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TECHNICAL PAPERS

Enrichment of the Finite Element Method With the Reproducing Kernel Particle Method

[+] Author and Article Information
Wing Kam Liu, Y. Chen

Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208

R. A. Uras

Reactor Engineering Division, Argonne National Laboratory, 9700 S. Cass Avenue, Bldg. 208, Argonne, IL 60439

J. Appl. Mech 64(4), 861-870 (Dec 01, 1997) (10 pages) doi:10.1115/1.2788993 History: Received December 05, 1996; Revised May 06, 1997; Online October 25, 2007

Abstract

The reproducing kernel particle method (RKPM) has attractive properties in handling high gradients, concentrated forces, and large deformations where other widely implemented methodologies fail. In the present work, a multiple field computational procedure is devised to enrich the finite element method with RKPM, and RKPM with analytical functions. The formulation includes an interaction term that accounts for any overlap between the fields, and increases the accuracy of the computational solutions in a coarse mesh or particle grid. By replacing finite element method shape Junctions at selected nodes with higher-order RKPM window functions, RKPM p-enrichment is obtained. Similarly, by adding RKPM window functions into a finite element method mesh, RKPM hp-enrichment is achieved analogous to adaptive refinement. The fundamental concepts of the multiresolution analysis are used to devise an adaptivity procedure.

Copyright © 1997 by The American Society of Mechanical Engineers
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