Generalized shape operator for nonlinear shells
Date:
The slides can be found here.
Abstract:
In computing the bending energy of nonlinear shells, the surface curvature represented by the shape operator plays a fundamental role. Discrete differential geometry (DDG) aims to approximate curvature quantities of discretized domains. By embedding DDG within a finite element context, rigorous numerical analysis tools become available for investigating and extending those algorithms. So-called distributional finite elements are essential in the process. They entail weak regularity, so that differential operators must be understood in the sense of distributions.
In this talk, we approximate the shape operator on surfaces, where the discretized surface is described by Lagrange finite elements, by combining the concept of dihedral angles from DDG with Hellan-Herrmann-Johnson finite elements. Then, we discuss their application to nonlinear Kirchhoff-Love shells by approximating the bending energy term, namely, the difference between the curvatures of the initial and deformed configurations. We present numerical examples using the finite element library NGSolve (www.ngsolve.org).