119 research outputs found
A low-order nonconforming finite element for Reissner-Mindlin plates
We propose a locking-free element for plate bending problems, based
on the use of nonconforming piecewise linear functions for both rotations and
deflections. We prove optimal error estimates with respect to both the meshsize
and the analytical solution regularity
The TDNNS method for Reissner-Mindlin plates
A new family of locking-free finite elements for shear deformable
Reissner-Mindlin plates is presented. The elements are based on the
"tangential-displacement normal-normal-stress" formulation of elasticity. In
this formulation, the bending moments are treated as separate unknowns. The
degrees of freedom for the plate element are the nodal values of the
deflection, tangential components of the rotations and normal-normal components
of the bending strain. Contrary to other plate bending elements, no special
treatment for the shear term such as reduced integration is necessary. The
elements attain an optimal order of convergence
Numerical results for mimetic discretization of Reissner-Mindlin plate problems
A low-order mimetic finite difference (MFD) method for Reissner-Mindlin plate
problems is considered. Together with the source problem, the free vibration
and the buckling problems are investigated. Full details about the scheme
implementation are provided, and the numerical results on several different
types of meshes are reported
Multigrid methods for parameter dependent problems
Multigrid methods for parameter dependent problems are discussed. The contraction numbers of the algorithms are proved within a unifying framework to be bounded away from one, independent of the parameter and the mesth levels. Examples include the pure displacement and pure traction boundary value problems in planar linear elasticity, the Timoshenko beam problem, and the Reissner-Mindlin plate problem
Locking-free HDG methods for Reissner-Mindlin plates equations on polygonal meshes
We present and analyze a new hybridizable discontinuous Galerkin method (HDG)
for the Reissner-Mindlin plate bending system. Our method is based on the
formulation utilizing Helmholtz Decomposition. Then the system is decomposed
into three problems: two trivial Poisson problems and a perturbed saddle-point
problem. We apply HDG scheme for these three problems fully. This scheme yields
the optimal convergence rate (th order in the norm) which
is uniform with respect to plate thickness (locking-free) on general meshes. We
further analyze the matrix properties and precondition the new finite element
system. Numerical experiments are presented to confirm our theoretical
analysis
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