定常温度热弹性双层梁的精化理论  

The refined theory of thermo-elastic bi-layer beam under steady temperature

作　　者：刘婷婷[1] 赵宝生[1] 

机构地区：[1]辽宁科技大学机械工程与自动化学院,鞍山114051

出　　处：《应用力学学报》2015年第4期563-569,702,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11172319)

摘　　要：将Cheng氏精化理论的研究思路引入到热弹性双层梁的研究当中。首先,利用不失一般性的Biot通解和调和函数的Lur’e算子函数表示,在不作任何预先假设的情况下,对热弹性双层梁进行分析,获得了由双层梁交界面上的位移和应力所表示的位移场和应力场;其次,分析了双层梁表面同时作用垂直于梁面的横向载荷和温度载荷的变形和应力状态,获得了该双层梁结构的精化方程,该结果满足全部的弹性方程,比其他梁变形理论精确;再次,为了方便计算,将精化方程中的高阶项略去后,得到了定常温度热弹性双层梁的近似挠度控制方程;最后,令上下两层系数相同,则定常温度热弹性双层梁的挠度控制方程退化为定常温度热弹性单层梁的挠度控制方程。The research mentality of the refined theory is extended to study thermo-elastic bi-layer beams under steady temperature. Firstly, by using thermo-elastic solution and Lur'e method without any assumption, displacements fields and stress states of a bi-layer beam can be represented by displacement and strain of the interface between upper layer and lower layer. Secondly, the refined equations for thermo-elastic bi-layer beam with nonhomogeneous boundary conditions are derived directly from the exact theory, thus the exact solutions can be obtained. Thirdly, due to the fact that refined equations are of infinite order, Taylor series of the trigonometric functions is used and all the higher-order terms are dropped, the approximate expressions of the mid-plane displacement functions are obtained. Finally, by letting the coefficients of the upper and lower layers to be the same, the deflection control equations of a thermo-elastic bi-layer beam under steady temperature can be degenerated into the deflection control equations of thermo-elastic plates under steady temperature.

关 键 词：精化理论 热弹性 双层梁 Biot通解 

分 类 号：O343[理学—固体力学]