极正交各向异性圆板非线性弯曲的定性分析及单调迭代解

尚新春; 程昌钧

极正交各向异性圆板非线性弯曲的定性分析及单调迭代解

兰州大学力学系

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出版历程
- 收稿日期: 1990-04-26
- 刊出日期: 1990-12-15

Qualitative Investigation and Monotonic Iterative Solutions for Nonlinear Bending of Polar Orthotropic Circular Plates

Deportment of Mechanics, Lanzhou University, Lanzhou

摘要

摘要: 本文对极正交各向异性圆板在任意轴对称载荷和边界条件下的非线性弯曲问题进行了较为系统的研究.首先,将边值问题归结为等价的积分方程,并且借助于广义函数得到了线性问题的一般解答.其次,对导出的非线性积分方程解的性质作了较为细致的讨论,例如边缘皱褶,非负性和奇性等.然后,构造了解的双边单调迭代格式,并给出了迭代格式的收敛性判据和误差估计,同时还讨论了解的全局存在唯一性.最后,给出了一个数值例子来说明本文方法和结论的应用.本文某些结果是由作者新得到的.
- 非线性弯曲 /
- 定性分析 /
- 单调迭代解 /
- 收敛性判据 /
- 全局唯一性 /
- 误差估计
Abstract: This paper presents a systematical investigation of the nonlinear bending of polar orthotropic circular plates under arbitrarily axisymmetric loads and a variety of boundary conditions.Firstly,the oundary value problem reduces to the equivalent integral equations,and the so tions to the linearized problem are given by means of generalized functions.Secondly,the general properties of the solutions of the nonlinear integral equations are investigated in detail,such as,wrinkling,non-negativity,and singularity etc.Then,the monotonic iterative solutions are formally given and the convergence criteria and the global uniqueness of the solutions are discussed.The error estimate of the iterative process is obtained.Finally,a special example is discussed,which shows that the conclusions and methods of this paper are valid.Several results in the paper are presented for the first time.
- nonlinear bending /
- qualitative analyses /
- monotonic iterative solu-tions /
- convergence criteria /
- global uniqueness /
- estimation of error

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参考文献(17)

[1]	Nath,Y.and R.S.Alwar,Nonlinear dynamic analysis of orthotropic circular plates,Int.J.Solid Structures,16(1980),433-443.
[2]	Nowinisi,J.,Cylindrically orthotropic circular plates,ZAMP,11-(1960),218-228.
[3]	Gandhi,M.L.,P.C.Dumir and Y.Nath,Nonlinear axisymmetric static analysis of orthotropic thin circular plates with elastically restrained edge,Computer Structures,20(1985),841-853.
[4]	Shilkrut,D.,Investigations of axisymmetric deformation of geometrically nonlinear,rotationally orthotropic,circular plates,Int.J.Non-Linear Mech.,18(1983),95-118.
[5]	Cheo,L.S.and E.L.Reiss,Unsymmetric wrinkling of circular plates,Q.App!.Math.,76(1973),75-91.
[6]	Yanowitch,M.,Nonlinear buckling of circular plates,Comm.Pure Appl.Math.,9(1956),661.
[7]	Vol'mir,A.S.,Flexible Plates and Shells,Moscow(1956).(in Russian).
[8]	Reiss,E.L.,A uniqueness theorem for the nonlinear axisymmetric bending of circular plates,AIAA J.,1(1963),2650-2652.
[9]	Weinitschke,H.J.,On uniqueness of axisymmetric deformations of elastic plates and shells,SIAM J.Math.Anal.,19(1988),580-592.
[10]	尚新春、程昌钧,圆板非线性轴对称弯曲的定性分析(待发表).
[11]	Keller,H.B.and E.L.Reiss,Iterative solutions for the nonlinear bending of circular plates,Comm.Pure Appl.Math.,11(1958),273-298.
[12]	Lekhnitskii,S.G.,Theory of Elasticity of an Anisotropic Elastic Body,Holden-Bay Sense in Mathematical Physics,Julius J.Brandstaffer,Ed.(1963),85.
[13]	Lekhnitskii,S.G.,Ani.cotropic Plates.Moscow(1975).(in Russian).
[14]	Mason,J.,Methods of Functional Analysis for Application in Solid Mechanics,Elsevier Sci.Pubs.B.V.,Amsterdam(1985),82-83.
[15]	Roseau,M.,Equations Differentialles,Masson(1976).中译本.《常微分方程》,叶彦谦译,上海科学技术出版社出版(1981).
[16]	Oden,J.T.,Qualitative Methods in Nonlinear Mechanics,Noordhoff lnt.Pubs.Leyden(1977).
[17]	Weinitschke,H.J.,Some mathematical problems in the nonlinear theory of elastic membranes,plates and shells,Trends in Applications of Pure Mathematics to Mechanics,G.Fichera.Ed.,Pitman Pub.London(1976).