The Hellan-Herrmann-Johnson Method for Nonlinear Shells

Abstract

In this paper we derive a new finite element method for nonlinear shells. The Hellan-Herrmann-Johnson (HHJ) method is a mixed finite element method for fourth order Kirchhoff plates. It uses convenient Lagrangian finite elements for the vertical deflection, and introduces sophisticated finite elements for the moment tensor. In this work we present a generalization of this method to nonlinear shells, where we allow finite strains and large rotations. The geometric interpretation of degrees of freedom allows a straight forward discretization of structures with kinks. The performance of the proposed elements is demonstrated by means of several established benchmark examples.

References in corpus (2)

• The TDNNS method for Reissner-Mindlin plates
• Kirchhoff-Love shell theory based on tangential differential calculus

Cited by in corpus (8)

• Avoiding Membrane Locking with Regge Interpolation
• The Hellan-Herrmann-Johnson and TDNNS method for linear and nonlinear shells
• Numerical shape optimization of the Canham-Helfrich-Evans bending energy
• Diffusion of tangential tensor fields: numerical issues and influence of geometric properties
• Higher-order, mixed-hybrid finite elements for Kirchhoff-Love shells
• Intrinsic mixed finite element methods for linear Cosserat elasticity
• Mixed Finite Elements for Geometrically Exact Beams using Discontinuous Rotations and Discrete Curvature
• Simultaneous analysis of curved Kirchhoff beams and Kirchhoff--Love shells embedded in bulk domains