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Hybrid-Mixed Low-Order Finite Elements for Geometrically Exact Shell Models: Overview and Comparison

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Abstract

We critically review and compare fifteen mixed and mixed-hybrid nonlinear shell finite element formulations with 4 nodes in order to identify those that are closest to the “optimal” one. We consider formulations that are based either on Assumed Natural Strain concept, Enhanced Assumed Strain concept, Hellinger–Reissner functional or Hu–Washizu functional, and those that effectively combine several of the mentioned approaches. Most of the formulations are state-of-the-art, but some are also presented for the first time. We show that the flexibility of mixed-hybrid formulations requires careful consideration of theoretical and numerical aspects in the process of design of a high-performance element. We make extensive numerical experiments in order to assess convergence properties, mesh distortion sensitivity, and computational speed (that is associated with the ability to achieve large steps during the solution search) of the considered formulations. We show that the application of the idea to combine mixed-hybrid formulations of the Hellinger–Reissner and Hu–Washizu type with the Assumed Natural Strain and/or the Enhanced Assumed Strain concepts generates the formulations that perform excellent. We also identify the formulations that are currently closest to the “optimal” one.

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This study was funded by the Slovenian Research Agency (Grant Number J2-1722).

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    Marko Lavrenčič & Boštjan Brank

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Lavrenčič, M., Brank, B. Hybrid-Mixed Low-Order Finite Elements for Geometrically Exact Shell Models: Overview and Comparison. Arch Computat Methods Eng 28, 3917–3951 (2021). https://doi.org/10.1007/s11831-021-09537-2

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