复合材料层合厚圆柱壳高阶理论的改进及其应用

建立了一个改进的LCW型的精化高阶理论,以分析厚圆柱壳的振动。提出u,v为三次多项式、w为二次多项式的位移模式,并利用上、下自由表面横向剪应力为零的边界条件,对所假定的位移场作了化简,将三阶剪切变形理论的未知数缩减为7个,在此基础上建立了相应的有限元列式。通过一个典型算例,与Soldatos和Lam的高阶剪切变形理论的解析解作了比较,说明笔者的精化高阶理论是可行的,而且具有较高的精确性,比LCW高阶理论更具有实用性。还通过频率参数随长度半径比L/R的变化,说明由于考虑了法向应力和法向应变,本文方法更适用于长度半径比较小的结构。

HIGHER-ORDER THEORY AND ITS FINITE ELEMENT METHOD FOR THICK LAMINATED COMPOSITE CYLINDRICAL SHELLS

In this paper, an improved LCW type refined higher order, thick laminated shell theory is presented to analyze vibration of thick cylindrical shells. The new displacement model is developed, which is in the form of a cubic function of the thickness coordinate and is in the form of a quadric function. Using the boundary conditions, transverse shear forces of the upper and nether surfaces are zero, the above mentioned displacement field is predigested and unknown quantities are reduced to seven. A finite element expression based on the above theory is suggested. The accuracy of the present theory is examined by applying it to a typical free vibration problem. The results are compared with analytic solutions of higher order shear deformation theory by Soldatos and Lam. The present theory shows the deflections more accurately than those obtained from the previous works. In this paper, the variation of fundamental frequency parameter for a thick shell with the L/R ratio shows that, owing to including effects of normal stress and normal strain, the present theory is more adaptive to structures with small length to radius L/R ratios.