Locking-free 6-noded triangular shell elements based on hierarchic optimisation

Conforming lower-order shell elements based on Reissner-Mindlin plate theory generally exhibit an over-stiff response under loading, typically manifested through various forms of locking. A recently developed hierarchic optimisation approach addresses locking by enriching the conforming strains with hierarchic strain terms towards an objective ‘smoother’ strain distribution afforded by the element, which has proven to be effective in relieving shear, membrane and distortion locking in 9-noded quadrilateral shell elements. Nevertheless, in some practical structural problems that involve complex geometry, triangular shell elements are required to avoid a highly distorted mesh of quadrilateral elements. This paper presents a family of 6-noded Reissner-Mindlin triangular shell elements based on the hierarchic optimisation approach. The proposed curved triangular shell elements not only effectively alleviate inaccuracies arising from locking, but also embrace the desirable characteristics of spatial isotropy and insensitivity to element distortion. The family of 6-noded triangular elements have been incorporated within a co-rotational framework to allow large displacement analysis of thin to moderately thick plates and shells. Several numerical examples are finally presented to demonstrate the effectiveness and accuracy of the proposed 6-noded shell element formulation as well as its superior locking-free performance compared to existing shell elements