曲线纤维增强复合材料圆环板的非轴对称弯曲问题

由自动铺丝机制造的结构具有面内变刚度特征。这种由空间变化引起的刚度变化使结构的控制方程成为了变系数偏微分方程,给求解非轴对称弯曲问题带来了很大挑战,难以求解其精确解。该文基于经典板壳理论,推导了柱坐标下正交各向异性变刚度圆环板非轴对称弯曲问题的控制方程。假定刚度分别随弹性模量指数函数和曲线纤维方向角连续变化,采用加权残值法计算了周边弹性约束时复合材料圆环板的挠度。通过与精确解结果的比对,验证该方法是有效的,并有较高精度。计算结果表明曲线纤维方向角的变化将使曲线纤维增强复合材料结构的相关力学性能明显优于同等比例的直线纤维增强复合材料结构。同时,结果还表明变刚度复合材料圆环板的非轴对称挠度与其周边的约束条件、材料参数、内外半径比值、纤维方向角等密切相关。

ASYMMETRIC BENDING OF CURVILINEAR-FIBER REINFORCED COMPOSITE ANNULAR PLATES

The components produced by automated tow-placement machines are of in-plane variable-stiffness. However, the spatial variation of the fiber orientation needs to solve partial differential equations with variable coefficients. Assuming the stiffness varying with young's modulus of exponential function and fiber angles, the classical plate theory is used to derive the governing differential equation of asymmetric bending of the orthotropic annular plates with variable stiffness. The deflections of composite annular plates with variable stiffness for elastically restrained edges were calculated by the method of weighted residuals. By comparing our numerical results with exact solutions, it can be found that the method of weighted residuals has fast convergence and the numerical results have high accuracy. However, the fiber orientation angles were varied from one element to another, it was found that such plates would be more effective than the plates with straight fibers. Moreover, the numerical results of the asymmetric bending analysis of the orthotropic annular plates with variable stiffness have a close relationship with the boundary conditions, material properties parameters, ratio of outer and inner radius and fiber orientation angles.