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A simple geometrically exact finite element for thin shells—Part 1: statics

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Abstract

This paper presents a new triangular nonlinear shell finite element with a novel kinematic model suitable for simulation with large displacements and rotations, herein introduced as “T6-3iKL”. This element has 6 nodes, a quadratic displacement field, and a linear rotation field based on Rodrigues incremental rotation parameters, giving in total 21 degrees of freedom. The novelty of this shell element concerns a new kinematic model with properties from Kirchhoff-Love shell theory, making it possible to eliminate the drilling DOF in the rotation field (compared to Mindlin-Reissner models), approximating the rotation continuity between adjacent elements by a single scalar and allowing multiple branch connections in the mesh, making this element very simple and interesting, with no artificial parameters imputed by the code (such as penalties or Lagrange multipliers). The element permits the implementation of different material constitutive equations, including elastic anisotropic models, and the thickness of the shell is optionally allowed to change through the simulation. The model developed in this article is numerically implemented and the results compared to different references in multiple examples, showing the consistency and reliability of the new formulation. It is believed that this new versatile triangular shell element, with no necessity of artificial penalty calibration, simple kinematics, a relatively small number of DOFs, geometric exactness, the possibility to use 3D material constitutive models, and easy connection with multiple branched shells and beams, implemented together with reliable mesh generation, may be an effective option for shell simulation in many engineering applications.

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Acknowledgements

Matheus, Paulo, and Adnan gratefully acknowledge the support by ANR-FAPESP through the thematic grant 2020/13362-1 with the title “Mechanics, Stochastics and Control with Code-Coupling: System-of-Multibody-Systems point-of-view to Optimize Off-Shore/In-Land Farms of Wind Turbines with Flexible Blades” (MS3C project) that made this work possible. Matheus Lucci Sanchez thankfully acknowledges Clark Solutions, where he works as a project engineer, for financial support, knowledge, applicability, and industrial experience. P. M. Pimenta acknowledges support by CNPq under grant 308142/2018-7 and the Alexander von Humboldt Foundation for the Georg Forster Award that made possible his stays at the Universities of Duisburg-Essen and Hannover in Germany.

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Authors and Affiliations

  1. Polytechnic School, University of São Paulo, Av. Prof. Almeida Prado, travessa 2, 83, São Paulo, SP, 05424-970, Brazil

    Matheus L. Sanchez & Paulo M. Pimenta

  2. Centre de Recherches Royallieu, Université de Technologie de Compiègne, Compiègne, 60203, France

    Adnan Ibrahimbegovic

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  1. Matheus L. Sanchez
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  2. Paulo M. Pimenta
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Correspondence to Matheus L. Sanchez.

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Sanchez, M.L., Pimenta, P.M. & Ibrahimbegovic, A. A simple geometrically exact finite element for thin shells—Part 1: statics. Comput Mech 72, 1119–1139 (2023). https://doi.org/10.1007/s00466-023-02339-2

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