湿热环境下复合材料层板的几何非线性分析

GEOMETRICALLY NONLINEAR ANALYSIS OF LAMINATED COMPOSITE PLATES UNDER HYGROTHERMAL ENVIRONMENTS

根据Reddy的高阶剪切变形理论,在应力应变本构关系中考虑湿热环境的影响,用虚位移原理推导出以位移形式表达的复合材料层板的几何非线性控制方程及相应的边界条件。选定的边界条件为弹性转动约束。选择不同的弹性转动系数,可以得到介于简支到固支之间的不同边界条件。假设材料的物性参数不随湿热环境而变化。用Galerkin方法求解控制方程。数值结果所用的边界条件为四边固支。最后讨论了温度和湿度、长厚比、长宽比和铺层数等各种参数变化的影响。计算和分析的结果均表明温度的升高对层合板的弯曲产生非常不利的影响;而加湿对层合板的弯曲影响是非常有限的。在其它几何条件不变的情况下,增加铺层数,不仅能降低挠度,也能明显地降低弯矩或弯曲应力。

According to the Reddy＇s higher-order shear deformation theory, geometrically nonlinear governing equations and their boundary conditions of laminated composite plates, including the hygrothermal effects, are obtained by the virtual displacement principle. The boundary conditions are elastic restraint against rotation. Specification between simply supported and clamped boundary conditions can be acquired using different elastic coefficients. It is assumed that the material properties are not affected by variation of temperature and moisture. The governing equations are solved by Galerkin method. Four clamped edges are assumed in numerical analysis. The factors of hygrothermal environments, length-thickness ratios, aspect ratios and total number of plies are discussed. Results show that temperature rise leads to disadvantageous effect on the bending behavior of composite laminated plates, but the effect of moisture is insignificant. Increase of the number of plies will lead to evident decrease of bending deflection and moment or bending stress if other geometrical conditions remain unchanged.