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Dual-mixed \(hp\) finite element model for elastic cylindrical shells. (English) Zbl 1241.74036

Summary: A dimensionally reduced cylindrical shell model using a three-field complementary energy-based Hellinger – Reissner’s variational principle of non-symmetric stresses, rotations, and displacements is presented. An important property of the shell model is that the classical kinematical hypotheses regarding the deformation of the normal to the shell mid-surface are not applied. A dual-mixed hp finite element model with stable polynomial stress- and displacement interpolation and \(C^{0}\) continuous normal components of stresses is constructed and presented for the bending-shearing problem, using unmodified three-dimensional inverse stress-strain relations for linearly elastic materials. It is shown through an example that the convergences in the energy norm as well as in the maximum norm of stresses and displacements are rapid for both h-extension and p-approximation, not only for thin but also for moderately thick shells loaded axisymmetrically, even if the Poisson ratio is close to the incompressibility limit of 0.5.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K25 Shells
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