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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 obtain accurate results of temperature warping of free rectangular plates on four sides of Winkler foundation and to check whether the accuracy of Westem’s temperature warping stress meets the engineering requirements, the vertical displacement of the composite plate by bidirectional triangular series , An analytic solution of the existence of temperature gradient in the thickness direction of the free rectangular thin plate on four sides of Wenkele foundation is deduced. The warping stress of two-way trigonometric series solution and Wilhelm’s solution is introduced, and the example of the plate torque distribution caused by the plate temperature gradient and the accuracy of Warren temperature warping stress solution are analyzed. The results show that the deviation of Wiegand’s solution increases with the increase of P 2 Poisson’s ratio, but the absolute amount of deviation is not large. For cement concrete pavement with Poisson’s ratio of 0.15, the accuracy of Wiese’s solution can satisfy the engineering Claim.