非理想边界拱的面内失稳模式与屈曲荷载

该文研究了集中荷载作用下弹性扭转约束层合拱的非线性面内稳定，基于虚功原理建立了拱的微分平衡方程及屈曲平衡方程，追踪了拱的平衡路径，获得了屈曲临界荷载的解析表达，提出了修正长细比参数及柔度系数以表征拱的失稳模式，通过有限元模拟验证了解析结果的正确性，着重分析了铺层模式及边界条件对层合拱的屈曲及后屈曲的影响。研究结果表明：当长细比及柔度系数给定，层合拱的屈曲临界荷载随着开口角及修正长细比的增大而增大；铺层模式显著影响拱的屈曲临界荷载，随着90°铺层逐渐远离中面，拱的承载能力明显降低。

Large deflection analysis of planar curved beams made of functionally graded materials using variational iterational method

This paper investigates the nonlinear in-plane behavior of rotationally restrained shallow laminated arches under a central concentrated load. Both the differential equilibrium equation and the buckling equation are established by using a virtual work method. The nonlinear equilibrium paths of the arch are traced and the corresponding analytical buckling loads are obtained. A modified slenderness ratio and a flexibility parameter are proposed to characterize the buckling modes. Finite element analysis is performed to verify the accuracy of the analytical solutions. Particular focuses are on the effect of the boundary condition and the layer-ups on the buckling and post-buckling responses of the arch. The results show that the buckling load of the arch increases with increasing included angles and modified slenderness ratios. It is also observed that the stacking sequence significantly influences the buckling load and decreases when the 90-degree lamina is placed far away from the mid-plane.