FGM夹层圆柱壳在扭转载荷作用下的弹性稳定性

Elasticity Stability of Circular Cylindrical Shells with FGMs Layers under End Torsion Force

用半解析方法研究了两端简支的功能梯度材料夹层圆柱壳在端部扭转载荷作用下的弹性稳定性,考虑圆柱壳的外层由金属材料构成,内层由陶瓷材料构成,中间层为材料性质沿厚度方向以幂函数连续变化的功能梯度材料,并且在界面处的材料性质保持连续.首先,基于Flügge薄壳理论建立了位移形式的结构静态屈曲控制方程,然后根据边界条件将位移表示为三角级数形式,获得了近似的线性代数特征值问题,最终通过数值方法求得了表征结构失稳特征的临界屈曲载荷.结果表明,屈曲载荷随半径与厚度比的增加而减小,随FGM层陶瓷组分的增加而增加.

By using the semi-analytical method, the elasticity stability of a simply supported circular laminated cy- lindrical shell with FGMs middle layer under the end torsions was investigated. The inner layer of the shell is com- prised of the ceramic material, the outer layer is metal and the middle layer is made of functionally graded material whose properties continuously change in a power law function across the thickness direction from the inner layer to the outer layer,with continuation in the material properties at the interface. Firstly, based on the Fltigge thin shell theory,the governing equations for static buckling of the structure were formulated in terms of the displacements. Then,by expressing the solution in terms of trigonometric series that identically satisfy the boundary conditions of the displacements, an approximate eigenvalue problem for linear algebraic equations was obtained. Finally, the criti- cal buckling load showing the characteristics of the structures was obtained by the numerical method. From the nu- merical results it can be seen that the buckling load decreases with an increase in the radius to thickness ratio and increases with the increment in the volume fraction of ceramic in the middle FGM layer.