A family of mixed finite elements for the elasticity problem
Numerische Mathematik
Mixed finite element methods for elliptic problems
Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Locking effects in the finite element approximation of plate models
Mathematics of Computation
Stable hp mixed finite elements based on the Hellinger-Reissner principle
Journal of Computational and Applied Mathematics
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Dimensionally reduced cylindrical shell models using complementary energy-based variational formulations of a priori non-symmetric stresses are compared. One of them is based on the three-field dual-mixed Hellinger-Reissner variational principle, the fundamental variables of which are the stress tensor, the rotation and displacement vectors. The other one is derived from the two-field dual-mixed Fraeijs de Veubeke variational principle in terms of the self-equilibrated stress field and rotations. The most characteristic properties of the shell models are that the kinematical hypotheses used in the classical shell theories are not applied and the unmodified three-dimensional constitutive equations are employed. Our investigations are restricted to the axisymmetric case. The developed dual-mixed hp finite element models with C^0 continuous tractions and with discontinuous rotations and displacements are presented for bending-shearing (including tension-compression) problems. The computational performance of the constructed shell elements is compared through two representative model problems. It is numerically proven that no significant differences can be experienced between the two well-performing shell elements in the convergence rates.