A DISCONTINUOUS PETROV-GALERKIN METHOD FOR REISSNER-MINDLIN PLATES

We present a discontinuous Petrov-Galerkin 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.

Automated summary

We propose a discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model. The method utilizes a variational formulation based on a Helmholtz decomposition, which provides approximations for the primitive variables and bending moments. The method achieves quasi-optimal convergence for any chosen boundary conditions and is locking-free for hard-clamped convex plates. Numerical experiments validate our findings.