Enrichment of the finite element method with the reproducing kernel particle method.(English)Zbl 0920.73366

We present a multiple field computational procedure to enrich the finite element method with the reproducing kernel particle method (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 functions at selected nodes with higher-order RKPM window functions, we obtain RKPM $$p$$-enrichment. 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.

MSC:

 74S30 Other numerical methods in solid mechanics (MSC2010) 74S05 Finite element methods applied to problems in solid mechanics
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