properties of an equivalent materia

properties of an equivalent material associated to the carbon
bonds represented by beams in Single-Walled Carbon Nanotubes
(SWCNTs). Meo and Rossi [7] developed a similar model by using
modified Morse potential to simulate graphene and carbon
nanotube properties. Sakhaee-Pour et al. [8,9] used MSM to study
the application of single-layer graphene sheets as strain and mass
sensors. Sakhaee-Pour [10] also studied the elastic buckling
behavior of single-layer graphene sheets. In the classical MSM, the
covalent bonds between the carbon atoms are modeled as an
equivalent beam with circular cross-section. The sectional prop￾erties of the element are obtained regarding the bond stretching,
torsion and angle variation. When the cross-section is circular, the
out-of-plane bending stiffness of the equivalent beam will be the
same as the in-plane bending stiffness, leading to inaccurate
results in the transverse deflection and buckling analysis of gra￾phene. The experiments and MD simulations also confirm that the
out-of-plane bending stiffness of graphene is considerably less
than that predicted via classical MSM. Recently some researchers
proposed modifications to the molecular structural mechanics.
Wan and Delale [11] considered a rectangular cross-section for the
equivalent beam element to analyze local bending of the carbon
nanotubes. They also derived an analytical closed-form solution
for the sectional properties of the beam element. In their model,
the torsional energy is neglected and the Poisson's ratio of the
equivalent beam element is 0.3. Chen et al. [12] proposed a model
in which the interaction between two carbon atoms is modeled by
the second generation force field using continuum pseudo￾

結果 (中文) 1:

相关的碳当量材料性能债券由梁 Single-Walled 碳纳米管（电学）。Meo 和罗西 [7] 通过使用开发了一个类似的模型修改 Morse 势来模拟石墨烯和碳纳米管性能。Sakhaee-倒等人 [8，9] MSM 用于研究作为应变和大众单层石墨烯的应用传感器。Sakhaee-倒 [10] 也研究了弹性屈曲单层石墨烯薄片的行为。在古典的 msm 人群中，碳原子之间的共价键被建模为圆形截面的等效梁。元素的截面定型得到关于债券的伸展，扭转和角度的变化。当截面为圆形，平面外抗弯刚度等效梁将同样作为平面内的抗弯刚度，导致不准确在横向挠度和 gra 苯的屈曲分析的结果。分子动力学模拟与实验也证实，平面外抗弯刚度的石墨烯是相当少比预测通过古典 MSM。最近一些研究人员对分子结构力学的拟议的修改。万和 Delale [11] 考虑矩形截面等效梁单元来分析局部弯曲的碳纳米管。他们还导出了封闭形式的解析解对梁单元的截面属性。在他们的模型，忽略了扭转能源和泊松比的等值梁元素是 0.3。Chen 等人 [12] 提出了一种模型在这两个碳原子之间的相互作用是由建模第二个使用连续伪代力场

結果 (中文) 3:

与碳有关的等效材料的性质单壁碳纳米管中束的键（SWCNTs）。梅奥和罗西[ 7 ]开发了一个类似的模型利用改进的Morse势模拟石墨烯和碳碳纳米管的性质。萨哈伊倒等人。[ 8,9 ]用MSM研究单层石墨烯片作为应变和质量的应用传感器.萨哈伊倒[ 10 ]研究了弹性屈曲单层石墨烯片的行为。在经典的MSM，碳原子之间的共价键被建模为圆截面等效梁。获得关于债券拉伸截面支柱￾性能的因素，扭转和角变化。当横截面为圆形时平面外弯曲刚度的等效梁将相同的平面内弯曲刚度，导致不准确GRA￾苯在横向变形和屈曲分析结果。实验和MD模拟也证实外平面弯曲刚度的石墨烯是相当少通过经典的MSM比预测。最近一些研究人员分子结构力学的修正。湾和Delale [ 11 ]认为是对矩形截面碳纤维局部弯曲的等效梁单元分析纳米管。他们还派生了解析封闭形式的解决方案对于梁单元的截面特性。在他们的模型中，的扭转能量被忽略和泊松比的等效梁单元为0.3。陈等。[ 12 ]提出了一个模型其中两个碳原子之间的相互作用是仿照第二代力场采用连续的伪￾