Spatial asymmetric/symmetric buckling of Mises truss with out-of-plane lateral linear spring

Abstract

This paper deals with the equilibrium problem of the Mises truss, with out-of-plane lateral linear spring, analyzed as a three DOF system. It is shown that, as a consequence of the geometry of the structure, the system can undergo three buckling modes which are asymmetric in-plane buckling, symmetric out-of-plane buckling and asymmetric out-of-plane buckling. The analysis takes into account the influence of local buckling and yielding of bars on global instabilities.The Green–Lagrange strain is adopted as the strain measure and the theorem of the stationarity of the total potential energy is employed to derive the nonlinear equilibrium equations. The tangent stiffness matrix is derived and, through the solution of the eigenvalue problem, the stability of the equilibrium solutions is investigated. Analytical formulations for the instabilities of the truss are presented.For the numerical approach, a linear elastic constitutive model is assumed for the uniaxial stress–strain relationship of the truss bars. To take into account the yielding of bar elements, a perfect elastoplastic model is assumed. A computer program was developed in Fortran to perform comparisons with the results of the theoretical formulation. Finally, the numerical results obtained demonstrate the accuracy and effectiveness of the presented truss element.The main novelty of this paper is the introduction of an additional DOF in the Mises truss which allows to study a more complex scenario of equilibrium paths and instabilities.