Exact satisfaction of boundary and interface conditions in nodal-integration-based finite element methods
Résumé
In spite of some drawbacks, finite element methods based on nodal rather than Gaussian integration present major advantages, especially in the context of elastoplastic or elastoviscoplastic problemsnotably the elimination of locking problems due the plastic or viscoplastic incompressibility condition, and the reduction of computation and storage requirements pertaining to internal variables. This paper investigates another potential advantage of such methods, namely the possibility to account exactly-instead of approximately like with Gaussian integration-for conditions of prescribed traction on external surfaces, and continuity of the traction-vector across internal interfaces separating different materials. The technique proposed is somewhat similar to that classically used to satisfy plane stress conditions in 2D elastoplastic problems: it consists, when using the constitutive law to evaluate the stresses from the strains, in adjusting the outof-plane components of the strain, so as to enforce either identity of the traction-vector and its prescribed value on external surfaces, or identity of the traction-vectors on both sides of internal interfaces. The examples provided for both traction-free boundaries and interfaces between materials evidence the efficiency of the technique.
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