【摘要】 本文用两个单三角级数和一个重三角级数相迭加的方法,求得了自由边矩形板的精确解。一般问题按其对称与反对称性分解为四个问题,然后对每一问题给出解答。所得结果不仅满足四边自由条件,而且满足角点反力为零的条件。最后给出两个算例,与有限元法、差分法结果进行比较二者相当吻合,证实我们的解是正确的。更多还原

【Abstract】 In this paper, the exact solution of the rectangular plate with the free edges on the elastic foundations has been obtained by using the method of superposition of the trigonometric series. The results obtained satisfy not only the conditions of the free edges but also the free corners. Two examples have been calculated and compared with the results obtained by the finite-difference approximation and the finite-element method. Our results may check nicely with the approximate solutions which prove the validity of the present solutions.更多还原