Numerical treatment of a geometrically nonlinear planar Cosserat shell model

• DOI: 10.1007/s00466-016-1263-5
• Publication Date: 2016-02-09T09:01:21Z
• Authors: Oliver Sander; Patrizio Neff; Mircea Bîrsan
• Keywords: 65N30 (Primary), 74K25 (Secondary); Mathematik; FOS: Mathematics; Mathematics - Numerical Analysis; Numerical Analysis (math.NA)

We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general 6-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite elements, which leads to an objective discrete model which naturally allows arbitrarily large rotations. Finite elements of any approximation order can be constructed. The resulting algebraic problem is a minimization problem posed on a nonlinear finite-dimensional Riemannian manifold. We solve this problem using a Riemannian trust-region method, which is a generalization of Newton's method that converges globally without intermediate loading steps. We present the continuous model and the discretization, discuss the properties of the discrete model, and show several numerical examples, including wrinkles of thin elastic sheets in shear.<br/>- redo numerical example 3 after bugfix in program - redo example 2 with a better parameter value L_c<br/>