碳纳米管增强复合材料Timoshenko梁弯曲和屈曲行为分析

考虑碳纳米管(carbon nanotubes,CNTs)的尺度效应,研究宏观尺度下碳纳米管增强复合材料(carbon nanotubes reinforced composites,CNTRCs)梁的弯曲和屈曲行为。在EMT(Eshelby-Mori-Tanaka)方法的基础上,利用非局部理论提出了可表征CNTs尺度效应的非局部EMT本构模型。根据Timoshenko梁理论,采用哈密顿原理得到CNTRCs梁的静力学微分方程和边界条件。求解简支边界条件下CNTRCs梁的弯曲响应和极限屈曲载荷,并与文献进行对比验证所建模型和求解方法的正确性。分析了CNTs的尺度效应参数和体积分数以及复合材料梁的长细比等因素对简支CNTRCs梁弯曲响应和极限屈曲载荷的影响规律。结果表明,考虑CNTs的尺度效应会削弱结构等效刚度,且CNTs体积分数和尺度效应参数对大长细比CNTRCs梁的弯曲响应和极限屈曲载荷的影响幅度较大。

Bending and buckling behavior analysis of the carbon nanotubes reinforced composites Timoshenko beams

Bending and buckling behavior of the macro CNTRCs (carbon nanotubes reinforced composites) beam was studied considering the scale effect of CNTs (carbon nanotubes). Based on the EMT (Eshelby-Mori-Tanaka) method and using nonlocal theory to characterize the scale effect of CNTs, the nonlocal EMT constitutive model was established. According to the Timoshenko beam theory, the static differential equations and boundary conditions of CNTRCs beams were derived through Hamilton principle. Bending response and ultimate buckling load of CNTRCs beams at S-S (simply supported) edges were obtained and compared with the literature to verify the correctness of the proposed model and solution method. Influences of the scale effect parameters and volume fraction of CNTs and the slenderness ratio of composite beams on the bending response and ultimate buckling load of S-S CNTRCs beams were analyzed. Results show that the equivalent stiffness of the CNTRCs beam is weakened by considering the scale effect of CNTs, and the volume fraction of CNTs and the scale effect parameter both have a great impact on the bending response and ultimate buckling load of the CNTRCs beam with a large slenderness ratio.