槽形梁动力反应分析的能量变分法

以分析箱形梁剪滞效应提出的方法为基础,考虑了剪滞翘曲应力的自平衡条件,为了准确反应槽形梁翼板的动位移变化,三个广义动位移η(x,y,z,t)、w(x,t)和θ(x,t)被引入。利用能量变分原理建立了槽形梁动力反应w(x,t)、u(x,t)和θ(x,t)的控制微分方程和自然边界条件,获得了相应广义位移的闭合解,据此对槽形梁的动力反应特性进行了研究,揭示了槽形梁桥动力反应的规律。算例中,该解析解与有限元数值解进行了比较,证明了该动力分析方法的有效性。

Dynamic response of U-shape beams in consideration of shear lag effect

Abstract: Based on the analysis methods of box girders about shear lag effect, and a new warping displacement mode of the U-shaped beams is chosen to meet the axial self-equilibrium condition for corresponding stress，three generalized displacement functions , , are employed in analyzing dynamic response of the U-shaped beam in consideration of shear lag effect by calculus of variations, the differential equations and the corresponding natural boundary conditions of the U-shaped beam are induced based on the minimum potential principle, according to the fundamental differential equations and the corresponding natural boundary conditions, the dynamic characteristics of U-shaped beams are discussed. The calculation examples compare the finite element solutions with the analytical solutions and verify the validity of the proposed approach, the formulas obtained in this study develop the shear lag theory.