矩形中厚板弯曲问题的解耦解法

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.

Ananalytical method for bending rectangular plates with all edges clamped supported

In order to simplifying the analytic method of bending problem of rectangular thick plate, the decoupling method and the modified Navier method are combined for accurate bending analysis of rectangular thick plates with all edges clamped supported. By using the transition function, the basic governing equations for Mindlin plates are first decoupled into independent differential equations which can be solved separately. With the different series corns unified by modified navier method, analytic solution of rectangular thick plate with all edges clamped supported is derived simply. Numerical comparisons show the correctness and accuracy of the results at last. The method used in this paper leaves out the complicated derivation for calculating coefficients and obtain the solution to problems directly.