An analysis is presented for a recently proposed nite element method for the Reissner{ Mindlin plate problem. The method is based on the standard variational principle, uses nonconforming linear elements to approximate the rotations and conforming linear elements to approximate the transverse displacements, and avoids the usual \locking problem" by interpolating the shear stress into a rotated ...

In this paper, we will consider the modelling of problems in linear elasticity on thin plates by the models of Kirchhoff–Love and Reissner– Mindlin. A fundamental investigation for the Kirchhoff plate goes back to Morgenstern [Herleitung der Plattentheorie aus der dreidimensionalen Elastizitätstheorie. Arch. Rational Mech. Anal. 4, 145–152 (1959)] and is based on the two-energies principle of P...

The application of finite element methods to problems in structural acoustics ( the vibration of an elastic body coupled to an acoustic fluid medium) is considered. New stabilized methods based on the Hellinger-Reissner variational principle with a generalized least-squares modification are developed which yield improvement in accuracy over the standard Galerkin finite element method for both i...

this paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. the characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal mindlin plate. this theory is considering both the small length scale effects and transverse shear deformation ef...

Four quadrilateral elements for the Reissner-Mindlin plate model are considered. The elements are the stabilized MITC4 element of Lyly, Stenberg and Vihinen [27], the MIN4 element of Tessler and Hughes [35], the Q4BL element of Zienkiewicz et al [39] and the FMIN4 element of Kikuchi and Ishii [21]. For all elements except the Q4BL element, a unifying variational formulation is introduced, and o...

In this paper we present a solution to a shape optimization problem involving plate and shell structures subject to natural vibration. The volume is chosen as the response to be minimized under a specified eigenvalue constraint with mode tracking. The designed boundaries are assumed to be movable in the in-plane direction so as to maintain the initial curvatures. The surfaces are discretized by...

In this paper, micromechanics methods are applied to characterize the damage of plate structures, both Love-Kirchhoff and Reissner-Mindlin plates, due to microcrack distribution. Analytical expressions for effective stiffness of a damaged plate with distributed microcracks are derived for the first time. The results are compared with the results based on continuum damage theory, and it is found...