宽翼薄壁工字形梁动力反应的能量变分法  

ENERGY-VARIATIONAL METHOD FOR THE DYNAMIC RESPONSE OF THIN-WALLED I-BEAMS WITH WIDE FLANGE

作　　者：王根会[1] 甘亚南[2] 王振波[3] 

机构地区：[1]兰州交通大学土木工程学院,甘肃兰州730070 [2]河南理工大学土木工程学院,河南焦作454010 [3]南京工业大学土木工程学院,江苏南京211800

出　　处：《工程力学》2010年第8期15-20,共6页Engineering Mechanics

基　　金：兰州交通大学"青蓝"人才工程基金项目

摘　　要：采用四个独立的广义位移w(x,t)、θ(x,t)、u1(x,t)和u2(x,t)对宽翼缘薄壁工字形梁的动位移进行了准确描述,同时考虑剪滞翘曲应力的轴向自平衡条件,提出了一种能对工程中常用的上翼板、下翼板具有不同宽度工字形梁动力反应的分析方法。以能量变分原理为基础,推导出了工字形梁动力反应的控制微分方程和自然边界条件,获得了相应广义动位移的闭和解,据此对薄壁工字梁的动力反应特性进行了研究,揭示了工字形梁动力反应的规律。算例中,该文解析解与有限元数值解进行了比较,证明了该文分析方法的有效性。This paper proposes an approach to analyzing the dynamic response of thin-walled I-beam with wide flange generally used in structural engineering. Four independent generalized dynamic displacement functions w（ x , t ）, θ （ x , t）u1 （ x , t ）, u 2（ x , t ）are employed to reflect the displacement variation of thin-walled I-beams（ b1 ≠ b2）, and a new warping displacement mode of I-beams is used to meet the axial self-equilibrium condition. The minimum potential principle is applied to establish the governing differential equations and corresponding natural boundary conditions, and closed-form solutions of generalized dynamic displacements are obtained. The dynamic characteristics of I-beams are discussed. Through calculation examples, the analytical solutions of this paper are compared with the finite solid element solutions, and the validity of the proposed approach is verified.

关 键 词：工字形梁 剪力滞后 动力反应 能量变分法 桥梁工程 

分 类 号：TU311.3[建筑科学—结构工程] TU323.3