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<p>This paper presents a new triangular multi-layer nonlinear shell finite element, suitable for large displacements and rotations, and a formulation to obtain through the thickness shear stress considering both geometrical and material nonlinearity. This is a nonconforming element with 16 nodes, cubic displacement interpolation and enforcement of the rotation field based on Rodrigues rotation parameters and Lagrange Multipliers in 6 side nodes, with a total of 42 degrees of freedom. Associated with the new element, the development of a multilayer kinematical model with Kirchhoff-Love theory, approximating the shell director across layers as constant, and the formulation to obtain through the thickness shear stress considering both geometrical and material nonlinearity is presented. The model is numerically implemented, and, results are compared to different references in multiple examples, showing the enhanced capabilities of the formulation. Although Lagrange Multipliers and penalty parameters are used to enforce <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^1\)</EquationSource> </InlineEquation> continuity, it is believed that, due to it being possibly the simplest multilayer extension, simple kinematic, a relatively small number of degrees of freedom, possibility to use various 3D material models, easily connected with multiple branched shells and beams, and geometric exact theory, this is a simple yet powerful shell element. The shear stress formulation, used with nonlinear materials, presents itself as a novelty, deviating from the standard use of linear material behaviour with co-rotational formulations, with good results.</p>

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A fully nonlinear cubic triangular multilayer Kirchhoff–Love shell element with accurate shear stress analysis

  • 期刊论文

  • 发表日期：

    2025年11月20日

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  • Gustavo Canário Gomes,
  • Paulo de Mattos Pimenta,
  • Adnan Ibrahimbegovic

摘要

This paper presents a new triangular multi-layer nonlinear shell finite element, suitable for large displacements and rotations, and a formulation to obtain through the thickness shear stress considering both geometrical and material nonlinearity. This is a nonconforming element with 16 nodes, cubic displacement interpolation and enforcement of the rotation field based on Rodrigues rotation parameters and Lagrange Multipliers in 6 side nodes, with a total of 42 degrees of freedom. Associated with the new element, the development of a multilayer kinematical model with Kirchhoff-Love theory, approximating the shell director across layers as constant, and the formulation to obtain through the thickness shear stress considering both geometrical and material nonlinearity is presented. The model is numerically implemented, and, results are compared to different references in multiple examples, showing the enhanced capabilities of the formulation. Although Lagrange Multipliers and penalty parameters are used to enforce \(C^1\) continuity, it is believed that, due to it being possibly the simplest multilayer extension, simple kinematic, a relatively small number of degrees of freedom, possibility to use various 3D material models, easily connected with multiple branched shells and beams, and geometric exact theory, this is a simple yet powerful shell element. The shear stress formulation, used with nonlinear materials, presents itself as a novelty, deviating from the standard use of linear material behaviour with co-rotational formulations, with good results.