Abstract In this paper, we develop the mixed variational formulation with independent displacement, rotation and stress fields based on the work of Hughes and Brezzi (1989). However, we further suppress rotation field to obtain element superior performance for classical continuum case with hybrid-stress interpolation. The lowest order Whitney’s interpolation or Raviart–Thomas vector space is employed to discretize stress field, which delivers superior performance by enforcing the continuity of traction field across element boundary. We further extend this optimal choice of hybrid-stress discrete approximation to dynamic analysis, by choosing the appropriate time-integration scheme that enforces stability for long-term computation. Several numerical simulations are given to illustrate an enhanced performance of the proposed element and algorithm.

中文翻译：

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具有增强的静力学和动力学性能的混合应力三角形有限元

摘要 在本文中，我们基于 Hughes 和 Brezzi (1989) 的工作开发了具有独立位移、旋转和应力场的混合变分公式。然而，我们进一步抑制旋转场以获得具有混合应力插值的经典连续介质情况下的单元优越性能。最低阶 Whitney 插值或 Raviart-Thomas 矢量空间用于离散应力场，通过加强跨单元边界的牵引场的连续性来提供卓越的性能。我们通过选择适当的时间积分方案来加强长期计算的稳定性，将这种混合应力离散近似的最佳选择进一步扩展到动态分析。给出了几个数值模拟来说明所提出的元素和算法的增强性能。