## Derivation of a dual-mixed $$hp$$-finite element model for axisymmetrically loaded cylindrical shells.(English)Zbl 1271.74413

Summary: The two-field dual-mixed Fraeijs de Veubeke variational formulation of three-dimensional elasticity serves as the starting point of the derivation of a dimensionally reduced shell model presented in this paper. The fundamental variables of this complementary energy-based variational principle are the not a priori symmetric stress tensor and the skew-symmetric rotation tensor. The tensor of first-order stress functions is applied to satisfy translational equilibrium, while the rotation tensor plays the role of a Lagrange multiplier to ensure rotational equilibrium. The volumetric locking-free shell model uses unmodified three-dimensional constitutive equations, and no classical kinematical hypotheses are employed during the derivation. The numerical performance of the related low-order $$h$$-, and higher-order $$p$$-version finite elements developed for axisymmetrically loaded cylindrical shells is investigated by two representative model problems. It is numerically proven that no negative effect can be experienced when the thickness is small and tends to zero.

### MSC:

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

### Keywords:

dual-mixed; cylindrical shell; locking-free; hp-finite element
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