基于分层法石墨烯增强功能梯度梁的有限元分析

Finite element analysis of graphene-reinforced functionally graded beams based on layered method

基于分层法的思想,对石墨烯增强功能梯度梁进行有限元力学分析。在有限元计算的分层模型中,每层的材料参数为常数,并根据修正后的Halpin-Tsai微观力学模型计算得到,然后按照标准化步骤完成石墨烯增强功能梯度梁的有限元建模和力学分析。通过数值算例,分析了石墨烯的质量含量、分布形式和尺寸等因素对梁的弯曲性能的影响。数值算例结果表明,加入少量的石墨烯可以显著减少梁的弯曲挠度,在梁的上下表面分布更多的石墨烯是减少弯曲挠度的最有效的方法。在相同质量含量的情况下,长厚比较大的正方形石墨烯片更能够提高梁的弯曲性能。

Based on the idea of layered method, the finite element analysis of graphene-reinforced functionally graded beam is carried out in this paper. In the layered model of finite element calculation, the material parameters of each layer are constant, and the values of those material parameters are calculated according to the modified Halpin Tsai model. Then, the finite element modeling and mechanical analysis of the graphene-reinforced functionally graded beam are completed according to the standardized steps of finite element method. Numerical examples are presented to analyze the influence of the mass content, distribution patterns and size of graphene on the bending properties of the beam. Numerical results show that adding a small amount of graphene can significantly reduce the bending deflection of the beam, and distributing more graphene on the upper and lower surfaces of the beam is the most effective method to reduce the bending deflection. At the same mass content, the square graphene sheet with larger length thickness ratio can improve the bending performance of the beam more.