Efficient Co-Rotational 3-Node Shell Element

Abstract

Geometric nonlinear FE-analysis of thin-walled shell structures, using a co-rotational formulation and the Cell Smoothed Discrete Shear Gap triangular shell element (CS-DSG3) is presented in this study. The CS-DSG3 element formulation uses the Mindlin-Reissner kinematic hypothesis to include transverse shear effects. In order to avoid locking effects Discrete Shear Gap (DSG) method is applied. In addition, cell based smoothing technique is adopted in order to improve accuracy and stability of the element. For the purpose of comparison, the Discrete Kirchhoff-Constant strain-Triangle (DKT-CST) is also implemented and studied in the linear static analysis. In the framework of the co-rotational FE-analysis rotations and displacements are adopted as finite, while strains are infinitesimal. Large rotation theory has been utilized to take into account the non-vectorial characteristic of rotations. Several static linear and nonlinear benchmark examples are presented and compared with commercial FE software Abaqus and analytical results. The presented approach, using CS-DSG3 element in co-rotational nonlinear analysis, illustrates very good results compared to reference solution and Abaqus results. The numerical effort can be reduced compared to Lagrange formulation with a similar accuracy for the studied cases. The formulation (including CS-DSG3 shell element) has been implemented into a test program.