局部均布荷载作用下非均匀弹性地基上厚矩形板的弯曲

在建筑结构设计中的局部均布荷载作用下非均匀弹性地基上矩形板的计算一般采用有限元法和图表,在理论上很难获得一般性的解析解.本文以局部均布荷载作用下非均匀弹性地基上四边简支厚板的弯曲问题为例,由功的互等法导出了一般封闭解析解的表达式,给出了图表形式的计算结果,并与有限元结果进行了对照.证明了本文给出的一般性封闭解析解的表达式是正确的.

Bending of thick plate on non-homogeneity elastic foundation under uniformly distributed loads in parts of plate

In architectonics, the calculation of rectangular plate on elastic foundation, in common, is used by the finite element method and chart. It is difficult to obtain the universal analytic solution. The bending problem of thick plate with four simply-supported edges, which is loaded by uniformly distributed loads in parts of the plate on elastic foundation, being taken for a example, the universal analytic formula for thin and thick plates is derived by reciprocal theorem method. The calculating results are given by the mode of chart and contrasted with those of finite element method. It is proved that the universal analytic solution is right.