Large displacement nonlinear analysis of space trusses

This paper presents a method for the nonlinear analysis of large-scale space trusses in the presence of both geometric and material nonlinearities. The incremental formulation is derived from a discrete model of the structure using the fundamental relations of equilibrium, compatibility and constitutive laws. This formulation involves complementarity (orthogonality of two sign-constrained vectors) as a key mathematical structure. For ease of solution, the exact nonholonomic (path-dependent) constitutive rate problem is transformed into its finite incremental stepwise holonomic (path-independent) counterpart by adopting a backward difference approximation scheme. The resulting governing equations lead to a nonlinear complementarity problem (NCP) which exhibits symmetry as a result of the introduction of so-called “nonlinear residuals”. The proposed solution algorithm for the NCP is based on an iterative predictorcorrector computational scheme. An example is given to illustrate application of the approach to a fairly large size and realistic space truss problem in the presence of softening.