Reissner-Mindlin Plate Bending Elements with Shear Freedoms

摘要

This paper presents the formulation of a new triangular Reissner-Mindlin plate bending element based on the displacement finite element method. This element utilises cubic and quadratic shape functions for the transverse displacement field (w) and the two rotational fields ( θ ), respectively. However, the tangential shear strain is constrained along each element edge to a constant value, thereby allowing the tangential rotation and the two displacement freedoms internal to each edge to be replaced by a single shear freedom. The paper proceeds by deriving the shape functions for the new element, with particular consideration given to simple edge supports, which are not normally associated with constant tangential shear strains. Two alternative approaches are then suggested to enable the proposed element to pass the patch test, the first employing an internal element freedom and the second based on a substitute shear field. Significantly, the conforming formulation has the added benefit of representing linear curvature exact solutions, whereas the nonconforming formulation can be applied as a discrete Kirchhoff element by restraining all edge shear freedoms. A new procedure is suggested for evaluating the ‘shear locking’ characteristics of individual elements as well as element assemblages, which is applicable to the general case in which the sampled shear strains are dependent. The proposed triangular element has been implemented within ADAPTIC, which is used in two numerical examples to investigate the performance of both the conforming and non-conforming element types. These examples show that the conforming element generally exhibits superior convergence characteristics.