初始和边界不同恒温时二维梯度板瞬态温度场  

UNSTEADY TEMPERATURE FIELDS IN THE 2D-FGM PLATE UNDER DIFFERENT CONSTANT TEMPERATURES OF INITIAL AND BOUNDARY

作　　者：许杨健[1] 王飞[1] 杜海洋[1,2] 

机构地区：[1]河北工程大学土木工程学院,邯郸056038 [2]哈尔滨工业大学航天学院,哈尔滨150001

出　　处：《固体力学学报》2014年第2期209-216,共8页Chinese Journal of Solid Mechanics

基　　金：河北省自然科学基金项目(E2010001007;E2011402033)资助

摘　　要：为了研究二维功能梯度板的平面瞬态温度场及影响因素,假设热导率和容积比热容在板的高和宽方向为同一类型指数函数分布,基于该板的瞬态热传导基本方程,采用分离变量法,导出在初始和边界不同恒温时该板平面瞬态温度场的级数解析解.通过两种方法的对比,验证了论文研究结果的正确性.结果表明:方板内的等温线,在梯度参数α=β时,对称于板的45°对角线分布,在α=β=0时,对称于板的中心分布;在α≠β时,板的等温线不具对称性;随着冷却时间的增加,非均匀板的等温线向左下(或右上)角移动,右上(或左下)角等温线间距变宽,左下(或右上)角等温线间距变窄,且矩形板的冷却过程比方板更快.因此,可选择适合的梯度参数和几何形状来满足设计、应用和热应力分析的需要,该解析解可作为检验其他近似方法的参考标准.To study the plane unsteady temperature field and its influence factors in the 2D-FGM plate with the distributions of both thermal conductivity and volumetric specific heat capacity along the height and width directions of plate following the same exponential functions α=β ,the unsteady heat conduction basic equation of the plate was solved with the aid of the variable separation method and the series analytical solution of the plane unsteady temperature field in the plate subjected to the different initial and bound- ary conditions of constant temperature was obtained. Our results show that （1） the isotherms in the square plate are symmetrical to the 45° diagonal of the plate when the gradient parameter a=/9,and symmetrical to the center of the plate when α=β=0;（2） the isotherms in any plate are not symmetrical when a≠β（3） with the increase of cooling time,the isotherms in the non-homogenous plate move to the lower left （or up- per right） corner,the isotherms spacing in the upper right （or lower left） corner becomes wide but the iso- therms spacing in the lower left （or upper right） corner becomes more narrow, and the cooling process of the rectangular plate is faster than that of the square plate. Thus,the need of the design,application and a- nalysis of the thermal stress of the plate can be satisfied by choosing suitable gradient parameters and ge- ometry. In addition, the present analytical solution also can be used as a reference for other approximate methods.

关 键 词：二维梯度板 平面瞬态温度场 分离变量法 冷却过程 恒温 梯度参数 

分 类 号：TB34[一般工业技术—材料科学与工程]