# Large-deformation instability behaviors of 3D beams supported with 3D hinge joints subjected to axial and torsional loadings

Damanpack, A. and Bodaghi, M. ORCID: 0000-0002-0707-944X, 2021. Large-deformation instability behaviors of 3D beams supported with 3D hinge joints subjected to axial and torsional loadings. Acta Mechanica. ISSN 0001-5970

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## Abstract

In this paper, an instability analysis of three-dimensional (3D) beams supported with 3D hinges under axial and torsional loadings is presented in large displacement and rotation regime. An exact displacement field is proposed based on the central line and orientation of the cross-section consisting of nine parameters corresponded to 3D centroid movements and rotations. Cauchy-Green deformation tensor is derived in the local coordinate system according to the proposed displacement field. Deformation tensor and a normal-shear constitutive model with highly polynomial non-linearity are developed based on the continuum mechanics. A finite element formulation is then established based on the higher order shape functions to avoid shear and membrane locking issues. The elemental governing equations of equilibrium as well as 3D nodal forces and moments are obtained using the Hamiltonian principle. To solve the final nonlinear equilibrium equations, Newton-Raphson and Riks techniques through an incremental-iterative scheme are implemented. The numerical results are presented to assess instability behaviors of beams with different cross sections and various 3D boundary conditions. The effects of 3D hinge joints on the stability of beams under axial and torsional loadings are studied for the first time. The numerical results reveal instability in bending and lateral-torsional buckling for beams supported by 3D hinge joints. This phenomenon is proved by both finite strain model and its linearization for small deformations. The numerical results show that the present finite element formulation is robust, reliable as well as simple and easy to model instability of 3D beams in the large displacement regime.

Item Type: Journal article
Publication Title: Acta Mechanica
Creators: Damanpack, A. and Bodaghi, M.
Publisher: Springer (part of Springer Nature)
Date: 13 May 2021
ISSN: 0001-5970
Identifiers:
NumberType
10.1007/s00707-021-02977-8DOI
1433595Other
Divisions: Schools > School of Science and Technology
Record created by: Linda Sullivan
Date Added: 23 Apr 2021 08:11