Thomas Führer, Norbert Heuer, Antti H. Niemi
Published 2022-05-26Version 1
We present a discontinuous Petrov-Galerkin (DPG) method with optimal test functions for the Reissner-Mindlin plate bending model. Our method is based on a variational formulation that utilizes a Helmholtz decomposition of the shear force. It produces approximations of the primitive variables and the bending moments. For any canonical selection of boundary conditions the method converges quasi-optimally. In the case of hard-clamped convex plates, we prove that the lowest-order scheme is locking free. Several numerical experiments confirm our results.
An ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation
A DPG method for shallow shells
A DPG method for the quad-curl problem
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