What does this research mean for the field?

A higher-order shell theory for arbitrary geometries allows for the automatic satisfaction of shear-free surface boundary conditions and does not suffer from shear locking. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To propose a higher-order shell theory for arbitrary geometries that accommodates rotation and warping, while deriving internal force expressions.

March 7, 2026

A functional for shells of arbitrary geometry and a mixed finite element method for parabolic and circular cylindrical shells

Key Points

To propose a higher-order shell theory for arbitrary geometries that accommodates rotation and warping, while deriving internal force expressions.
Developed a higher-order shell theory allowing for rotation and warping of the shell cross-section.
Utilized the Gâteaux differential method to derive a new functional for arbitrary shell geometries.
Constructed boundary conditions systematically during the variational process.
Derived mixed elements PRSH 52 and CRSH 52 for parabolic and circular cylindrical shells.
Ensured the elements do not experience shear locking.
Successfully derived a new expression for internal forces based on the new kinematic assumption.
Validated the performance of the mixed elements through several test problems.

Abstract

Summary: A higher-order shell theory is proposed for arbitrary shell geometries, which allows the cross-section to rotate with respect to the middle surface and to warp into a non-planar surface. This new kinematic assumption satisfies the shear-free surface boundary condition (BC) automatically. We derive a new expression for internal forces based on this kinematic assumption. A new functional for arbitrary shell geometries is obtained employing Gâteaux differential method. During this variational process, we are able to construct BC and to introduce the functional in a systematic way. Two different mixed elements, PRSH 52 and CRSH52, are derived for parabolic and circular cylindrical shells, respectively, using the functional. The element does not suffer from shear locking. The performance of the elements is verified by test problems.

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