Comments on "Strain-Displacement Relations in Large Displacement Theory of Shells"

Berkowitz, Harvey M.

doi:10.2514/3.55214

AIAA Journal

1965

DOI: 10.2514/3.55214

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Comments on "Strain-Displacement Relations in Large Displacement Theory of Shells"

Harvey M. Berkowitz

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Cited by 3 publications

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“…Novozhilov !6]_assumed • = a~s --i in further derivations, proposed keeping terms to second order in u, v, and w and their derivatives inclusive in the determination of X in [9], It is noted in [8] that these assumptions reflect implicit constraints imposed on the magnitude of the angles of rotation when comparing them with the strains and the units.…”

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Nonlinear equations of thin shell theory

Chuiko¹

1983

Soviet Applied Mechanics

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The nonlinear equations usually used in thin shell theory [2,3] are constructed on the basis of geometric relationships in which the expressions for the strain contain nonlinear quadratic terms (in the displacements and their derivatives), and the expressions for the change in the curvature and torsion are only linear terms. In recent times equations [!, 4, 7] have become widespread, where the quadratic terms are conserved even in the expressions for the change in curvature and torsion. On the other hand, as is known, a complete expression for the curvagion of the elastic llne is used in investigations of the post-critical strain of a rod, while an approximate result can be obtained only by expanding this expression in series, and keeping two terms, of which the second contains derivatives of the displacements in the third degree.Let us examine the possibility of constructing a nonlinear theory of thin shells with cubic terms retain in the expressions for the change in curvature and torsion.i. For a thin-walled elastic shell the expressions for the elongations and shears, which are related to the displacements u, v, and w, are taken following [6] in the form ,n = Zle. +-fz I (e~, + e~2 + e~s);

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“…To obtain more general relationships in this paper, exactly as in [8] it is assumed to use the complete expression for X in (1.5) for determining 0 and 4, then (1.8)…”

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Nonlinear equations of thin shell theory

Chuiko¹

1983

Soviet Applied Mechanics

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Criterion of the validity of strain relations of thin shells in the region of arbitrary displacements

Kuznetsov

Soinikov

1992

J Appl Mech Tech Phys

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Accuracy of nonlinear relations of Timoshenko-type shell theory when transverse contraction is ignored

Semenyuk¹,

Zhukova²

1990

Soviet Applied Mechanics

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Comments on "Strain-Displacement Relations in Large Displacement Theory of Shells"

Cited by 3 publications

References 2 publications

Nonlinear equations of thin shell theory

Nonlinear equations of thin shell theory

Criterion of the validity of strain relations of thin shells in the region of arbitrary displacements

Accuracy of nonlinear relations of Timoshenko-type shell theory when transverse contraction is ignored

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