基于改进Reddy型三阶剪切变形理论的弹性地基上FG-CNTRC板屈曲无网格分析  

Meshless buckling analysis of FG-CNTRC plate on elastic foundation based on improved Reddy type third-order shear deformation theory

作　　者：许建文 严世涛 彭林欣[3] 陈卫 XU Jian-wen;YAN Shi-tao;PENG Lin-xin;CHEN Wei(Guangxi Xinfazhan Communication Group Co.,Ltd.,Nanning 530004,China;Guangxi Transport Vocational and Technical College,Nanning 530004,China;School of Civil Engineering and Architecture,Guangxi University,Nanning 530004,China;School of Civil Engineering,University of South China,Hengyang 421001,China)

机构地区：[1]广西新发展交通集团有限公司,南宁530004 [2]广西交通职业技术学院,南宁530004 [3]广西大学土木建筑工程学院,南宁530004 [4]南华大学土木工程学院,衡阳421001

出　　处：《计算力学学报》2024年第3期572-581,共10页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(12162004,11562001);广西高校中青年教师科研基础能力提升项目(2022KY1140)资助.

摘　　要：针对含碳纳米管转向的Pasternak地基上功能梯度碳纳米管增强复合材料FG-CNTRC(functionally graded carbon nanotube-reinforced composite)板的屈曲问题,提出了一种基于改进Reddy型三阶剪切变形理论TSDT(third-order shear deformation theory)和移动最小二乘近似MLS(moving-least square)的无网格分析模型。该模型避免了无网格法第二类边界条件的施加困难问题,且能够满足中厚/厚板的自由表面条件,无需额外引入剪切修正因子。基于最小势能原理推导了弹性地基上FG-CNTRC板的无网格屈曲控制方程,采用完全转换法处理本质边界条件。通过基准算例验证了本文方法的收敛性及有效性,讨论了碳纳米管的转向角、体积分数、分布形式、地基系数、宽厚比和边界条件等对FG-CNTRC板临界屈曲荷载的影响。In order to solve the buckling problem of functionally graded carbon nanotube reinforced composite(FG-CNTRC)plates with carbon nanotubes(CNTs)orientation angle resting on an elastic foundation,a meshless analysis model based on improved Reddy’s third-order shear deformation theory(TSDT)and moving least square(MLS)is proposed.This model avoids the difficulty of imposing the second kind of boundary condition in the meshless method,and can satisfy the free surface conditions of medium thick/thick plates without introducing additional shear correction factors.Based on the principle of minimum potential energy,the governing meshless equations for the buckling of FG-CNTRC plates on an elastic foundation are derived.The convergence and effectiveness of this method are verified by a benchmark example.The effects of the orientation angle,volume fraction,distribution pattern,foundation coefficient,width-to-thickness ratio and boundary condition on the critical buckling loads of FG-CNTRC plates are analysed.

关 键 词：改进Reddy型三阶剪切变形理论 功能梯度碳纳米管增强复合材料板 PASTERNAK地基 临界屈曲荷载 移动最小二乘近似 

分 类 号：TU339[建筑科学—结构工程] O343.9[理学—固体力学]