Approximation of the vibration modes of a plate by Reissner-Mindlin equations

Approximation of the vibration modes of a plate by Reissner-Mindlin equations

This paper deals with the approximation of the vibration modes of a plate modelled by the Reissner-Mindlin equations. It is well known that, in order to avoid locking, some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods. In particular, one of the most widely used procedures is the mixed interpolation tensorial components,...

Vibration of a Reissner-Mindlin-Timoshenko plate-beam system

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 ...

Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate

This paper deals with the finite element approximation of the vibration modes of a laminated plate modeled by the Reissner-Mindlin equations; DL3 elements are used for the bending terms and standard piecewise linear continuous elements for the in-plane displacements. An a priori estimate of the regularity of the solution, independent of the plate thickness, is proved for the corresponding load ...

Finite Elements for the Reissner-Mindlin Plate

Wilson's element for the Reissner-Mindlin plate

A new method for the Reissner-Mindlin plate has been proposed. The nonconform-ing Wilson element is used for transverse displacement, rotation is approximated by the usual bilinear element, and an orthogonal projection is applied to the shear stress term. The uniform convergence with respect to the plate thickness is established. Numerical results are provided. The new method is simple in imple...