弹性地基上四边自由矩形薄板分析的有限积分变换法

将弹性地基视为Winkler模型,利用双重有限余弦积分变换的方法推导出了弹性地基上四边自由矩形薄板问题解析解的表达式。由于在求解过程中不需要事先人为地选取挠度函数,而是从弹性地基上薄板的基本方程出发,直接利用数学的方法求出可以完全满足四边自由边界条件,弹性地基上矩形薄板问题的解析解,使得问题的求解更加合理化。最后通过实例验证了本文方法及公式的正确性。

Analytical solution for rectangular thin plate on elastic foundation with four edges free by finite cosine integral transform method

The analytical solution for a rectangular thin plate on foundation with four edges free was derived by the double finite cosine integral transform method. In the analytical process the elastic foundation was regarded as Winkler foundation model. Only the basic elasticity equations of the thin plate on elastic foundation were used and it was not needed to first select the deformation function arbitrarily. Therefore, the present solution was reasonable. In order to prove the correctness of formulations, the numerical results were also presented to compare with those of other references.