A novel mixed shell finite element (FE) is presented. The element is obtained from the Hellinger–Reissner variational principle and it is based on an elastic solution of the generalized stress field, which is ruled by the minimum number of variables. As such, the new FE is isostatic because the number of stress parameters is equal to the number of kinematical parameters minus the number of rigid body motions. We name this new FE MISS-8. MISS-8 has generalized displacements and rotations interpolated along its contour and drilling rotation is also considered as degree of freedom. The element is integrated exactly on its contour, it does not suffer from rank defectiveness and it is locking-free. Furthermore, it is efficient for recovering both stress and displacement fields when coarse meshes are used. The numerical investigation on its performance confirms the suitability, accuracy, and efficiency to recover elastic solutions of thick- and thin-walled beam-like structures. Numerical results obtained with the proposed FE are also compared with those obtained with isogeometric high-performance solutions. Finally, numerical results show a rate of convergence between h2 and h4.

An efficient isostatic mixed shell element for coarse mesh solution

Madeo A.;Liguori F. S.;
2021

Abstract

A novel mixed shell finite element (FE) is presented. The element is obtained from the Hellinger–Reissner variational principle and it is based on an elastic solution of the generalized stress field, which is ruled by the minimum number of variables. As such, the new FE is isostatic because the number of stress parameters is equal to the number of kinematical parameters minus the number of rigid body motions. We name this new FE MISS-8. MISS-8 has generalized displacements and rotations interpolated along its contour and drilling rotation is also considered as degree of freedom. The element is integrated exactly on its contour, it does not suffer from rank defectiveness and it is locking-free. Furthermore, it is efficient for recovering both stress and displacement fields when coarse meshes are used. The numerical investigation on its performance confirms the suitability, accuracy, and efficiency to recover elastic solutions of thick- and thin-walled beam-like structures. Numerical results obtained with the proposed FE are also compared with those obtained with isogeometric high-performance solutions. Finally, numerical results show a rate of convergence between h2 and h4.
Allman kinematics
drilling rotation
Hellinger–Reissner variational principle
mixed shell element
spurious energy modes
Trefftz method
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/316939
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