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Abstract:
Mixed 4-node elements based on the Hu–Washizu (HW) functional are developed for the representation of the assumed strain in the natural basis at the element’s center, i.e. for the contravariant transformation rule. In other aspects, the formulation is identical as in our previous paper [9], to which this note is an addendum.

Two mixed HW elements based on the 5-parameter stress are developed; they use either the 7-parameter or 9-parameter strain representation. The stress and strain representations are assumed in terms of skew coordinates, see [10]. The numerical tests involving coarse distorted meshes are used to assess the effects of using the contravariant strain representation.

The tests show that both elements pass the discrete inf-sup test. Accuracy of the element based on the 9-parameter strain, designated as HW14-S and selected as the best in [9], remains unaffected. Accuracy of the element based on the 7-parameter strain is significantly improved.

Keywords:
Four-node finite elements, Hu–Washizu functional, Plane stress, Mixed elements, Skew coordinates, Contravariant assumed strain