A Theory for the Small Unsymmetric Deformations of Cylindrical Shells
A Theory for the Small Unsymmetric Deformations of Cylindrical Shells
Edward L Reiss
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>. / % I' — '-^ k' ^l-ll ih - i V + ^^?Vi) + ' 1 - Ik. Here /\ is the two-dimensional biharraonio operator and the coefficients in (2^) are given in (19). The differential equations and stress displacement relations of the ''first order interior problem" are similarly obtained from (18) - (23)» These expressions will be referred to as Eq, (27), They are identical with (2[j. ) - (26) provided that a, 1, is added to the superscript of each term. If the deformations are rotationally symmetric then... all the previous results reduce to those of reference 1, The differential equations (2I4. ) and the stress displacement relations (2^) are, in our notation, identical with those of the thin shell theory of Donne 11, '' Equations (26), which are not given in the Donnell theory, provide "thick shell corrections" to this thin shell theory. Thus the Donnell equations appear in a natural way as part of the first approximation of the exact theory, " The differential equations and stress displacement relations for interior problems of order tvjo or greater are obtained, in a similar fashion, from (10 - 13 )• Because of the complexity of the analysis they are not explicitly shovm here.
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