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.
Highlights
Thin-walled structures are widely used in engineering practice
An overview of the DSG3 formulation (Bletzinger et al, 2000) is given, followed by the further development (Nguyen-Thoi et al, 2013) which leads to the CS-DSG3 element formulation
A geometrically nonlinear co-rotational Finite Element Method (FEM) formulation implies that the geometrical nonlinearities in structural behavior are accounted for by means of an auxiliary, local reference frame that is attached to the material and performs the same rigid-body motion as the structural material
Summary
Thin-walled structures are widely used in engineering practice. This is the consequence of the optimization strategy to reduce the structural dead-load whereby the structural carrying capacity is kept at a very high level. The main requirements for shell elements are high efficiency, reliability and applicability over a wide range of thickness and curvature. Thinwalled structures are characterized by high susceptibility to geometrically nonlinear behavior, caused by large transverse deflections and therewith local rotations and the developed FEM formulations are supposed to cover this aspect. Certain developments are essentially based on the updated Lagrangian formulation but use local reference frame attached to the structure for computation of the Cauchy stresses (Marinković et al, 2008). The CR formulation applied in this study is employing the element-base reference frame This means that each single element is provided with an attached co-rotational frame and the resolution of accounting for rigid-body motion is element-wise (Marinković et al, 2012)
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