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Structural Engineering and Mechanics
  Volume 43, Number 4, August25 2012, pages 411-437

A continuum mechanics based 3-D beam finite element with warping displacements and its modeling capabilities
Kyungho Yoon, Youngyu Lee and Phill-Seung Lee

    In this paper, we propose a continuum mechanics based 3-D beam finite element with crosssectional discretization allowing for warping displacements. The beam element is directly derived from the assemblage of 3-D solid elements, and this approach results in inherently advanced modeling capabilities of the beam element. In the beam formulation, warping is fully coupled with bending, shearing, and stretching. Consequently, the proposed beam elements can consider free and constrained warping conditions, eccentricities, curved geometries, varying sections, as well as arbitrary cross-sections (including thin/thick-walled, open/closed, and single/multi-cell cross-sections). We then study the modeling and predictive capabilities of the beam elements in twisting beam problems according to geometries, boundary conditions, and cross-sectional meshes. The results are compared with reference solutions obtained by analytical methods and solid and shell finite element models. Excellent modeling capabilities and solution accuracy of the proposed beam element are observed.
Key Words
    beams; finite elements; torsion; twisting; warping; arbitrary cross-sections
Kyungho Yoon, Youngyu Lee and Phill-Seung Lee: Division of Ocean Systems Engineering, Korea Advanced Institute of Science and Technology, Yuseong-gu, Daejeon 305-701, Korea

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