An edge center based strain-smoothing element with discrete shear gap for the analysis of Reissner–Mindlin shell

In this paper, an edge center based strain-smoothing element with discrete shear gap method (ECSSE-DSG) based on triangular Reissner–Mindlin flat shell element is proposed to solve shell problems. In the proposed ECSSE, the strains for three edge centers were calculated by the strain-smoothing method, which performed strain-smoothing operation directly on the three edges of a linear finite element instead of requiring an extra smoothing domain. In this way, not only could a linear strain field be constructed within an element, but strain consistency at the center of the element’s intersecting edges could also be ensured. The proposed ECSSE was adopted to manage membrane and bending strains. Meanwhile, the discrete shear gap (DSG) method was organically combined with the ECSSE for processing the shear strain to eliminate shear-locking. The ECSSE-DSG showed outstanding performance in a variety of tests, including those for plates, folded plates and curved shells; static, free vibration, dynamic, and buckling analyses; benchmark and engineering examples. High accuracy was obtained for both displacement and strain energy, there was no appearance of shear-locking, a smoother stress field was produced, and there was temporal stability. The excellent performance of the ECSSE-DSG when employed for engineering problems indicated its promising practical application prospects. •An Edge Center Based Strain-Smoothing Element (ECSEE) with Discrete Shear Gap (DSG) is proposed to solve shell problems.•In ECSSE, a linear strain field is constructed within the element, and the strain at the center of element junction is consistent.•The ECSSE is adapted to process membrane and bending strain, and the DSG is employed for avoiding shear-locking.•The proposed ECSSE-DSG has demonstrated outstanding performance in a variety of numerical examples.