In this study, a beam theory with cross-sectional deformation due to torsion is proposed, applicable to arbitrary cross-sections. A new degree of freedom, independent of the angle of twist, which determines the magnitude of the warping deformation is introduced. The cross-sectional deformation is obtained numerically by a finite element analysis of the representative volume element with periodic boundary conditions. This homogenization method makes the present theory applicable to arbitrary cross-sections. The deformation is used to obtain not only the warping function but also the cross-sectional deformation parameters introduced in the proposed torsion theory. The results show that the distribution shape of the cross-sectional deformation can be successfully reproduced by the proposed theory. A beam element based on the proposed theory is also developed. Comparison with the analytical solution by the proposed theory shows good convergence of the developed beam element.

Key Words : torsion, deformation of cross section, warping, representative volume element

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