In this work-in-progress we report on a new approach to obtaining stable locking-free discretizations of the Reissner–Mindlin plate model. For a plate of thickness t with midplane section Ω ⊂ R the clamped Reissner–Mindlin plate model determines ω , the transverse displacement of the midplane, and φ , the rotation of fibers normal to the midplane, as the unique minimizer over H̊1(Ω)× H̊(Ω) of the...

For a plate subject to stress boundary condition, the deformation determined by the Reissner–Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner–Mindlin model has a wider range of applicability than the Kirchhoff–Love model, but it does not always converge to the elasticity theory. In the...

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, and traction free boundary conditions. For the transverse displacement, rotation, and shear stress, we develop asymptotic expansions in powers of the plate thickness. These expansions are uniform up t...

A Balancing Domain Decomposition Method by Constraints (BDDC) is constructed and analyzed for the Reissner-Mindlin plate bending problem discretized with MITC finite elements. This BDDC algorithm is based on selecting the plate rotations and deflection degrees of freedom at the subdomain vertices as primal continuity constraints. After the implicit elimination of the interior degrees of freedom...

A new two-eigenfunctions theory, using the amplitude deflection and the generalized curvature as two fundamental eigenfunctions, is proposed for the free vibration solutions of a rectangular Mindlin plate. The three classical eigenvalue differential equations of a Mindlin plate are reformulated to arrive at two new eigenvalue differential equations for the proposed theory. The closed form eigen...

This is the first part of a two-part paper dedicated to a new plate theory for out-of-plane loaded thick plates where the static unknowns are those of the Kirchhoff-Love theory (3 in-plane stresses and 3 bending moments), to which six components are added representing the gradient of the bending moment. The new theory, called the Bending-Gradient plate theory is described in the present paper. ...

geometrically nonlinear governing equations for a plate with linear viscoelastic material are derived. the material model is of boltzmann superposi¬tion principle type. a third-order displacement field is used to model the shear deformation effects. for the solution of the nonlinear governing equations the dynamic relaxation (dr) iterative method together with the finite difference discretizati...

In the first part (Lebée and Sab, 2010a) of this two-part paper we have presented a new plate theory for out-of-plane loaded thick plates where the static unknowns are those of the Kirchhoff-Love theory (3 inplane stresses and 3 bending moments), to which six components are added representing the gradient of the bending moment. The new theory, called Bending-Gradient plate theory is an extensio...

Abstract. The Reissner-Mindlin plate theory models a thin plate with thickness t. The condition numbers of finite element approximations of this model deteriorate badly as the thickness t of the plate converges to 0. In this paper, we develop an overlapping domain decomposition method for the Reissner-Mindlin plate model discretized by the Falk-Tu elements with the convergence rate which does n...

The structure of the solution of the Reissner–Mindlin plate equations is investigated, emphasizing its dependence on the plate thickness. For the transverse displacement, rotation, and shear stress, asymptotic expansions in powers of the plate thickness are developed. These expansions are uniform up to the boundary for the transverse displacement, but for the other variables there is a boundary...