A simple fully nonlinear cubic triangular element for multilayer Kirchhoff-Love shells - nonlinear dynamics
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ABSTRACT This work presents a new triangular multi-layer nonlinear shell finite element, suitable for large displacements and rotations, with a dynamic behaviour described with the Newmark method for the time integration as in [1]. The current work is a dynamics extension of the statics formulation of the base element, first presented in [2], which is a nonconforming element with 16 nodes, cubic displacement interpolation, and enforcement of the rotation field based on Rodrigues rotation parameters and Lagrange Multipliers or penalty parameters in 6 side nodes, with a total of 42 degrees of freedom. Here, we focus on the displacement of the structures over time when subjected to a load, without focusing on the analysis of energy and momentum conservation. Associated with the new element, the development of a multilayer kinematical model with Kirchhoff-Love theory, approximating the shell director across layers as constant, is presented. The model is numerically implemented, and results show the excellent capabilities of the formulation. Although Lagrange Multipliers and penalty parameters are used to enforce C1 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 both in static as in dynamic analysis. REFERENCES [1] Viebahn N., Pimenta P. M., Schröder J. (2017). A simple triangular finite element for nonlinear thin shells: statics, dynamics and anisotropy. Computational Mechanics, v. 59, n. 2, p. 281-297. [2] Gomes G. C., Pimenta P. M., Ibrahimbegovic A. (2025). A fully nonlinear cubic triangular multilayer Kirchhoff–Love shell element with accurate shear stress analysis. Computational Mechanics, p. 1-23
