Stability and load capacity of an elasto-plastic pyramidal truss

Abstract

The present work investigates, using a corotational finite element formulation considering large displacements and rotations, geometric imperfections and an elasto-plastic material constitutive law, the nonlinear behavior of a pyramidal space truss under vertical and horizontal loads. Additionally novel analytical closed-form solutions for the nonlinear equilibrium paths, natural frequencies and critical parameters are derived for comparison purposes and investigation of the influence of geometric and material parameters on the truss stability. This geometry has an immediate practical interest since these structures are currently used in many present-day applications, either as main structural component or as a constitutive element. Four types of nonlinear instability phenomena are investigated theoretically and numerically: saddle-node (limit point) bifurcation, pitchfork bifurcation, individual Eulerian bars buckling and elasto-plastic buckling. Through a detailed parametric analysis the interaction between these buckling phenomena, using the FE tool, is investigated. In addition, the effect of elastic supports is considered. The influence of these phenomena on the load carrying capacity of the structure and its imperfection sensitivity is duly discussed in the present work. Finally, a detailed parametric analysis of a large roof composed of pyramidal truss units is conducted and the influence of the geometric parameters on its bistable behavior and load carrying capacity is investigated.