Adaptive search space decomposition method for pre- and post- buckling analyses of space truss structures

TL;DR

This paper introduces an adaptive search space decomposition method combined with a gradient-free optimization approach to analyze pre- and post-buckling behavior of space truss structures, capturing complex equilibrium paths including unstable stages.

Contribution

The work presents a novel adaptive search space decomposition technique and a gradient-free optimization formulation for nonlinear buckling analysis of space trusses, enabling robust identification of equilibrium states.

Findings

Successfully analyzed benchmark buckling problems

Achieved accurate load-displacement curves

Demonstrated robustness of the method on real structures

Abstract

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.