用高阶剪切变形理论研究双模量梁的弯曲

Research on the Bending of Double Modulus Beam by Higher-Order Shear Deformation Theory

利用高阶剪切变形理论研究了双模量梁的弯曲变形问题,推导出了双模量梁的挠曲线方程及弯曲正应力公式.讨论分析了翘曲函数的指数n对挠度、正应力的影响.研究结果表明:拉压弹性模量的差异对梁的弯曲应力有较大影响.把高阶剪切变形理论的计算结果与弹性理论计算结果进行比较,可知该方法计算精度非常高.

The bending deformation of double modulus beam is studied by higher order shear deformation theory.The flexural equation and the bending normal stress formula of double modulus beams are derived.The influence of exponential n of warping function on deflection and normal stress is analyzed.The results show that the difference between elastic modulus of tension and compression has great influence on the bending stress of beam.The comparison between the results of the higher order shear deformation theory and the elastic theory shows that the proposed method possesses excellent accuracy.