复合载荷下圆薄板的大挠度问题

Large Deflection of Circular Plate under Compound Load

摘要: 本文引入载荷分布函数使复合载荷依单参数变化,并选取平均挠角作为单一的位移摄动参数,给出了在均布载荷和中心集中力联合作用下边缘固定夹紧的圆薄板大挠度问题的摄动解,并讨论了中心点挠度为零的特殊情况.

Abstract: By means of the perturbation method, this paper presents an approximate solution for large deflection of clamped circular plate under uniform pressure together with a concentrated load at the center. The special case of vanishing central deflection is also discussed. In this paper, a load distribution function is introduced so as to make the compound loads depend on a single load parameter, and average angular deflection is being used as the single displacement perturbation parameter.

[1]	von Kármán,Th.,The engineer grapples with nonlinear problem,Bull,.Amer,Math,Soc.,46,(1940).615-683.
[2]	Chien Wei-zang(钱伟长),Large deflection of a circular clamped plate under uniform pressure,linese Journal of P hysies.,(1947),102-113.
[3]	钱伟长、叶开沅,圆薄板大挠度问题,物理学报,10(1954),209-238,
[4]	叶开沅,边缘载荷下环形薄板的大挠度问题,物理学报,9(1953),110-129.
[5]	胡海昌,在均布及中心集中载荷作用下圆板的大挠度问题,物理学报,10,(1954),383-394.
[6]	潘立宙,固定边椭圆形薄板的大挠度问题,未发表.(1954).
[7]	钱伟长,林鸿荪、胡海昌、叶开沉,弹性圆薄板大挠度问题,(文集),中国科学院,(1954).
[8]	陈山林,浅正弦波纹圆板在均布载荷下的大挠度弹性特征,应用数学和力学,1,2(1980).261-272.
[9]	Nash,W,A,and I,D,Cooly,Large deflection of a clamped elliptical plate subjected to uniform pressure,Trans,ASME,J,of Appl.Mech,26,2(1959),291-293.
[10]	Sehmidt,R,and D,A,DaDeppo,A new approach to the analysis of shells,plates and membranes with finite deflections,Inter,J.of Non-linear Mecla.,9,5(1974),409-419.
[11]	DaDeppo,D,A,and R,Schmidt,Moderately large deflections of a loosely damped circular plate under a uniformly distributed pressure,Indus,Math.,25,1(1975).17-28.
[12]	陈山林、光积昌,圆薄板大挠度问题的摄动参数,应用数学和力学,2,1(1981),131-144.