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张靖华 李世荣 马连生. 功能梯度截顶圆锥壳的热弹性弯曲精确解[J]. 力学学报, 2008, 40(2): 185-193. DOI: 10.6052/0459-1879-2008-2-2007-160
引用本文: 张靖华 李世荣 马连生. 功能梯度截顶圆锥壳的热弹性弯曲精确解[J]. 力学学报, 2008, 40(2): 185-193. DOI: 10.6052/0459-1879-2008-2-2007-160
Jinghua Zhang, Shirong Li, Liansheng Ma. Exact solution of thermoelastic bending for functionally graded truncated conical shells[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(2): 185-193. DOI: 10.6052/0459-1879-2008-2-2007-160
Citation: Jinghua Zhang, Shirong Li, Liansheng Ma. Exact solution of thermoelastic bending for functionally graded truncated conical shells[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(2): 185-193. DOI: 10.6052/0459-1879-2008-2-2007-160

功能梯度截顶圆锥壳的热弹性弯曲精确解

Exact solution of thermoelastic bending for functionally graded truncated conical shells

  • 摘要: 研究了功能梯度材料截顶圆锥壳在横向机械载荷与非均匀热载荷同时作用下的变形问题. 基于经典线性壳体理论推导出了以横向剪力和中面转角为基本未知量的功能梯度薄圆锥壳轴对称变形的混合型控制方程. 假设功能梯度圆锥壳的材料性质为沿厚度方向按照幂函数连续变化的形式. 然后采用解析方法求解,得到了问题的精确解. 分别就两端简支和两端固支边界条件,给出了圆锥壳的变形随其载荷、材料参数等变化的特征关系曲线,重点分析和讨论了载荷参数与材料梯度变化参数对变形的影响.

     

    Abstract: The deformation of functionally graded truncated conicalshell subjected to transverse mechanical load as well as non-uniformlythermal load is studied. Based on classical linear theory of shell, themixed-form equations governing the axi-symmetrical deformation of FGMconical shells are derived, taking transverse shear force and mid-surfaceangle of rotation as basic unknown functions. In the analysis, it is assumedthat the material properties of the shell vary continuously as a powerfunction of the thickness coordinate. And then obtain exact solution of theproblem by using analytic method. For FGM shells with simply supported andfixed boundary conditions, characteristic curves of the deformation versusthe loads and gradient of the material parameters are plotted. Especially,the effects of temperature rise and the parameter of gradient of thematerials variation on the deflection of the FGM conical shell are examinedand discussed.

     

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