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    On the Form of Variationally Derived Shell Equations

    Source: Journal of Applied Mechanics:;1964:;volume( 031 ):;issue: 002::page 233
    Author:
    Eric Reissner
    DOI: 10.1115/1.3629591
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: In the first part of the paper the basic equations of three-dimensional elasticity are formulated as a system of four equilibrium equations and seven stress displacement relations, together with a variational problem which has these eleven equations as Euler equations. In the second part of the paper, the new variational problem is used for a derivation of shell theory which accounts particularly simply for the differences between the resultants N12 and N21 and the couples M12 and M21 . In the third part of the paper a solution is given of the torsion problem for circumferentially nonhomogeneous circular cylindrical shells, as an explicit demonstration of the fact that certain terms in the shell equations which are often of negligible influence sometimes are of considerable influence.
    keyword(s): Equations , Shells , Elasticity , Stress , Equilibrium (Physics) , Torsion , Circular cylindrical shells AND Displacement ,
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      On the Form of Variationally Derived Shell Equations

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    http://yetl.yabesh.ir/yetl1/handle/yetl/98457
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    contributor authorEric Reissner
    date accessioned2017-05-08T23:17:52Z
    date available2017-05-08T23:17:52Z
    date copyrightJune, 1964
    date issued1964
    identifier issn0021-8936
    identifier otherJAMCAV-25749#233_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/98457
    description abstractIn the first part of the paper the basic equations of three-dimensional elasticity are formulated as a system of four equilibrium equations and seven stress displacement relations, together with a variational problem which has these eleven equations as Euler equations. In the second part of the paper, the new variational problem is used for a derivation of shell theory which accounts particularly simply for the differences between the resultants N12 and N21 and the couples M12 and M21 . In the third part of the paper a solution is given of the torsion problem for circumferentially nonhomogeneous circular cylindrical shells, as an explicit demonstration of the fact that certain terms in the shell equations which are often of negligible influence sometimes are of considerable influence.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleOn the Form of Variationally Derived Shell Equations
    typeJournal Paper
    journal volume31
    journal issue2
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.3629591
    journal fristpage233
    journal lastpage238
    identifier eissn1528-9036
    keywordsEquations
    keywordsShells
    keywordsElasticity
    keywordsStress
    keywordsEquilibrium (Physics)
    keywordsTorsion
    keywordsCircular cylindrical shells AND Displacement
    treeJournal of Applied Mechanics:;1964:;volume( 031 ):;issue: 002
    contenttypeFulltext
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