正交各向异性功能梯度圆柱壳的应力分析及材料剪裁

发布时间：2018-04-14 11:09

本文选题：功能梯度材料 + 正交各向异性　；参考：《力学季刊》2016年01期

【摘要】：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.
[Abstract]:It is assumed that the elastic coefficients of orthotropic functionally graded materials vary along the radial direction of cylindrical shells according to arbitrary continuous functions.A new numerical solution for stress analysis of cylindrical shells under non-axisymmetric loads is derived by using the stress function method and the weighted residual method.In this paper, the basic equation of the timing material cutting problem for the stress state in the cylindrical shell is established, and the analytical solution of the material elastic coefficient changing along the radial direction is proposed to realize a special stress distribution in the cylindrical shell.A numerical example is given to verify the correctness and convergence of the numerical solution of the stress analysis derived in this paper. The influence of the variation of elastic coefficient along the radial direction on the stress distribution in the cylindrical shell is analyzed.Numerical examples are given to show three different variations of the elastic coefficient of functionally graded materials along radial direction when the circular stress and shear stress are uniformly distributed along the radial direction.The results can be used as a reference for the design of orthotropic functionally graded materials cylindrical shells, and the analytical results of material tailoring can also be used as an examination question to verify the results of other numerical methods.
【作者单位】：同济大学航空航天与力学学院;
【基金】：国家自然科学基金(11372225)
【分类号】：O343

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