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<p>This paper investigates the applicability of the DK (Discrete Kirchhoff) and DKM (Discrete Kirchhoff–Mindlin) shell element classes for the first time within the framework of the standard (and sequential) finite-element-based limit analysis, which is a direct method used for determining the plastic collapse (and post-collapse) behavior of structures. Despite these elements not being able to guarantee a strict upper bound, it is shown that they exhibit a significantly lower discretization error compared to the strict upper-bound formulated shell elements used in literature. The higher numerical efficiency of quadrangle elements over triangle elements is observed. The behavior of the tested shell elements on distorted meshes is also explored and discussed. The convergence orders of the tested shell elements are also estimated.</p>

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Performance of the DK and DKM shell elements in the standard, and the sequential, finite-element based limit analysis

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月13日

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  • Vítězslav Štembera

摘要

This paper investigates the applicability of the DK (Discrete Kirchhoff) and DKM (Discrete Kirchhoff–Mindlin) shell element classes for the first time within the framework of the standard (and sequential) finite-element-based limit analysis, which is a direct method used for determining the plastic collapse (and post-collapse) behavior of structures. Despite these elements not being able to guarantee a strict upper bound, it is shown that they exhibit a significantly lower discretization error compared to the strict upper-bound formulated shell elements used in literature. The higher numerical efficiency of quadrangle elements over triangle elements is observed. The behavior of the tested shell elements on distorted meshes is also explored and discussed. The convergence orders of the tested shell elements are also estimated.