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A new beam element for analyzing geometrical and physical nonlinearity

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Abstract

Based on Timoshenko’s beam theory and Vlasov’s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange (UL) and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle–Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.

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Authors and Affiliations

  1. College of Civil Engineering, Tongji University, 709 Civil Building, 1239 Siping Road, Shanghai, 200092, China

    Xiao-Feng Wang & Qi-Lin Zhang

  2. School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, China

    Qing-Shan Yang

Authors
  1. Xiao-Feng Wang
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  2. Qing-Shan Yang
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  3. Qi-Lin Zhang
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Correspondence to Xiao-Feng Wang.

Additional information

The project was supported by the National Natural Science Foundation of China (50725826), Specific Research on Cable-reinforced Membranes with Super Span and Complex Single-shell Structures of Expo Axis (08dz0580303) and Shanghai Postdoctoral Fund (10R21416200).

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Wang, XF., Yang, QS. & Zhang, QL. A new beam element for analyzing geometrical and physical nonlinearity. Acta Mech Sin 26, 605–615 (2010). https://doi.org/10.1007/s10409-010-0354-3

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  • DOI: https://doi.org/10.1007/s10409-010-0354-3

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