【作者】 刘麟闻；

【导师】 陈江瑛；

【作者基本信息】 宁波大学 ， 固体力学， 2009， 硕士

【摘要】 本文从薄板小挠度理论出发，研究了混凝土路面板的热应力稳定问题。将实际工程中路面板在缩缝处的连接方式分别简化为固定铰支和旋转弹性铰支两种边界条件。由于沿板厚度方向的温差相对于容许温差可以忽略不计，因此可以不考虑沿板厚度方向的温度场对板弯曲的影响，从而将热应力稳定问题转化为等效热压力作用的稳定问题来研究。选择Poisson比和表征支座弹性的量β作为小参数，求得了两种边界条件下混凝土路面板的临界容许温差和挠度的摄动解。在求解过程中对于出现非齐次边界条件的摄动方程，结合最小二乘法求得近似解。数值计算结果表明：混凝土路面板挠度的摄动解沿板宽方向关于板中心截面对称，有必要考虑挠度二级摄动解的影响；临界温差随厚度而递增，但几乎不随Poisson比和长宽比λ而变化；临界温差的二级与零级摄动解的相对偏差随表征支座弹性的小参量β线性递增。与Euler压杆理论的比较指出，压杆理论所得的临界温差值等于板理论所得零级摄动解且总小于板理论的值，这意味着压杆理论所得的临界温差作为临界值总是使路面设计偏于安全，由此表明可以应用压杆理论指导路面板铺设温度的设计。将临界热压力值摄动解与有限元解相比较得出，临界热压力的摄动解与有限元计算解之间的误差随着λ的增大而减小；对于固定铰支的混凝土路面板，当λ小于0.25时，两者的误差大于3%；当λ大于1时，两者间的误差小于1%并随着λ的增大逐步趋向于0，由此说明Ansys程序中的板壳单元不适用于模拟长宽比小于0.25的板的屈曲问题更多还原

【Abstract】 In this paper, based on the thin plate theory of a small deflection, we discussed the thermal stress stability of concrete pavement in the engineering. We considered two kinds of boundary conditions (BC) as the style of connection at the contraction joints, one is called a fixed-hinged and the other is rotating flexible hinge. However, compared with the critical temperature variation, we can ignore the temperature variation along the thickness direction. So we didn’t consider the impact of the temperature field along the thickness direction of the bending plate. As a result, we considered the problem of the thermal stress stability as the stability under the equivalent thermal pressure. We chose the Poisson ratio and the parameterβwhich characterized the form of elastic supports in the BC as the perturbation arguments, and obtained perturbation solutions of the permissible critical temperature variations and the deflections of the concrete pavement in two kinds of boundary conditions. We get a approximate solution by means of the Least Square Method when the Non-homogeneous boundary conditions of the perturbation equations occured.Numerical results show that: the perturbation solutions of the deflection of the concrete pavement plate present symmetry about the center section on the plate along the width direction, the second order perturbation solution of the deflection must be concerned; critical temperature variation increases with the thickness, but do a little change with the Poisson ratio, and aspect ratioλ; the ratio of the perturbation solution of second-order and the zero-order of the critical temperature variation has a linear increments with the parameterβ. Comparison with the theory of Euler struts, we obtain that the value of the critical temperature variation of is equal to the perturbation solution of zero-order which derived from the plate theory and it is less than the value of the plate theory, this means that the critical variable temperature of using Euler’s theory as a design method is inclined to safety, so Euler’s theory can be applied as a guidance in the pavement design. We also have a brief compare the perturbation solution of the critical heat stress with the finite element solution, it shows that, the error between the perturbation solution of the critical heat stress and the finite element solution reduced whenλincreases; as the fixed-hinged concrete pavement, whenλis less than 0.25, the error between the two is greater than 3%; whenλis larger than 1, the error is less than 1% and tends to 0 gradually asλincreases, this result implies that the solution abtained from Ansys can only be used whenλis higther than 0.25.更多还原