The Nonlinear Strain Components of Thin Shells

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1982 > 3(4): 505-512

Tao Qi-kun. The Nonlinear Strain Components of Thin Shells[J]. Applied Mathematics and Mechanics, 1982, 3(4): 505-512.

Citation:

Tao Qi-kun. The Nonlinear Strain Components of Thin Shells[J]. Applied Mathematics and Mechanics, 1982, 3(4): 505-512.

Citation:

Tao Qi-kun. The Nonlinear Strain Components of Thin Shells[J]. Applied Mathematics and Mechanics, 1982, 3(4): 505-512.

Abstract

The nonlinear strain components of thin shells are the foundations of nonlinear shell mechanics. They are needed in the investigation of various thin shell stability and large displacement problems. Due to the geometrical variety of thin shells we have not seen in existing literatures a complete set of general formulae expressing nonlinearity of shell strain components. In this paper we have derived six of them expressed in Lame coefficients and orthogonal curvilinear coordinates, including both linear and nonlinear parts, three of them are tensile strain components,the other three are shear strain components.

[1]	Love,A.E.H.,A Treatise on Mathematical Theory of Elasticity.4th.ed.,The University Press(Cambridge),(1934).
[2]	Sokolnikoff,I.S.and Specht,R.D.,Mathematical Theory of Elasticity.Mc-Graw-Hill Book Co.,Inc.(1946).
[3]	Timoshenko,S.and Goodier,J,N.,Theory of Elasticity.McGraw-Hill Book Co.,Inc.(1951).
[4]	Reissner,E.,A New Derivation of the Equations for the Deformation of Elastic Shells.Am.J.Math..Vol.63.No.1,(Jan.1941).
[5]	Hildebrand,F.B.,Reissner,E.and Thomas,G.B.,Notes on the foundations of the Theory of Small Displacements of Orthotropic Shells.National Advisory Committee for Aeronautics,(NACA),Technical Note.No.1833,(1949).
[6]	Новожилов,В.В.,Основы Нелцнейной Теории Упрусоми