ELEMENT-FREE GALERKIN METHODS

An element-free Galerkin method which is applicable to arbitrary shape s but requires only nodal data is applied to elasticity and heat condu ction problems. In this method, moving least-squares interpolants are used to construct the trial and test functions for the variational pri nciple (weak form); the dependent variable and its gradient are contin uous in the entire domain. In contrast to an earlier formulation by Na yroles and coworkers, certain key differences are introduced in the im plementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of fin ite elements significantly and a high resolution of localized steep gr adients can be achieved: The moving least-squares interpolants and the choices of the weight function are also discussed in this paper.