Shear Locking in Isoparametric Spline Finite Strips (No. R876)

Abstract

The Mindlin plate bending theory includes shear deformations in the formulation to better reproduce the behaviour of thick plates and to avoid difficulties in satisfying continuity requirements along strip boundaries. Unfortunately, in many thin plate applications over-stiff solutions are encountered due to the development of spurious stiffness contributions in the numerical solution. This phenomenon is usually referred to as “locking” and if associated with an insufficient representation of bending and shear deformations is called “shear locking”. A method for testing the performance of finite elements with regard to shear locking is described. The method is called “the monomial test” and has been introduced by Briassoulis (1988) who applied it to a series of beam and plate elements. The monomial test is applied for the first time to the isoparametric spline finite strip method. The effect of shear locking on the performance of the isoparametric spline finite strip is investigated in detail as is the ameliorating influence of selective reduced integration. The influence of the order and magnitude of the distortion of the strip, the integration scheme and the number of longitudinal sections of the isoparametric spline finite strip are analysed. Numerical examples are included to illustrate the concepts described.