碳纳米管增强功能梯度圆柱曲板的后屈曲分析
摘要本毕业设计研究的是在轴向受压作用下，CNTR-FG圆柱曲板的后屈曲分析。考虑了CNT在复合材料板中的不同分布的影响，并运用混合扩展规则来计算相应的复合材料的力学特性。运用第一剪切变形板理论(FSDT)、冯卡门中等大变形理论和板壳的本构方程推导出曲板的总势能方程。并运用再生核粒子法(RKPM)构造形函数，然后用里茨法(RITZ)形成离散系统方程。然后运用稳态节点积分和节点积分来计算刚度矩阵。最后运用牛顿-拉夫逊法结合弧长法求解非线性方程来跟踪前屈曲和后屈曲分析路径。论文中进行了详尽的参数研究，并讨论了各种参数对碳纳米管增强功能梯度圆柱曲板的后屈性能的影响。84693
毕业论文关键词 碳纳米管 后屈曲 再生核粒子发 里茨法
毕业设计说明书外文摘要
Title Postbuckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshfree approach
Abstract This thesis is to study the postbuckling analysis of carbon nanotube-reinforced functionally graded (CNTR-FG)cylindrical curved plate under axial compression。 The post- buckling response of carbon nanotube composite plates with three different kind of structures is considered, and the mechanical properties of the composites are calculated by the extended rule of mixture。 The first-order shear deformation shell theory(FSDT), von karman’s assumptions for moderately large deformation and the constitutive equation are employed to obtain the total potential energy equation。And the reproducing kernel particle method (RKPM) is used to construct the shape function, then the Ritz method (RITZ) is used to form the discrete system equations。Then, the stiffness matrix is calculated by using the direct nodal integration method and the stabilized conforming nodal integration scheme。In the present study, the arc-length method combined with the modified Newton-Raphson method is used to trace the postbuckling path。Detailed parametric studies are carried out to investigate effects of various parameters on postbuckling behaviors of CNTR-FG cylindrical panels。
Key words carbon nanotube postbuckling reproducing kernel particle method Ritz method
目 次
1 绪论 1
2 碳纳米管复合材料板 3
2。1 三种不同结构的CNTR-FG 3
2。2 复合材料属性参数的计算 4
3 理论公式 6
3。1 总势能 6
3。1。1 FSDT理论 6
3。1。2 冯卡门中等大变形理论 6
3。1。3 板壳的本构方程 7
3。1。4 总势能公式推导 8
3。2 形函数的构造 9
3。2。1 无网格法及RKPM法 9
3。2。2 边界条件的处理方法 12
3。3 离散方程组的形成 14
3。3。1 RITZ法形成离散系统方程 14
3。3。2 稳态结点积分 15
3。3。3 结点积分 18
3。3。4 高斯结点积分 19
3。4 N-R法结合弧长法求解方程组