Imposition of essential boundary conditions by displacement constraint equations in meshless methods

One of major difficulties in the implementation of meshless methods is the imposition of essential boundary conditions as the approximations do not pa ss through the nodal parameter values. As a consequence, the imposition of essential boundary conditions in meshless methods is quite awkward. In this paper, a displacement constraint equations method (DCEM) is proposed for t he imposition of the essential boundary conditions, in which the essential boundary conditions is treated as a constraint to the discrete equations ob tained from the Galerkin methods. Instead of using the methods of Lagrange multipliers and the penalty method, a procedure is proposed in which unknow ns are partitioned into two subvectors, one consisting of unknowns on bound ary Gamma (u), and one consisting of the remaining unknowns. A simplified d isplacement constraint equations method (SDCEM) is also proposed, which res ults in a efficient scheme with sufficient accuracy for the imposition of t he essential boundary conditions in meshless methods. The present method re sults in a symmetric, positive and banded stiffness matrix. Numerical resul ts show that the accuracy of the present method is higher than that of the modified variational principles. The present method is a exact method for i mposing essential boundary conditions in meshless methods, and can be used in Galerkin-based meshless method, such as element-free Galerkin methods, r eproducing kernel particle method, meshless local Petrov-Galerkin method. C opyright (C) 2001 John Wiley & Sons, Ltd.