矩形板大挠度问题的样条函数解
The Solution of Rectangular Plates with Large Deflection by Spline Functions
-
摘要: 本文以中心挠度为摄动参数,将矩形板大挠度问题的非线性偏微分方程缉转化为几个线性的偏微分方程组,然后分别用样条有限点法和样条有限元法求解,得到了在多种边界条件下具有任意长宽比的,受均布荷载的矩形板的解答,给出了板中面的位移、挠度的解析表达式;并编制了相关的计算机程序.计算的结果与现有的其他理论的结果作了比较,表明本文的结果是良好的.Abstract: In this paper, Von Kármán's set of nonlinear equations for rectangular plates with large deflection is divided into several sets of linear equations by perturbation method, the dimensionless center deflection being taken as a perturbation parameter. These sets of linear equations are solved by the spline finite-point(SFP) method and by the spline finite element(SFE) method. The solutions for rectangular plates having any length-to-width ratios under a uniformly distributed load and with various boundary conditions are presented, and the analytical formulas for displacements and deflections are given in the paper. The computer programs are worked out by ourselves. Comparison of the results with those in other papers indicates that the results of this paper are satisfactorily better.
-
[1] Way,S.,Uniformly loaded,clamped,rectangular plates with large deflection,Proc.Fifth Int.Cong.Appl.Mech.(Cambridge,Mass.U.S.A.1938),(1939),123-128. [2] Levy,S.,Bending of rectangular plates with large deflections,T.N.No.846,NACA(1942);Square plate with clamped edges under normal pressure producing large deflections T.N.No.847,NACA,(1942). [3] Wang,C.T.Nonlinear large deflection boundary value problems of rectangular plates,NACA,T.N.1425(1948). [4] Chien,W.Z.and K.Y.Yeh,On the large deflection of rectangular plate,Proc.Ninth Int.Cong.Appl.Mech.,Brussels,6(1957),403. [5] Brown,J.C.and J.M.Harvey,Large deflections of rectangular plates subjected to uniform lateral pressure and compressive edge loading,Journal Mech.Eng.Sci.,11,3(1969),305-317. [6] Hooke,R.,Approximate analysis of the large deflection elastic behaviour of clamped,uniformly loaded,rectangular plates,J.Mech.Eng.Sci.,11,3(1969),256-269. [7] 叶开沅、房居贤、王云,在法向均布载荷下四边固定的矩形板大挠度问题的摄动解,《第六届全国弹性元件会议论文集》(厦门),(1981). [8] 潘立宙、王蜀,均布载荷下矩形板大挠度问题的摄动变分解,应用数学和力学,了,8(1988),876-888. [9] 石钟慈,样条有限元,计算数学,1(1979),60-72. [10] 秦荣,《结构力学的样条函数方法》,广西人民出版社(1986). -
点击查看大图
计量
- 文章访问数: 1608
- HTML全文浏览量: 35
- PDF下载量: 662
- 被引次数: 0
下载:
