  The paper proposes a novel adaptive search space decomposition method and a
novel gradient-free optimization-based formulation for the pre- and
post-buckling analyses of space truss structures. Space trusses are often
employed in structural engineering to build large steel constructions, such as
bridges and domes, whose structural response is characterized by large
displacements. Therefore, these structures are vulnerable to progressive
collapses due to local or global buckling effects, leading to sudden failures.
The method proposed in this paper allows the analysis of the load-equilibrium
path of truss structures to permanent and variable loading, including stable
and unstable equilibrium stages and explicitly considering geometric
nonlinearities. The goal of this work is to determine these equilibrium stages
via optimization of the Lagrangian kinematic parameters of the system,
determining the global equilibrium. However, this optimization problem is
non-trivial due to the undefined parameter domain and the sensitivity and
interaction among the Lagrangian parameters. Therefore, we propose formulating
this problem as a nonlinear, multimodal, unconstrained, continuous optimization
problem and develop a novel adaptive search space decomposition method, which
progressively and adaptively re-defines the search domain (hypersphere) to
evaluate the equilibrium of the system using a gradient-free optimization
algorithm. We tackle three benchmark problems and evaluate a medium-sized test
representing a real structural problem in this paper. The results are compared
to those available in the literature regarding displacement-load curves and
deformed configurations. The accuracy and robustness of the adopted methodology
show a high potential of gradient-free algorithms in analyzing space truss
structures.
