论文部分内容阅读
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。
Structures made by automatic wire laying machines have in-plane variable stiffness characteristics. The change of stiffness caused by space change makes the governing equation of the structure become a variable coefficient partial differential equation, which poses a great challenge for solving the non-axisymmetric bending problem and it is difficult to solve the exact solution. Based on the classical shell theory, the governing equations for the non-axisymmetric bending of orthotropic rigid plates with variable stiffness are deduced. Assuming that the stiffness varies continuously with the exponential function of elastic modulus and the direction angle of the curved fiber, the deflection of the composite annular plate is calculated by the weighted residual method. Through the comparison with the exact solutions, it is proved that this method is effective and has high accuracy. The calculated results show that the change of the direction angle of the curved fiber will make the mechanical properties of the curved fiber reinforced composite structure obviously better than that of the linear fiber reinforced composite structure with the same proportion. At the same time, the results also show that the non-axisymmetric deflection of the variable stiffness composite annular plate is closely related to its surrounding constraints, material parameters, internal and external radius ratio, fiber orientation angle and so on.