含局部支承弹性地基板弯曲问题的迭代解法

研究了任意载荷作用下含局部支承弹性地基板在典型边界条件下的弯曲问题。首先利用纳维解和卷积叠加方法给出了任意载荷作用下无局部支承弹性地基板在典型边界条件下的解析解，然后采用未知待定反力来处理局部支承的影响，这些未知反力可以采用迭代格式进行求解。在此基础上建立了一种求解含局部支承弹性地基板弯曲问题的迭代解法。最后给出了数值算例来说明本文方法的具体应用，所得结果和有限元方法结果吻合较好。

An interactive method for bending problems of thin plate on elastic foundation with local point supporting

The bending problem of plates on elastic foundation with local point supporting under the classical boundary conditions was discussed. Firstly, the analytical solution of plates on elastic foundation without local point supporting was obtained for arbitrary distributed loading problem by using Navier solution and the principle of superposition, Furthermore, a series of undetennined supported forces determined by the use of interactive method was introduced to deal with the action of local supporting. Finally, several examples were presented to illustrate the applications of interactive method proposed. The numerical results show good agreement with the results by finite element method.