圆薄板大挠度问题的摄动参数

The Perturbation Parameter in the Problem of Large Deflection of Clamped Circular Plates

摘要: 本文研究了在用正规摄动法求解均布载荷下的圆薄板大挠度问题时,与载荷,挠度,转角,内力等有关的各种摄动参数,并对一般摄动参数情形用变分原理求得了解答本文从实验的角度阐明了各参数的适用范围,结果表明,相应的解答与用中心挠度为参数的解有较好的一致性;对均布载荷的情形,中心挠度仍可看做是较为合适的摄动参数;本文推荐的摄动参数及用变分原理确定摄动解的方法,具有普遍的适用性,可以用来处理载荷联合作用等更为复杂的情形.

Abstract: In the problems of large deflection of clamped circular plates under uniformly distributed loads, various perturbation parameters relating to load, deflection, slope of deflection, membrane force, etc, are studied. For a general perturbation parameter, the variational principle is used for the solution of such a problem. The applicable range of these perturbation parameters are studied in detail. In the case of uniformly loaded plate, perturbation parameter relating to central deflection seems to be the best among all others. The method of determination of perturbation solution by means of variational principle can be used to treat a variety of problems, including the large deflection problems under combine loads.

[1]	Chien Wei-zang(钱伟长),Large deflection of a circular clamped plate under uniform pressure,Chinese Journal of Physics,V7(1947),102-113.
[2]	Vincent,J.J.,The bending of a thin circular plate,Phil.Mag.,V12(1931),185-196.
[3]	胡海昌,在均布及中心集中载荷下圆板的大挠度问题,物理学报,V 10. 4 (1954).383-392.
[4]	钱伟长、叶开沅,圆板的大挠度问题,物理学报,V10,3 (1954),209-238.
[5]	叶开沅,边缘载荷下环形薄板的大挠度问题,物理学报,V9,1(1953). 110-129.
[6]	钱伟长,林鸿荪,胡海昌,叶开沅,“弹性圆薄板大挠度门题”(文集)中国科学院(1954).
[7]	Nash,W.A.,Cooly,I.D.,Large deflection of a clamped plate subjected to uniform pressure,Transactions of A.S.M.E.,J.of Appl.Mech.,V26,2(1959) 291-293.
[8]	Chien,W.Z(钱伟长).and Yeh,K.Y(叶开沅).,Large deflection of a rectangular plate under uniform pressure,Proc.Ninth Intern.Congr.Appl.Mech.,Brussels,V6,403(1957).
[9]	Волъмир,А.С.,柔韧板与柔韧壳(中译本)科学出版社(1959).
[10]	Schmidt,R.and DaDeppo,D.A.,A new approach to the analysis of shells,plates and membranes with finite deflection,Int.J.of Non-Linear Mech.V9,5(1974),409-419.
[11]	DaDeppo,D.A.,Schmidt,R.,Moderately Large deflection of a loosely clamped circular plate under a uniformly distributed load,Indus.Math.,V25,1(1975),17-28.
[12]	McPherson,A.E.,Ramberg,W.,Levy,S.,Normal pressure tests of circular plates with clamped edges,NACA Report 744(1944).