ABSTRACT
The locking phenomena in finite elements is characterised by degraded element performance, principally owing to the inability of the finite element to generate lower-order strain modes. An optimisation approach was previously established to overcome locking, which remedies locking by enriching conforming strain terms with a set of hierarchic terms, and optimising the enriched strains towards an objective low-order strain distribution via mathematical optimisation. In this paper, a J 2 invariant-based optimisation function is proposed, which ensures the improved strain tensor to be invariant to the choice of local coordinates and nodal ordering. The modified optimisation approach provides a systematic way of eliminating locking in shell elements for both quadrilateral and triangular elements. Its application to 6-noded and 9-noded shell elements is presented, within the context of large displacement analysis. Linear and geometrically nonlinear numerical examples are finally provided to demonstrate the effectiveness of the proposed shell elements.
