Admissible approximations for essential boundary conditions in the reproducing kernel particle method

In the reproducing kernel particle method (RKPM), and meshless methods in general, enforcement of essential boundary conditions is awkward as the ap-proximations do not satisfy the Kronecker delta condition and are not admis-sible in the Galerkin formulation as they fail to vanish at essential boundaries. Typically, Lagrange multipliers, modied variational principles, or a coupling procedure with nite elements have been used to circumvent these shortcom-ings. Two methods of generating admissible meshless approximations, are pre-sented; one in which the RKPM correction function equals zero at the boundary, and another in which the domain of the window function is selected such that the approximate vanishes at the boundary. An extension of the RKPM dilation parameter is also introduced, providing the capability to generate approxima-tions with arbitrarily shaped supports. This feature is particularly useful for generating approximations near boundaries that conform to the geometry o