Nonlinear Shells - Avoiding Locking by the Hellan–Herrmann–Johnson Method and Regge Interpolation
Date:
The slides can be found here.
Abstract:
Finding appropriate discretizations for nonlinear shells is still a challenging problem. For Kirchhoff plates the Hellan–Herrmann–Johnson method introduces a moment tensor for computing the fourth order equation as a mixed method.
In this talk we present a generalization of these methods to nonlinear shells, where we allow large strains and rotations. We may assume the Kirchhoff–Love hypothesis to neglect shearing terms and focus on the bending energy, which is defined as the difference between the curvatures of the deformed and undeformed configuration of the shell. Therefore, we introduce the moment tensor in the finite element space H(divdiv) as the difference between these curvatures. With these elements, also non-smooth surfaces with kinks can be handled directly without rewriting terms.
To overcome membrane locking for triangular meshes an interpolation operator into the so-called Regge space is inserted in the membrane energy term, weakening the number of implicitly given constraints.
Finally, the method, which is implemented in the finite element library Netgen/NGSolve (www.ngsolve.org), is demonstrated by means of several numerical examples.