A triangular element with rotational degrees of freedom

Abstract

A new plane-stress triangular element is derived using the free formulation of Bergan and Nygård. The triangle possesses nine degrees of freedom: six corner translations and three corner normal rotations. The element is coordinate-invariant and passes the patch test for any geometry. Two free parameters in the formulation may be adjusted to optimize the behavior for in-plane bending patterns. With the recommended parameter choices the element performance is significantly better than that of the constant-strain triangle. Because of the presence of the rotational freedoms, this new element appears especially suitable as membrane component of a flat triangular element for modelling general shell structures.