Instability analysis of space trusses

Abstract Reduction methods and computational procedures are presented for the instability analysis of space trusses with both geometric and material nonlinearities subjected to combined loads. A mixed formulation is used with the fundamental unknowns consisting of both the member forces and the joint displacements. The governing equations of the truss consist of the two sets of member constitutive relations and joint equilibrium equations. The vector of fundamental unknowns is expressed as a linear combination of a small number of path derivatives (derivatives of nodal displacements and member forces with respect to path parameters), and a Bubnov-Galerkin technique is used to approximate the governing equations by a small system of algebraic equations. The reduced equations are then used to determine the stability boundary and trace the nonlinear equilibrium paths. The potential of the proposed approach is discussed and its effectiveness is demonstrated by means of numerical examples of space trusses with combined geometric and material nonlinearities. The constitutive relations in these examples are assumed, for convenience, to be represented by Rambergsgood polynomials.