A REFINED 4-NODED MEMBRANE ELEMENT WITH ROTATIONAL DEGREES OF FREEDOM

The paper begins by noting the development and recent success of membrane elements which include in-plane nodal rotations as degrees of freedom. Particular attention is given to D. J. Allman's solution for the three-noded triangular element and the extension of his method by D. Cook to four-noded quadrilaterals. Three modifications are then proposed whose combined effects is to correct the deficiencies while preserving satisfaction of the C//0 patch test. The modifications include least square smoothing of the strains computed from displacement shape functions so as to retain only linear terms, the addition of two auxiliary strain terms whose adjoint effect is to enforce internal stress equilibrium, and spurious mode control. Test results are described.