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 rotation regime. An exact field proposed based on central line orientation cross section consisting nine parameters corresponding to centroid movements rotations. The Cauchy–Green deformation tensor derived local coordinate system according field. a normal-shear constitutive model highly polynomial nonlinearity are developed continuum mechanics. A finite element formulation then established higher-order shape functions avoid shear membrane locking issues. elemental governing equations equilibrium as well nodal forces moments obtained using Hamiltonian principle. To solve final nonlinear equations, Newton–Raphson Riks techniques by incremental-iterative scheme implemented. numerical results assess behaviors different sections various boundary conditions. effects hinge joints stability studied for first time. reveal bending lateral-torsional buckling joints. This phenomenon proved both strain its linearization small deformations. show that present robust, reliable simple easy