this paper presents the bending analysis of annular plates by the indirect trefftz boundary approach. the formulation for thin and thick plates is based on the kirchhoff plate theory and the reissner plate theory. the governing equations are therefore a fourth-order boundary value problem and a sixth-order boundary value problem, respectively. the trefftz method employs the complete set of solu...

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. ...

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...

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...

The Reissner-Mindlin plate theory models a thin plate with thickness t. The condition number of finite element approximations of this model deteriorates badly as the thickness t of the plate converges to 0. In this thesis, we develop an overlapping domain decomposition method for the Reissner-Mindlin plate model discretized by Falk-Tu elements with a convergence rate which does not deteriorate ...

The Reissner-Mindlin plate theory models a thin plate with thickness t. The condition number of finite element approximations of this model deteriorates badly as the thickness t of the plate converges to 0. In this thesis, we develop an overlapping domain decomposition method for the Reissner-Mindlin plate model discretized by Falk-Tu elements with a convergence rate which does not deteriorate ...

We consider the plate bending problem in the framework of the Reissner-Mindlin theory. For a clamped plate, the problem can be written in variational form as follows. Find (θ, w) ∈ (H 0 (Ω)) ×H 0 (Ω) : ∫ Ω Cε(θ) : ε(η) + μ t−2 ∫ Ω (∇w − θ) · (∇v − η) = ∫