丝束轴向变角度复合材料梁的弹性分析

Elastic Analysis of Composite Beams with Axially Variable Angle Tows

丝束变角度复合材料具有变刚度的特点,因此其结构分析具有相当难度.本文采用状态空间法和微分求积法联合的半解析数值方法对丝束轴向变角度复合材料梁的弯曲问题进行研究.假设纤维方向角沿梁的轴向按照任意连续函数变化,选取位移和位移的一阶导数作为状态变量,建立了丝束轴向变角度复合材料梁弹性分析的状态空间方程,将状态变量对轴向坐标的导数采用微分求积法进行求解,进而可得问题的半解析数值解.通过与现有文献及ABAQUS计算结果的比较,验证了本文方法的正确性,并对微分求积法求解本问题的收敛性进行了分析.通过数值算例研究了纤维方向角沿梁轴向的变化对丝束轴向变角度复合材料梁的位移及应力分布的影响,研究结果可为该种结构的设计提供一定的参考.

The composite with variable angle tows has characteristics of variable stiffness, making it difficult to carry out the structural analysis of such composite. In this paper the state space method and differential quadrature method are employed to semi-analytically solve the elastic problem of composite beams with axially variable angle tows. Assuming that the orientation of fibers is varied continuously along the length of a composite beam, the governing equation of elastic analysis of the beam with axially variable angle tows is established by taking the displacement components and their first derivatives as the state variables. The derivatives of state variables with respect to the axial coordinate are solved by the differential quadrature method and then the semi-analytical solution of the problem is obtained. The accuracy of the results obtained in this paper is verified by comparing them with the existing results and the ABAQUS computational results. And the convergence of solving this problem with the differential quadrature method is analyzed through numerical examples. The effect of the variation of the orientation of fibers along the axial direction on the displacements and stresses of the beam is studied. The solutions obtained here may be helpful for the design of this kind of composite beams.