A simple fully nonlinear Kirchhoff-Love shell finite element with thickness variation

Resumo

The current paper develops a new multi parameter Kirchhoff-Love shell finite element with thickness
variation able to reliably simulate thin nonlinear shell for static structural boundary value problems. The study is
a continuation of previous elements developed in Sanchez et al [1] and Costa e Silva [2]. The element has 6 nodes
and uses penalty (or optionally Lagrange method) to deal with the C1 continuity, which is a kinematical
requirement of the Kirchhoff-Love shell model. It is also used a nonconform field of an incremental rotation
variable φΔ (this parameter is firstly introduced in Costa e Silva [2]) to assist with the C1 continuity on element
edges. As a novelty in this study, the C1 continuity on the edges between elements is not further guaranteed by the
maintenance of the kinking angle (as done in Viebahn et al [3]) or by the equivalence of φΔ calculated through
the displacements and the DoF shared by elements (as done in Sanchez et al [1] and Costa e Silva [2]). Now the
C1 continuity is achieved by enforcing the transverse shear strain to zero. For the thickness variation, it is
implemented a double linear non conform field similarly to Pimenta et al [4] to represent the quadratic
displacement at transverse normal to midplane of the shell. The quadratic displacement field of the mid plane is
represented as usual by the 6 parameters at the 6 nodes of the element.