1. Abstract Equations governing the behavior of rectangular plates made of functionally graded materials (FGMs) are determined in this paper using the variational approach. Derivation of such equations is based on Reissner–Mindlin plate theory that is extended to handle two-constituent material distribution through the thickness. Material properties are assumed to vary with the power law in ter...

Plate-type structural members are commonly used in engineering applications like aircraft, ships nuclear reactors etc. These structural members often have cracks arising from manufacture or from material defects or stress concentrations. Designing a structure against fracture in service involves consideration of strength of the structure as a function of crack size, dimension and the applied lo...

This study deals with the elastic-plastic impact on moderately thick rectangular plate subjected to uniform in-plane compressive loads resting on the Pasternak elastic foundation. The proposed rectangular plates have two opposite edges simply-supported, while all possible combinations of free, simply-supported and clamped boundary conditions are applied to the other two edges. The dimensionless...

We consider a stabilized finite element formulation for the Reissner-Mindlin plate bending model. The method uses standard bases functions for the deflection and the rotation vector. We apply a standard multigrid algorithm to obtain a preconditioner. We prove that the condition number of the preconditioned system is uniformly bounded with respect to the multigrid level and the thickness paramet...

The mixed method for the biharmonic problem introduced in [12] is extended to the Reissner-Mindlin plate model. The Reissner-Mindlin problem is written as a system of first order equations and all the resulting variables are approximated. However, the hybrid form of the method allows one to eliminate all the variables and have a final system only involving the Lagrange multipliers that approxim...

In this paper, we consider a plate–beam system inwhich the Reissner–Mindlin platemodel is combined with the Timoshenko beam model. Natural frequencies and vibration modes for the system are calculated using the finite element method. The interface conditions at the contact between the plate and beams are discussed in some detail. The impact of regularity on the enforcement of certain interface ...

We consider the BDDC preconditioner for Reissner-Mindlin plate problems, discretized with the MITC element, introduced and analyzed in [11]. In that contribution the authors prove that the condition number of the ensuing linear system is independent of the plate thickness and scalable with respect to the mesh. We here prove, in addition, that the BDDC preconditioner of [11] is also quasi-optima...

On arbitrary regular quadrilaterals, a new finite element method for the Reissner-Mindlin plate is proposed, where both transverse displacement and rotation are approximated by isoparametric bilinear elements, with local bubbles enriching rotation, and a local reduction operator is applied to the shear energy term. This new method gives optimal error bounds, uniform in the thickness of the plat...