REISSNER-MINDLIN EXTENSIONS OF KIRCHHOFF ELEMENTS FOR PLATE BENDING

A method of extending various existing Kirchhoff elements to Reissner-Mindlin elements for plate bending is developed and tested. The essential idea is to use independent transverse shear strains and a special mixed formulation. The Nedelec edge element is effective for assuming the shear strains. Furthermore, the displacements are carefully constructed so that the strain-displacement relations are strictly satisfied for the transverse shear strains. We present our approach for displacement-based three-node triangular elements including both conforming and non-conforming ones as the base Kirchhoff elements. It is also possible to reduce the shear variables from the element degrees of freedom by means of a special technique called the beam element approximation. Numerical results are obtained for some fundamental test problems and are generally reasonable over wide range of plate thickness. In particular, it is observed that the tested elements actually reduce to the base Kirchhoff element in the thin plate range and are free from transverse shear locking.