无拉力Winkler地基上自由薄梁板的接触区及其影响因素分析

ANALYSISONCONTACTREGIONANDIT′SINFLUENCE FACTOROFTHINBEAMSANDTHINPLATESWITH FREE EDGELAIDONTENSIONLESSWINKLERFOUNDATION

采用无拉力Ｗｉｎｋｌｅｒ 地基模型对作用其上的自由薄梁、薄板的接触区问题进行分析， 发现其接触区具有对荷载幅值的不变性， 仅受梁板尺寸、梁板刚度和地基刚度系数的影响。数值算例借助常微分方程边值问题ＣＯＬ９０ 求解器， 根据推导出的控制方程和边界条件编程求解， 得出各因素对其接触区的影响规律和四点结论， 对工程中弹性地基梁板受力变形分析具有参考意义。

The contact region problem ofthin beam s and thin plates w ith free edge laid on tensionless Win- klerfoundation is solved. Itis found thatthe contactregion is a constantfor the load and itis only affected by subgrade m odulus, the size and the flexuralrigidity ofthe thin beam s and thin plates. According to the governing equations and boundary conditions, num ericalexam ples are solved by using the ODE boundary value problem ′s COL90 solvers. The influenceofevery factorson contactregion and fourconclusionsare ob- tained, w hich is very usefulfor the analysis on beam s and plates on the elastic foundation in applications.