文克勒地基上四边自由矩形薄板温度翘曲解

Temperature Warping Solution of Rectangle Plates with Four Free Edges on Winkler Foundation

为获得文克勒地基上四边自由矩形板温度翘曲精确结果,检验威斯特卡德(威氏)温度翘曲应力的精度是否满足工程要求,采用双向三角级数叠加合成板的竖向位移,推演得到了文克勒地基上四边自由矩形薄板在板厚度方向存在温度梯度时的解析解。对双向三角级数解和威氏解得到的板的翘曲应力进行了介绍,并结合算例分析了板温度梯度引起的板扭矩分布状况以及威氏温度翘曲应力解的精度。结果表明:威氏解的偏差随着板泊松比的增大而加大,但偏差绝对量并不大;对于泊松比为0.15的水泥混凝土路面而言,威氏解的精度可满足工程要求。

In order to find out the accurate temperature warping result of rectangle plates with four free edges on Winkler foundation and check whether the accuracy of Westergaard temperature warping stress satisfies the requirement of project,by using two-dimension trigonometric series method to superimpose the vertical displacements of composite plates,temperature warping analytical solution of rectangle plates with four free edges on Winkler foundation was derived when there was temperature gradient along the thickness of the plate.Warping stresses obtained by the two methods were introduced.Then the torque distribution on the plate caused by temperature gradient and the accuracy of Westergaard temperature warping solution were analyzed combining with examples.The results show that deviation of Westergaard temperature warping increases with the increase of Poisson＇s ratio,but the absolute value of the deviation is small;for cement concrete pavement with Poisson＇s ratio of 0.15,the accuracy of the Westergaard temperature warping solution can satisfy the engineering demand.