正交各向异性功能梯度圆柱壳的应力分析及材料剪裁

Stress Analysis and Material Tailoring of Orthotropic Functionally Graded Hollow Circular Cylinders

假设正交各向异性功能梯度材料的弹性系数沿圆柱壳的径向按照任意连续函数变化,采用应力函数法和加权残值法导出了圆柱壳在非轴对称载荷作用下应力分析的一种新的数值解.建立了圆柱壳内部应力状态给定时材料剪裁问题的基本方程,提出了实现圆柱壳内部一种特殊的应力分布时所需要的材料弹性系数沿径向变化的解析解.通过数值算例验证了本文所导出的应力分析的数值解的正确性和收敛性,分析了弹性系数沿径向的变化对圆柱壳内部应力分布的影响.数值算例还给出了实现圆柱壳内部环向应力和切应力沿径向均匀分布时功能梯度材料的弹性系数沿径向的三种不同变化形式.所得研究结果可为正交各向异性功能梯度材料圆柱壳的设计提供一定的参考,同时材料剪裁的解析结果也可作为其他数值方法计算结果验证的考题.

Assuming that the elastic moduli of the material vary arbitrarily along the radial direction of the cylinder according to a continuous function, a new numerical solution of stress analysis of the cylinder under non-axisymmetric loads was derived by the stress function method and the weighted residual method. The basic equation of material tailoring was established while the stress state of the cylinder was given. And the analytical solution of the variation of elastic moduli with the radius was presented in order to achieve a special stress state in orthotropic functionally graded cylinder. The accuracy and convergence of numerical solution given in this paper was verified and the influence of the variation of elastic moduli along the radial direction on the stresses was exhibited in numerical examples. And the different variation of elastic moduli along the radial direction was also given in order to achieve the uniform distribution of the hoop stress and the shear stress within an orthotropic functionally graded cylinder under nonaxisymmetric load. The solutions here will be helpful for the design of orthotropic functionally graded hollow circular cylinders. The analytical solution of material tailoring can be used to verify the numerical solution obtained by other methods.