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

DOI：10.7511/jslx20221106001

 作者 单位 E-mail 许建文 广西新发展交通集团有限公司, 南宁 530004 严世涛 广西交通职业技术学院, 南宁 530004 彭林欣 广西大学 土木建筑工程学院, 南宁 530004 陈卫 广西大学 土木建筑工程学院, 南宁 530004南华大学 土木工程学院, 衡阳 421001 w.chen@st.gxu.edu.cn

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.