Poisson 効果を考慮した一般化梁の定式化とその有限要素の開発

Generalized beam theory considering cross-sectional deformation due to Poisson’s effect and its finite element

田淵 航 (Ko TABUCHI) 

Beam elements, which are finite elements based on beam theory, are sometimes used for structural analysis of large structures such as bridges. The reason for this is that the number of degrees of freedom can be greatly reduced in the beam element compared to the continuum finite element. The elementary beam theory is based on the assumption that members are slender and do not deform in cross-section. However, since members handled in practice are not necessarily slender, it is useful to improve the accuracy of the beam theory by considering cross-sectional deformation. Many beam theories have been proposed that incorporate cross-sectional deformations associated with shear, such as transverse shear deformation and shear lag, into the displacement field. However, to the best of the author’s knowledge, there are few beam theories that incorporate the cross-sectional deformations associated with bending and axial forces caused by Poisson’s effect into the displacement field. In this study, we propose a beam theory that incorporates the cross-sectional deformation due to Poisson’s effect. The results show that the accuracy is improved compared to the conventional method that does not take Poisson’s effect into account

Key Words : Poisson’s effect, Timoshenko beam, cross-sectional deformation, shear lag, transverse shear