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

In this paper, an instability analysis of three-dimensional (3D) beams supported with 3D hinges under axial and torsional loadings is presented in the 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 corresponding to 3D centroid movements and rotations. The Cauchy–Green deformation tensor is derived in the local coordinate system according to the proposed displacement field. The deformation tensor and a normal-shear constitutive model with highly polynomial nonlinearity are developed based on 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 by 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 the 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.