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...

Problem statement: Rectangular steel plates are widely used in various steel structures and steel industries. For a proper design of steel plate structures and efficient use of material, the behavior, strength, buckling and post-buckling characteristics of plates should be accurately determined. Approach: Considering the significance of this matter, lateral vibration of thick rectangular plates...

1Department of Mathematics, Purdue University, 1395 Mathematical Sciences Building, West Lafayette, IN 47907-1395, USA. Email: [email protected]. 2Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR 72204, USA. Email: [email protected]. 3MAB, CNRS UPRESA 5466, Université de Bordeaux I, 351 Cours de la Libération, 33400 Takence, France. Email: hzhang@m...

Two new families of Reissner-Mindlin triangular finite elements are analyzed. One family, generalizing an element proposed by Zienkiewicz and Lefebvre, approximates (for k ≥ 1) the transverse displacement by continuous piecewise polynomials of degree k + 1, the rotation by continuous piecewise polynomials of degree k+ 1 plus bubble functions of degree k+ 3, and projects the shear stress into th...