A DPG method for Reissner-Mindlin plates

@article{Fhrer2022ADM,
  title={A DPG method for Reissner-Mindlin plates},
  author={Thomas F{\"u}hrer and Norbert Heuer and Antti H. Niemi},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.13301}
}
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… 

Figures from this paper

References

SHOWING 1-10 OF 32 REFERENCES
Numerical approximation of Mindlin-Reissner plates
We consider a finite element approximation of the so-called Mindlin-Reissner formulation for moderately thick elastic plates. We show that stability and optimal error bounds hold independently of the
A uniformly accurate finite element method for the Reissner-Mindlin plate
A simple finite element method for the Reissner–Mindlin plate model in the prim-itive variables is presented and analyzed. The method uses nonconforming linear finite elements for the transverse
A DPG method for shallow shells
TLDR
A discontinuous Petrov–Galerkin method with optimal test functions (DPG method) for a shallow shell model of Koiter type that converges robustly quasi-uniformly and gives rise to adaptive mesh refinements that are capable to resolve boundary and interior layers.
A DDR method for the Reissner-Mindlin plate bending problem on polygonal meshes
TLDR
A discretisation method for the Reissner–Mindlin plate bending problem in primitive variables that supports general polygonal meshes and arbitrary order is proposed and a locking-free error estimate is derived.
and a at
The xishacorene natural products are structurally unique apolar diterpenoids that feature a bicyclo[3.3.1] framework. These secondary metabolites likely arise from the well-studied, structurally
A robust DPG method for large domains
Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H(div)
TLDR
The findings from this work are applied to derive optimal a priori  $hp$-error estimates for mixed and least-squares finite element methods applied to a model diffusion problem.
An ultraweak formulation of the Reissner–Mindlin plate bending model and DPG approximation
TLDR
An ultraweak variational formulation of the Reissner–Mindlin plate bending model both for the clamped and the soft simply supported cases is developed and well-posedness is proved, uniformly with respect to the plate thickness t .
Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model
We investigate the structure of the solution of the Reissner–Mindlin plate equations in its dependence on the plate thickness in the cases of soft and hard clamped, soft and hard simply supported,
...
...