A new family of locking-free finite elements for shear deformable Reissner-Mindlin plates is presented. The elements are based on the "tangential-displacement normal-normal-stress" formulation of elasticity. In this formulation, the bending moments are treated as separate unknowns. The degrees of freedom for the plate element are the nodal values of the deflection, tangential components of the ...

Continuum element sensitivity analysis (CONTESA) and system optimization (SYSOPT) for Noise, Vibration, and Harshness (NVH) have been developed and applied to automobile structures for sizing, topology, and configuration design using Mindlin plate and Timoshenko beam theories. The topology optimization has been developed using the density approach, sequential linear programming, and the adjoint...

A meshless local Petrov-Galerkin (MLPG) method is applied to solve problems of Reissner-Mindlin shells under thermal loading. Both stationary and thermal shock loads are analyzed here. Functionally graded materials with a continuous variation of properties in the shell thickness direction are considered here. A weak formulation for the set of governing equations in the Reissner-Mindlin theory i...

In this paper, we develop two least-squares approaches for the solution of the Stokes equations perturbed by a Laplacian term. (Such perturbed Stokes equations arise from finite element approximations of the Reissner–Mindlin plate.) Both are two-stage algorithms that solve first for the curls of the rotation of the fibers and the solenoidal part of the shear strain, then for the rotation itself...

This paper deals with the approximation of the buckling coefficients and modes of a clamped plate modeled by the Reissner-Mindlin equations. These coefficients are related with the eigenvalues of a non-compact operator. We give a spectral characterization of this operator and show that the relevant buckling coefficients correspond to isolated nondefective eigenvalues. Then we consider the numer...

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 Reissner-Mindlin plate models thin plates. The condition numbers of finite element approximations of these plate models increase very rapidly as the thickness of the plate goes to 0. A Balancing Domain Decomposition by Constraints (BDDC) Deluxe method is developed for these plate problems discretized by Falk-Tu finite elements. In this new algorithm, subdomain Schur complements restricted t...

Experimentally determined natural frequencies and modes shapes are presented for an elastically point-supported isotropic plate with attached masses under impulsive loading. These results are compared to frequencies and to modes shapes determined from the Rayleigh–Ritz method and a finite element analysis using COMSOL. Accelerometers mounted at three locations on the plate, provide input for ME...

This paper establishes a very general theory for a posteriori error analysis of finite element methods of the Reissner-Mindlin plate problem in the literature. The theory assures reliability of explicit residual error estimates. The conclusion of this theory is sparsity in the mathematical research of uniform a posteriori error control. Indeed, the a posteriori error estimate for various finite...