A simple triangular finite element for nonlinear thin shells: statics, dynamics and anisotropy

A simple fully nonlinear Kirchhoff-Love shell finite element

“…The Kirchhoff-Love shell model, also known as shear rigid because of the absence of shear strain in consequence of its kinematical assumptions, developed in this paper may be understood as a continuation of the work developed by Costa e Silva et al 2018, Costa e Silva et al (2020). and Viebahn et al (2017). It includes a new methodology to approcimate C1 continuity between adjacent elements with penalty and is also is valid for finite deflections, rotations and strains.…”

“…However, classically, the mathematical model implemented on FEM code is based on the weak form of the equilibrium equation. The weak form (in this case, variational formulation) can be obtained applying the principle of virtual work (Wriggers, 2008) (Viebahn et al, 2017) and consequentily we have = − = 0 , ∀ and = ∫ :…”

“…As the displacement field is quadratic, this continuity is guaranteed inside the element. The present work and the work of Viebahn et al (2017) and Costa e Silva (2020) differ in the methodology to enforce C1 continuity in the element interfaces. The procedure adopted in this article can be regarded as a discrete Galerking approach (see Brezzi and Fortin, 1991).…”

“…In the same work, finite rotations were treated by using Euler-Rodrigues formula in a very conviniet way (due to its incremental formulation). Viebahn et al (2017), Costa e Silva et al 2018, Costa e Silva (2020) and Costa e Silva et al (2020) built finite element models based on Kirchoff-Love Hypothesis and are the basis for the current article. The main advantage for using Kirchoff-Love shells is that the element will carry less degrees of freedom per element, simplifying the numerical problem.…”

The Hellan–Herrmann–Johnson method for nonlinear shells

“…The class of rotation-free (RF) elements eliminate the rotational degrees of freedom by using out-of-plane translation degrees of freedom (dofs) [33,9,19]. Alternative approaches are discontinuous Galerkin (DG) methods [17,21,47] and Isogeometric Analysis (IGA) [26,40,28,16]. 1 Corresponding author.…”