摘要本文研究了功能梯度碳纳米管增强复合材料层合板的屈曲分析。在这项研究中，层合板是由碳纳米管增强复合材料层完美结合的，并在每一层中，碳纳米管为均匀分布或者梯度分布。因为板被设定为是中等厚度，所以一阶剪切变形理论掺入横向剪切变形和转动惯量的影响，并用无网格方法对板的屈曲行为进行研究。利用核粒子近似的场变量和最小化能量函数，并通过KP-Ritz无网格法，得到离散特征值方程。通过对比分析，验证了收敛性、数值稳定性和KP-Ritz法的精度。运用MATLAB  R2012a软件编写KP-Ritz无网格程序，计算得到了碳纳米管体积分数、板长度与宽度比、板宽度与厚度比、碳纳米管分布类型及边界条件和不同压缩条件下对复合材料层合板的屈曲行为的影响。此外,对层数和层压角的影响也进行了详细研究计算，并绘制出数值曲线。84696

毕业论文关键字：碳纳米管复合材料层合板  屈曲分析  KP-Ritz无网格方法  一阶剪切变形理论  MATLAB  数值计算 

毕业设计说明书外文摘要

Title      Bucking of CNT reinforced functionally  graded laminates composite plates             

Abstract This paper presented the buckling analysis of CNTR-FG composite laminated plates。In this study, the laminated plate is composed of perfectly bonded carbon nanotube reinforced functionally graded layers, and in each layer, the CNTs are assumed to be uniformly distributed or functionally graded 。 Because the plate considered is of moderate thickness, the first-order shear deformation theory (FSDT) is employed to incorporate the effect of transverse shear deformation and rotary inertia,and the buckling behavior of the laminated plate is studied by  the meshless method。 Using the kernel particle approximation in the field variables and minimizing the energy functional via the meshless KP-Ritz method, a discretized eigenvalue equation of the problem is derived。 Through the comparative analysis, the convergence, numerical stability and the accuracy of the KP-Ritz method are verified。 Using the MATLAB  R2012a writes a meshless program of the KP-Ritz method。 Influences of CNT volume fraction, plate length-to-thickness ratio, plate aspect ratio, distribution type of CNT , boundary conditions and different compression conditions on the buckling responses of the laminated nanocomposite plates are investigated。 In addition, the effects of number of layers and lamination angle are examined in detail, the numerical curves are also drawn。

Keywords:Carbon nanotube reinforced functionally graded composites ;buckling; first-order shear deformation theory; meshless KP-Ritz method;MATLAB;numerical calculation

目   次

1   引言   1

2   研究对象   2

2。1 碳纳米管发展及研究前景   2

2。2 碳纳米管复合材料   3

3   研究方法   4

3。1 一阶剪切变形理论   4

3。2 无网格法   5

4   问题定义   7

4。1 导出问题   7

4。2 研究原理   8

5   理论公式   11

5。1 能量公式   11

5。2 离散系统方程   13

6   MATLAB R2012a软件    17

6。1 程序编写   17

6。2 数值计算   18

7   层合板的屈曲分析    25

结论  27

致谢  28

参考文献    29