角支及多点支承矩形板的弯曲

BENDING OF RECTANGULAR PLATES SUPPORTED AT CORNERS OR AT SEVERAL POINTS

本文取两对边简支另两对边自由的板为初始解,用迭加法在两边简支板上迭代消去板边上的剪力。为了简化消去板边剪力的复杂迭代过程,作者提出了高精度的简化方法,将无限迭代简化为一次计算,将角支板的求解化为计算两个对边简支矩形板的简单问题。对于多点支承矩形板,则可取角点支承板为基本结构用力法求解。文中还提出了一些实用经验公式,列出了典型算例,验证了方法的适用性和高精度。

To solve the bending problem of rectangular plates supported at corners or at several points, authors of this paper take the solution of the rect angular plate with two opposite edges simply supported and other two edges free as the initial solution, and then eliminate the shearing forces of this rectangular plate by the method of superposition through a procedure of iteration. To simplify the procedure of iteration, authors succeed to introduce an effective technique to turn the iteration procedure to a single process of calculation. Ultimately, the bending problem of a rectangular plate supporting at corners may be solved by superposition of two rectangular plates simply supported at two opposite edges.For the solution of a rectangular plate supported at several points, the solution of the bending of a rectangular plate supported at corners may be used as the fundamental solution and then the force method is Used to get the final result, In the paper, some useful formulas are listed and numerical examples are given to show the validity as well asthe accuracy of this method.