A SIMPLE FULLY NONLINEAR KIRCHHOFF-LOVE SHELL FINITE ELEMENT

Abstract

THE CURRENT PAPER DOES AN IMPLEMENTATION OF A SIMPLE FULLY NON-LINEAR KIRCHHOFF-LOVEL SHELL PENALTY BASED FINITE ELEMENT. THE 6 NODES AND 21 DOF TRIANGULAR ELEMENT DEVELOPED IN THIS WORK HAS A QUADRATIC DISPLACEMENT FIELD ASSOCIATED TO IT AND THE C₁ CONTINUITY REQUIRED BY KIRCHHOFF-LOVE HYPHOTESIS IS APPROXIMATED BY AN INTERNAL PENALTY AUXILLIATED BY A SCALAR VARIABLE LOCATED AT EDGES BETWEEN NEIGHBORING ELEMENTS. THE KINEMATICAL MODEL AND ANALYTICAL DEVELOPMENT OF THE FINITE ELEMENT MAY BE UNDERSTOOD AS A CONTINUATION OF THE WORK OF COSTA E SILVA ET AL. (2020) AND VIEBAHN ET AL. (2017) AND THE BIGGEST NOVELTY IN THIS ARTICLE IS THE SIMULTANEOUS USE OF PENALTY AND A RODRIGUES INCREMENTAL ROTATION PARAMETER(SCALAR DOF) FURTHER EXPLAINED IN THE TEXT. THE NONLINEAR FINITE ELEMENT MODEL DEVELOPED IN THIS ARTICLE IS COMPARED TO ANALYTICAL RESULTS, COMMERCIAL FINITE ELEMENT CODE AND FEM MODEL DEVELOPED IN COSTA E SILVA ET AL. (2020). SIMULATIONS HAVE DEMONSTRATED CONSISTENCY AND IT IS DEEMED THAT RELIABLE MESH GENERATION TOGETHER WITH A POWERFULL TRIANGULAR FINITE ELEMENT IS A GOOD OPTION FOR TRUSTWORTHY THIN SHELL SIMULATIONS.