壳体的非线性应变分量
The Nonlinear Strain Components of Thin Shells
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摘要: 壳体的非线性应变分量是非线性壳体力学的基础,在壳体的稳定以及各种大变形问题中须要用到它们.由于壳体几何复杂,在现有文献中,还未见到较全面地表示此种非线性应变分量的一般公式,现在导出六个用正交曲线坐标表示的包括线性与非线性部分的壳体应变分量的公式,其中三个为拉伸应变分量,另三个为剪切应变分量.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.
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[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 -
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