Preconditioning discrete approximations of the Reissner-Mindlin plate model

Least-squares finite element approximations for the Reissner-Mindlin plate

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...

Finite Elements for the Reissner-Mindlin Plate

Some New Elements for the Reissner–Mindlin Plate Model

In this work-in-progress we report on a new approach to obtaining stable locking-free discretizations of the Reissner–Mindlin plate model. For a plate of thickness t with midplane section Ω ⊂ R the clamped Reissner–Mindlin plate model determines ω , the transverse displacement of the midplane, and φ , the rotation of fibers normal to the midplane, as the unique minimizer over H̊1(Ω)× H̊(Ω) of the...

The Boundary Layer for the Reissner–mindlin Plate Model*

The structure of the solution of the Reissner–Mindlin plate equations is investigated, emphasizing its dependence on the plate thickness. For the transverse displacement, rotation, and shear stress, asymptotic expansions in powers of the plate thickness are developed. These expansions are uniform up to the boundary for the transverse displacement, but for the other variables there is a boundary...

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...