A new beam element for analyzing geometrical and physical nonlinearity |
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Authors: | Xiao-Feng Wang Qing-Shan Yang and Qi-Lin Zhang |
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Institution: | Xiao-Feng Wang · Qing-Shan Yang · Qi-Lin Zhang College of Civil Engineering,Tongji University,709 Civil Building,1239 Siping Road,Shanghai 200092,China School of Civil Engineering,Beijing Jiaotong University,Beijing 100044,China |
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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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Keywords: | Spatial beams · Thin-walled section · Beam element · Geometrical and physical nonlinearity · FEM |
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