压电集成石墨烯增强功能梯度多孔板的等几何建模与分析

Isogeometric modeling and analysis of piezoelectric integrated functionally graded porous plates reinforced by graphene platelets

基于等几何分析方法和一种仅含有4自由度的简化一阶剪切变形理论(simple first-order shear deformation theory,S-FSDT)建立了压电集成石墨烯增强功能梯度多孔(piezoelectric integrated graphene platelets reinforced functionally graded porous,P-GPLs-FGP)板的数值分析模型。利用Halpin-Tsai微观力学模型、闭胞体高斯随机场理论和混合定律得到了石墨烯增强功能梯度多孔板的有效材料属性;基于等几何分析方法、S-FSDT和哈密顿原理推导了P-GPLs-FGP板的运动控制方程,并通过与已有算例对比验证了模型的准确性和有效性;利用所建模型分析了孔隙分布形式、孔隙系数、石墨烯分布形式、石墨烯质量分数、边界条件和宽厚比对P-GPLs-FGP板固有频率和机-电载荷作用下静态弯曲响应的影响。研究结果表明:板的刚度与孔隙系数成反比,而在基体材料中添加少量的石墨烯可以有效地增强结构的刚度;与其他组合形式相比,板的刚度在孔隙PD-S分布和石墨烯GPL-S分布时最大。

Based on the isogeometric analysis method and a simple first-order shear deformation theory(S-FSDT)with only four degrees of freedom per node,the numerical analysis model for piezoelectric integrated graphene platelets reinforced functionally graded porous(P-GPLs-FGP)plates was established.Firstly,the effective material properties of graphene platelets reinforced functionally graded porous plates were determined by using the Halpin-Tsai micromechanical model,the closed cell theory in Gaussian random field and the rule of mixture.Then,the governing equations of P-GPLs-FGP plates were derived based on the isogeometric analysis method,S-FSDT and Hamilton’s principle.The accuracy and effectiveness of the developed model were demonstrated through an examplic numerical experiment with its results comparison.Finally,the effects of the porosity distribution type,porosity coefficient,graphene platelets distribution pattern,graphene platelets weight fraction,boundary conditions and width-thickness ratio on the natural frequencies and static bending responses of P-GPLs-FGP plates under electro-mechanical loads were analyzed.The results show that the stiffness of the plates is inversely proportional to the porosity coefficient and can be effectively enhanced by adding a small amount of GPLs into the matrix material.Compared with other considered combinations,the plates with the porosity distribution of PD-S type and the grapheme platelets distribution of GPL-S pattern possess the highest stiffness.