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<p>The DKMT shell element, based on the discrete Kirchhoff–Mindlin theory, is effective and accurate for applications ranging from thick to thin shells. However, its incomplete quadratic approximation for rotations significantly reduces computational efficiency, and its reliance on penalty factors to suppress spurious drilling modes limits robustness. To address these issues, this study employs the physical stabilization method to achieve single-point integration, enhancing computational efficiency while maintaining compatibility. Additionally, an algorithm to obtain a continuous director field is proposed, and combined with an improved method to suppress spurious drilling modes, the element’s dependence on penalty factors is eliminated. This results in a robust, reliable, and efficient shell element, providing a valuable reference for drilling control in shell elements. Besides, this element successfully passes patch and zero-energy tests. Its excellent performance is demonstrated through various benchmark problems, including both geometric linear and nonlinear analyses.</p>

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An efficient and robust triangular shell element for geometric linear and nonlinear analysis

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • Qi Ran,
  • Huan Zhang,
  • Zeyu Chen,
  • Feiqi Wang,
  • She Li,
  • Jian Wu,
  • Xiangyang Cui

摘要

The DKMT shell element, based on the discrete Kirchhoff–Mindlin theory, is effective and accurate for applications ranging from thick to thin shells. However, its incomplete quadratic approximation for rotations significantly reduces computational efficiency, and its reliance on penalty factors to suppress spurious drilling modes limits robustness. To address these issues, this study employs the physical stabilization method to achieve single-point integration, enhancing computational efficiency while maintaining compatibility. Additionally, an algorithm to obtain a continuous director field is proposed, and combined with an improved method to suppress spurious drilling modes, the element’s dependence on penalty factors is eliminated. This results in a robust, reliable, and efficient shell element, providing a valuable reference for drilling control in shell elements. Besides, this element successfully passes patch and zero-energy tests. Its excellent performance is demonstrated through various benchmark problems, including both geometric linear and nonlinear analyses.