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

This 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.