditional layered method model will cause the bending stiffness of the X-shaped cantilever plate and the corresponding natural frequencies of each order to be larger than the actual values,while the bending stiffness of the O-shaped cantilever plate and the corresponding natural frequencies of each order are smaller than the actual values.Compared with the U-shaped distribution,the X-shaped gradient distribution can improve the bending stiffness of the cantilever plate,mentioning the natural frequencies of each order of the cantilever plate,while the O-shaped distribution can reduce the bending stiffness of the cantilever plate and reduce the natural frequencies of each order.The nonlinear gradient element method can solve the stress in the thickness direction of the functionally graded plate,which provides a theoretical basis for the fatigue life analysis of the functionally graded plate.