应用虚拟功的互等定理求解均载悬臂厚矩形板的弯曲

The Calculation of Thick Cantilever Rectangular Plate By Virtual Reciprocal Theorem

悬臂矩形板的弯曲问题一直是平板经典理论中的著名难题,利用中厚板虚拟功的互等定理,借助付宝连提出的角点静力边界条件,得到了均布载荷作用下悬臂厚矩形板弯曲的封闭解析解,并采用现代数值方法和计算软件对所得解析解进行了数值计算.结果表明功的互等法是求解中厚板弯曲问题的一个简明有效的方法.

The bending of cantilever rectangular plate used to be a difficult problem in the classical theories of plates. This paper obtains the closed analytical solutions to the bending of cantilever thick rectangular plate under uniform pressure by virtual reciprocal theorem, with tbe help of the exact static conditions at corner points which was found by Fu Baolian. Serials of numerical values are given by applying modern computational methods and software. Analysis and calculation show that reciprocal theorem method is simple and effective for the prohlems of the bending of thick plate.