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.

基于 Reissner-Mindlin 板理论的一致低阶壳单元通常在载荷下表现出过硬的响应，通常通过各种形式的锁定表现出来。最近开发的分层优化方法通过使用分层应变项来丰富符合应变以实现由单元提供的客观“更平滑”应变分布来解决锁定问题，这已被证明可有效缓解 9 节点四边形壳中的剪切、膜和变形锁定元素。然而，在一些涉及复杂几何形状的实际结构问题中，需要三角形壳单元来避免四边形单元的高度扭曲网格。本文提出了一个基于层次优化方法的 6 节点 Reissner-Mindlin 三角壳单元族。所提出的弯曲三角形壳单元不仅有效地减轻了锁定引起的不准确性，而且还具有空间各向同性和对单元变形不敏感的理想特性。6 节点三角形单元系列已被纳入同向旋转框架中，以允许对薄到中等厚的板和壳进行大位移分析。最后给出了几个数值例子来证明所提出的 6 节点壳单元公式的有效性和准确性，以及与现有壳单元相比其优越的无锁定性能。6 节点三角形单元系列已被纳入同向旋转框架中，以允许对薄到中等厚的板和壳进行大位移分析。最后给出了几个数值例子来证明所提出的 6 节点壳单元公式的有效性和准确性，以及与现有壳单元相比其优越的无锁定性能。6 节点三角形单元系列已被纳入同向旋转框架中，以允许对薄到中等厚的板和壳进行大位移分析。最后给出了几个数值例子来证明所提出的 6 节点壳单元公式的有效性和准确性，以及与现有壳单元相比其优越的无锁定性能。