natural vibration analysis of plates represents an important issue in engineering applications. in this paper, a new and simplify method for vibration analysis of circular and rectangular plates is presented. the design of an effective robust controller, which consistently attenuates transverse vibration of the plate caused by an external disturbance force, is given. the dynamics of the plate i...

Abstract We study how three-dimensional linearized elasticity for thin plates can be approximated by a two-dimensional projection. The classical approach using formal asymptotic expansions in powers of the thickness in the Hellinger-Reissner formulation, only provides error estimates in the H1 norm for the displacements, assuming at least L2 regularity for the applied forces, plus additional re...

We construct a conserved, symmetric energy-momentum (pseudo-)tensor for Chern-Simons modified gravity, thus demonstrating that the theory is Lorentz invariant. The tensor is discussed in relation to other gravitational energy-momentum tensors and analyzed for the Schwarzschild, Reissner-Nordstrom, and FRW solutions. To our knowledge this is the first confirmation that the Reissner-Nordstrom and...

Stabilized finite element formulation for the Reissner-Mindlin plate model is considered. Physical interpretation for the stabilization procedure for low order elements is established. Explicit interpolation functions for linear and bilinear stabilized MITC elements are derived. Some numerical examples including buckling and frequency analyses are presented. Copyright c © 2000 John Wiley & Sons...

We develop a family of locking-free elements for the Reissner– Mindlin plate using Discontinuous Galerkin techniques, one for each odd degree, and prove optimal error estimates. A second family uses conforming elements for the rotations and nonconforming elements for the transverse displacement, generalizing the element of Arnold and Falk to higher degree.

In this study, a dynamic Mindlin–Reissner-type plate is developed based on simplified version of Mindlin’s form-II first-strain gradient elasticity theory. The governing equations motion and the corresponding boundary conditions are derived using general virtual work variational principle. presented model contains, apart from two classical Lame constants, one additional microstructure material ...

This paper establishes a unified a posteriori error estimator for a large class of conforming finite element methods for the Reissner-Mindlin plate problem. The analysis is based on some assumption (H) on the consistency of the reduction integration to avoid shear locking. The reliable and efficient a posteriori error estimator is robust in the sense that the reliability and efficiency constant...

The near extremal Reissner-Nordström black holes in arbitrary dimensions can be modeled by the JackiwTeitelboim (JT) theory. The asymptotic Virasoro symmetry of the corresponding JT model exactly reproduces, via Cardy’s formula, the deviation of the Bekenstein-Hawking entropy of the Reissner-Nordström black holes from extremality. We also comment how can we extend this approach to investigate t...