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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.
Therefore, the structural analysis is quite difficult.In this paper, the semi-analytical numerical method combining the state space method and the differential quadrature method is used to study the bending problem of the variable angle beam of composite beam In this paper, we assume that the direction angle of fiber along the beam axis varies according to any continuous function, and the first derivative of displacement and displacement is selected as the state variable. The state space equation of beam elastic analysis of axial variable angle beam is established. The derivative of the axial coordinate is solved by differential quadrature method, and then the semi-analytical numerical solution of the problem can be obtained.Comparing with the existing literature and ABAQUS calculation results, the correctness of the method in this paper is verified and the differential quadrature method The convergence of the problem is analyzed.A numerical example is given to study the effect of the change of the fiber orientation along the beam axis on the displacement and stress distribution of the variable angle beam with variable angle. The design provides some reference.