Locking-Free Finite Elements forthe Reissner-Mindlin Plate Model

Richard Falk
Department of Mathematics
Rutgers University

Abstract: The Reissner-Mindlin plate model describes the bending of a thin plate subject to transverse loading in terms of the transverse displacement of the midplane and the rotation of fibers normal to the midplane. When standard low order finite elements are used to approximate these quantities, the problem of "locking" occurs, which results in poor approximations for thin plates.

After giving a brief derivation of the Reissner-Mindlin model and describing some of the key properties of the model, the talk concentrates on locking-free finite element methods for its approximation. A unified approach to error analysis is presented and several examples are given to show the effectiveness of this approach. Included are two new families of locking-free finite elements. Computational results show the sharpness of the estimates obtained. Time permitting, the talk will include a historical perspective of the main ideas behind the derivation of locking-free methods.