A finite-strain quadrilateral shell element based on discrete Kirchhoff-Love constraints

Abstract

SUMMARYThis paper improves the 16 degrees-of-freedom quadrilateral shell element based on pointwise Kirchhoff-Love constraints and introduces a consistent large strain formulation for this element. The model is based on classical shell kinematics combined with continuum constitutive laws. The resulting element is valid for large rotations and displacements. The degrees-of-freedom are the displacements at the corner nodes and one rotation at each mid-side node. The formulation is free of enhancements, it is almost fully integrated and is found to be immune to locking or unstable modes. The patch test is satisfied. In addition, the formulation is simple and amenable to efficient incorporation in large-scale codes as no internal degrees-of-freedom are employed, and the overall calculations are very efficient. Results are presented for linear and non-linear problems.

An Efficient Technique for Surface Strain Recovery from Photogrammetric Data using Meshless Interpolation

“…[53,51,52]) and finite element methods (cf. [35,19,6,20,7,13,16,15]). With the latter, crack propagation algorithms have been developed in the past two decades with successful results.…”

Computational shell mechanics by helicoidal modeling, II: Shell element

“…Other elements (for example, [Chróścielewski et al 1992;Arciniega and Reddy 2007]) rely on high-order interpolants in order to avoid, or mitigate, shear and membrane locking. Others are based on particular techniques, such as reduced integration [Wriggers and Gruttmann 1993;Hauptmann et al 2000;Cardoso and Yoon 2005], discrete Kirchhoff-Love constraints [Areias et al 2005], or incompatible modes [Ibrahimbegović and Frey 1994]. Most of the elements proposed in the literature, however, use the assumed natural strain or enhanced assumed strain concepts, such as those developed by [Büchter et al 1994;Bischoff and Ramm 1997;Sansour and Kollmann 2000;Fontes Valente et al 2003;Chróścielewski and Witkowski 2006;Brank 2008], to mention just a few.…”

“…Cylindrical shell pullout. The cylinder stretched by two opposite forces is a very popular benchmark test in the shell element literature, for example, in [Sansour and Bufler 1992;Sansour and Bednarczyk 1995;Sansour and Kollmann 2000;Sze et al 2002;Campello et al 2003;Fontes Valente et al 2003;Pimenta et al 2004;Areias et al 2005;Brank 2008], among others. The specimen is a cylindrical surface with open ends, pinched by two pulling forces along the mid diameter, see Figure 11.…”

A one-field discontinuous Galerkin formulation of non-linear Kirchhoff-Love shells

“…Although the mesh experiences large distortion during the deformation process, the solution is in good agreement with the ones obtained in the literature, and in particular with: (i) The hybrid stress formulation proposed by Sansour and Kollmann [12], for whom results are displayed for q <3000 N·m −1 (which is the maximum loading considered in this reference). (ii) The mixed formulation based on mid-side rotations proposed by Areias et al [13], which converges for an applied linear force reaching 12000 N·m −1 .…”