矩形中厚板弯曲问题的解耦解法

发布时间：2018-04-09 07:52

本文选题：Mindlin板　切入点：四边固支　出处：《哈尔滨工业大学学报》2016年03期

【摘要】：为简化中厚板弯曲问题解析解的求解方法,采用解耦法和改进的重三角级数法对问题进行求解.首先从板问题的原始控制方程组出发,通过引入过渡函数,用解耦法对变量相互耦合的偏微分方程组进行分解化简,分别解耦成可以直接求解和间接求解的独立偏微分方程,进而在四边固支边界条件下,利用改进的重三角级数法,将计算过程中不同的级数核统一化,分别求得原始控制方程中各个变量的级数解,最后将所得解析解与有限元解进行对比分析.结果表明:随着级数项的增加,级数解与有限元解趋于一致,从而验证了该方法及推导过程的正确性.同时,在整个求解过程中,通过对控制方程组的解耦化简,避免了复杂的运算过程,使得问题的整个解法更为简洁、直观.
[Abstract]:In order to simplify the analytical solution of plate bending problem, the decoupling method and the improved double trigonometric series method are used to solve the problem.Starting from the original governing equations of the plate problem, by introducing the transition function, the partial differential equations coupled with variables are decomposed and simplified by decoupling method, and the independent partial differential equations can be solved directly and indirectly, respectively.Then, under the condition of fixed boundary on the four sides, by using the improved double triangle series method, the different series kernels in the calculation process are unified, and the series solutions of each variable in the original governing equation are obtained, respectively.Finally, the analytical solution is compared with the finite element solution.The results show that with the increase of the series term, the series solution tends to be consistent with the finite element solution, which verifies the correctness of the method and the derivation process.At the same time, in the whole solution process, by decoupling and simplifying the control equations, the complicated operation process is avoided, and the whole solution of the problem is more concise and intuitionistic.
【作者单位】：大连理工大学交通运输学院;
【分类号】：O302

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