Reddy高阶组合梁弯曲的一般解析解法

GENERAL ANALYTICAL METHOD FOR COMPOSITE BEAMS' BENDING USING REDDY'S HIGHER ORDER BEAM THEORY

基于Reddy高阶梁的轴向位移模式,考虑组合梁界面滑移变形,利用最小势能原理建立了Reddy组合梁弯曲问题的控制微分方程和边界条件,并将控制方程转化为含12个基本未知量的一阶常微分方程组,给出其一般求解方法和解的表达式.其次,研究了横向均布荷载作用下Reddy简支组合梁的弯曲,所得结果与有限元解吻合良好,说明本文解析解的有效性和可靠性.最后,数值分析了组合梁界面滑移剪切刚度kcs、弹性模量-剪切模量比E/G、梁长-高比L/h和子梁厚度比hs/hc等参数对Reddy简支组合梁弯曲的影响.分析表明:滑移刚度显著影响横截面应力的分布;组合梁长-高比越小、弹性模量-剪切模量比越大或界面滑移刚度越大,组合梁的剪切效应对其挠度影响越显著,此时不宜忽略其剪切变形.

Based on the displacement mode of Reddy＇s higher-order beam, and taking account of the slip deformation at the interface of the composite beam, the governing equations and boundary conditions for bending of the Reddy＇s composite beam are formulated using the principle of minimum potential ener- gy. The governing equations are transformed into an ordinary differential equation system consisting of 12 fundamental unknowns, and the solution expressions and the general analytical method for solving the ODE system are presented. Then,the bending of the simply-supported Reddy composite beam subjected to a uni- form transversal load is studied,and the obtained results are in good agreement with those of the finite ele- ment method, which demonstrates the effectiveness and reliability of the general analytical method presen- ted in the paper. Finally,the influences of the slip shear stiffness hc~ at the composite beam interface,the Young＇s modulus to shear modulus ratio E/G, beam span to depth ratio L/h and the layer depth ratio h~/hc,etc, on the bending of the Reddy composite beam are examined numerically. It is revealed that the slip stiffness has a great influence on the distribution of the stresses on the cross-section of composite beam,and the influence of the shear effect on the composite beam＇s deflection becomes more remarkable with the beam span to depth ratio L/h decreasing and the Young＇s modulus to shear modulus ratio E/G or the slip stiffness increasing. In all cases, the shear effect can not be neglected.