Abstract
Consideration is given to three versions of nonlinear strain–displacement relations in the case of small strains and moderately small angles of rotation: (i) relations that neglect rotations about the normal in conformity with the hypotheses of the Donnel–Mushtary–Vlasov theory; (ii) relations, derived from the elasticity equations using Novozhilov's tensor, that exactly allow for rotations; and (iii) relations, proposed by Sanders, that allow for rotations but neglect shear strains. These versions are compared by comparing the solutions of the stability problem for a corrugated cylindrical shell. It is established that the critical loads are close when rotations are allowed for exactly and when Sanders' technique is used
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Semenyuk, N.P., Trach, V.M. Allowing for Rotations about the Normal in Nonlinear Theories of Shells. International Applied Mechanics 40, 694–701 (2004). https://doi.org/10.1023/B:INAM.0000041398.28447.45
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DOI: https://doi.org/10.1023/B:INAM.0000041398.28447.45