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

摘要

In the reproducing kernel particle method (RKPM), and meshless methods in general, enforcement of essential boundary conditions is awkward as the approx- imations do not satisfy the Kronecker delat condition and are not admissible in the Galerkin formulation as they fail to vanish at essential boundaries. Typically, Lagrange multipliers, modified variational principles, or a coupling procedure with finite elements have been used to cir- cumvent these shortcomings. Two methods of generating admissible meshless ap- Proximations, are presented; one in which the RKPM Correction function equals zero at the boundary, and an- Other in which the domain of the window function is se- Lected such that the approximate vanishes at the boundary.