具有不等厚表层的夹层旋转壳问题
On the Problems of Sandwich Shells Having the Form of a Surface of Revolution and Face Layers of Non-Equal Thicknesses
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摘要: 本文探讨了具有各向同性夹心及不等厚表层组成的三层旋转壳的小挠度问题,采用广义变分法,在考虑表层抗弯刚度的情况下,导出了基本方程,其特例即为文献[3],[4]的结果. 根据所导出的基本方程,本文求解对称加载的夹层旋转壳问题,将其归结为只含一个广义位移的六阶微分方程. 本文的理论可应用于复合装甲及其它工程设计.Abstract: Fundamental eguations which govern the behavior of an elastic sandwich shell having the form of a surface of revolution and face layers of non-equal thicknesses are derived, with the solution of refs.[3] and [4] as special examples.The problems of the shell under the action of symmetrical loads are reduced to the solution of a displacement-function ψa, where ψa satisfies a differential equation of sixth order.
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[1] 杜庆华,三合板的一般弹性理论,物理学报,10. 4 (1954) [2] 胡海昌,各向同性夹层板反对称小挠度的若干问题,力学学报,6,1(1963). [3] 中国科学院北京力学研究所板壳组,《夹层板壳的弯曲稳定和振动》,科学出版社,(1977). [4] 薛大为,具有不等厚表板的夹层板问题,固体力学学报,1(1981). [5] Ikegawa,M.,K.Washizu,Finite element method applied to analysis of flow over a spillway crest,Inter,J.of Num.Mech.in Eng.,6(1973). [6] Псусаков,А.П.,Основные уравнения изгиба и устойчивости трёхслойных пластин с лёгким заполнителем,П.М.М.,15,1(1951). [7] Hoff,N.J.,Bending and buckling of rectangular sandwich plates,NACA,TN 2225,(1950). [8] Fulton,R.E.,Nonlinear equations for a shallow unsymmetrical sandwich shell of double curvature,Developments in Mechanics,(1961),365-380. [9] Chien Wei-zang,The intrinsic theory of plates and shells,Journal of Mathematics and Physics,(1943). -
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