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许建文,严世涛,彭林欣,陈卫.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[J].计算力学学报,2024,41(3):572~581
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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
投稿时间:2022-11-06  修订日期:2022-12-21
DOI:10.7511/jslx20221106001
中文关键词:  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
英文关键词:improved Reddy’s third-order shear deformation theory  functionally graded carbon nanotube reinforced composite plate  Pasternak foundation  critical buckling load  moving-least square approximation
基金项目: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.
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 
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中文摘要:
      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。
英文摘要:
      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.
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