Polar decomposition based corotational framework for triangular shell elements with distributed loads

Abstract

A polar decomposition based corotational formulation for deriving geometrically nonlinear triangular shell elements is proposed. This formulation is novel in two aspects. (1) Original formulas for the projector operator and its variation are presented, leading to simple algorithms for the computation of the nodal residual vector and of the consistent tangent stiffness tensor. (2) For the first time in the context of a corotational kinematic description, a rigorous treatment of distributed dead and follower loads is performed, thoroughly accounting for the various contributions entailed in the residual vector and in the tangent stiffness. Numerical simulations of popular benchmark problems are reported, showing the effectiveness of the proposed approach. An accessible and adaptable MATLAB toolkit implementing the present formulation is provided as supplementary material. © 2013 John Wiley & Sons, Ltd.