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 ((k+1)th order in the L2 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