Tangential-Rotation and Normal-Normal-Momentum Continuous Mixed Finite Elements for Non-Linear Shell Models
Date:
The slides can be found here.
Abstract:
Many engineering applications involve thin elastic structures, which are typically treated by models of reduced dimensions, so called shell models.
We sketch the derivation of a 5-parameter shell model from geometric nonlinear 3D elasticity, and discuss proper continuity conditions of the involved fields: displacements shall be continuous, rotations tangential continuous, and bending moments normal-normal continuous.
We present a new finite element method, which is based on two existing formulations: The Hellan-Herrmann-Johnson method for Kirchhoff plates, and the tangential-displacement normal-normal-stress method for solid mechanics. Both are mixed methods using normal-normal continuous tensor-valued elements, and standard H1-elements or Nedelec elements, respectively.
We obtain a discrete constrained energy minimization problem, which is solved by Newton’s method with line-search. We discuss the implementation in ngs-py, and present several numerical examples including piecewise smooth structures with junctions.