【摘要】 对于具有复杂边界条件的矩形外伸板,在弹性薄板理论中是一个较难解决的问题.使用了变相的或广义简支边的概念,将四周简支局部作用分布载荷矩形板的解、四周简支一边作用分布弯矩矩形板的解及各种具有广义简支边的矩形板的解进行叠加,并应用边界连续性条件,令这样的解满足所有边界条件,得到了任意载荷作用下矩形外伸板的解析解.作为算例,具体求解了外伸部分作用均布载荷的矩形外伸板,并与有限元结果进行了比较.所采用的方法,对于求解具有复杂边界条件板的解析解十分有效.更多还原

【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.更多还原