复合材料夹层圆柱壳的轴对称失稳问题

Axisymmetric Instability of Cylindrical Composite Sandwich Shells

本文首先给出复合材料夹层圆柱壳大挠度问题的一般方程,然后在轴对称变形条件下进行简化,得到轴对称变形的非线性方程。在此基础上用摄动法,给出了复合材料夹层圆柱壳轴压轴对称屈曲方程,该方程与齐次边界条件一起构成分析轴对称失稳的特征值问题。通过详细分析得到了该特征值问题的解,无量纲的轴压临界值表达成无量纲的抗弯刚度参数,夹芯抗剪刚度参数和Badtoff几何参数的简单函数。通过这些无量纲参数,轴压临界值实际上是复合材料工程弹性常数,夹心横向剪切模量,各层纤维铺设角,铺层数,夹心相对于表层的厚度和圆柱壳参考中面几何尺寸的函数。

A set of general equations for large deflection of cylindrical composite sandwich shells is given at first .then the nonlinear equation under the condition of axisymmetric deformation is obtained through relevant reduction. Perturbation of the nonlinear equation gives the axisymmetric buckling equation of cylindrical composite sandwich shells which together with the associated homogeneous boundary condition constitutes an eigenvalue problem for analyzing the axisymmetric instability.Through detailed analysis,the solution of the eigenvalue problem is obtained. The non-dimensional critical compression can be expressed as a simple function of the non-dimensional parameters of bending stiff ness, transverse shear stiffness of the core and Badtoff geometrical parameter. Using these nondimen-sional parameters, the critical compression, in fact, is a function of the engineering elastic constants of the composite materials, transverse shear modulus of the core, the layout angles of fibers,plynumber of the composite faces,the relative thickness of the core to the faces and the geometry of the reference surface of the cylindrical shells,etc.