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Based on a variational principle with relaxed inter-element continuity requirements, a refined hybrid quadrilateral degenerated shell element GNRH6, which is a non-conforming model with six internal displacements, is proposed for the geometrically non-linear analysis. The orthogonal approach and non-conforming modes are incorporated into the geometrically non-linear formulation. Numerical results show that the orthogonal approach can improve computational efficiency while the non-conforming modes can eliminate the shear/membrane locking phenomenon and improve the accuracy. © 1998 John Wiley & Sons, Ltd.