关于简支厚板与薄板的关系

厚板的数学理论是建立在与薄板不同的力学假定的基础上的。本文分析了厚板与薄板之间静力学方面的关系。对于任意的简支多边形板,得到了厚板解通过薄板解的显式表达式,从而证明了:Reissner模型的厚板解与薄板解具有相同的剪力,但弯矩、转角、挠度有差别;而washizu模型的厚板解则与薄板解不仅剪力相同,连弯矩与转角亦相同,只是挠度有差别。

ON THE RELATIONS BETWEEN THICK AND THIN PLATES WITH SIMPLY SUPPORTED EDGES

A mathematical theory of thick plate is established on another mechanical hypothesis differed from a thin plate. In this paper a statical analysis for thick plate is given. For an arbitrary plate of polygonal shape with simply supported edges it is shown that the solution of thick plate can be "expressed explicitly by that of thin plate. It is then found that the shear forces of thick plate in the Reissner model are identical with those of thin plate, while in the washizu model of thick plate the shear forces as well as bending moments and angular rotations all are same as the classical thin plate tbeory.