A Discontinuous Petrov–Galerkin Method for Reissner–Mindlin Plates
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Date
2023
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Abstract
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.
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Keywords
DPG method, Plate bending, Reissner-Mindlin model, Locking