On elimination of shear locking in the element-free Galerkin method

In this study, a method for completely eliminating the presence of transver se shear locking in the application of the element-free Galerkin method (EF GM) to shear-deformable beams and plates is presented. The matching approxi mation fields concept of Donning and Liu has shown that shear locking effec ts may be prevented if the approximate rotation fields are constructed with the innate ability to match the approximate slope (first derivative of dis placement) fields and is adopted. Implementation of the matching fields con cept requires the computation of the second derivative of the shape functio ns. Thus, the shape functions for displacement fields, and therefore the mo ving least-squares (MLS) weight function, must be at least C-1 continuous. Additionally, the MLS weight functions must be chosen such that successive derivatives of the MLS shape function have the ability to exactly reproduce the functions from which they were derived. To satisfy these requirements, the quartic spline weight function possessing C-2 continuity is used in th is study. To our knowledge, this work is the first attempt to address the r oot cause of shear locking phenomenon within the framework of the element-f ree Galerkin method, Several numerical examples confirm that bending analys es of thick and thin beams and plates, based on the matching approximation fields concept, do not exhibit shear locking and provide a high degree of a ccuracy for both displacement and stress fields. Copyright (C) 2001 John Wi ley & Sons, Ltd.