关键词: 解析解, 矩形外伸板, 弹性分析, 协调条件, 广义简支边, 叠加法

Abstract: In the theory of elastic thin plates, to solve the problem of rectangular overhanging plates with complicated boundary conditions is very hard for long. A concept named modified or generalized simply supported edges is therefore introduced, i.e., superimposing altogether the solutions to the rectangular plate with four simply supported edges on which the uniformly distributed load locally acts, to the rectangular plate with four simply supported edges of which one of them is under the action of distributed bending moment and to the rectangular plate with various generalized simple supported edges and then taking the continuity condition of boundary, so as to let the result of superimposition satisfies all boundary conditions, an analytic solution is given to the rectangular overhanging plates on which any kinds of loads are acting. As an example, a specific problem that the uniformly distributed load acts on the overhanging section of rectangular overhanging plates is solved, and the solution to it is compared with the result of finite element method. It is proved that the method proposed is so effective to obtain an analytic solution to the rectangular overhanging plates with complicated boundary conditions.