Kirchhoff‐Love shell theory based on Tangential Differential Calculus

Abstract

We propose a parametrization-free reformulation of the classical Kirchhoff-Love shell equations in terms of tangential differential calculus. An advantage of our approach is that the surface may be defined implicitly, and the resulting shell equations and stress resultants lead to a more compact and intuitive implementation. Numerical tests are performed and it is confirmed that the obtained approach is equivalent to the classical formulation based on local coordinates.This is an open access article under the terms of the Creative Commons Attribution-Non-Commercial-NoDerivs Licence 4.0, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

A higher‐order Trace finite element method for shells

“…In this section, the proposed numerical method for implicitly defined Reissner–Mindlin shells is tested on a set of benchmark examples, consisting of the partly clamped hyperbolic paraboloid from References 56,57, the partly clamped gyroid from Reference 58 and a clamped flower‐shaped shell inspired by References 47,48. In the case of the first two examples the shells are rather thin and locking phenomena can be expected, especially in the case of low ansatz orders.…”

Implicit Analysis of Reissner–Mindlin shells with the Trace FEM

“…The reformulation of the classical shell equations in the frame of the TDC generalizes the shell equations to explicitly and implicitly defined manifolds. For further information regarding the TDC we refer to [3][4][5].…”

A nonlinear thermomechanical formulation for anisotropic volume and surface continua

“…Schöllhammer and Fries [74] propose a Kirchhoff–Love shell theory based on tangential differential calculus without the introduction of a local coordinate system. See also Duong et al [71] and Schöllhammer and Fries [74] for recent reviews of shell formulations.…”

“…Duong et al [71] propose a rotation-free multi-patch shell formulation based on the curvilinear membrane and shell formulations of Sauer et al [72] and Sauer and Duong [73]. Schöllhammer and Fries [74] propose a Kirchhoff-Love shell theory based on tangential differential calculus without the introduction of a local coordinate system. See also Duong et al [71] and Schöllhammer and Fries [74] for recent reviews of shell formulations.…”