A computational strategy for enhanced nonlinear structural stability analysis in Abaqus

Abstract

The global pursuit of net-zero emissions intensifies the demand for sustainable and lightweight structures, heightening challenges associated with nonlinear buckling instabilities. Simultaneously, a paradigm shift is emerging: strategically leveraging these instabilities to unlock unprecedented functionalities in areas like soft robotics, 4D printing, and flexible electronics. This convergence creates a critical need for advanced, automated computational tools capable of systematic nonlinear bifurcation analysis. While commercial software like Abaqus provides robust equilibrium path tracing, it lacks integrated capabilities for explicit critical point pin-pointing and – crucially – automated branch switching at bifurcation points without resorting to symmetry-breaking imperfections. Addressing this significant gap, we introduce a novel computational strategy enabling rigorous bifurcation analysis directly within Abaqus. The core methodological innovation is a probing-based technique that exploits the critical eigenvector’s topology and multi-stability principles near bifurcations to traverse secondary equilibrium paths while rigorously preserving structural symmetry. We demonstrate the framework’s efficacy and broad applicability through three diverse case studies exhibiting complex instabilities: 1) buckling of 2D soft circular ring under uniform inward pressure; 2) interactive buckling of thin-walled rectangular hollow section strut; 3) a concentrically loaded shallow shell roof exhibiting complex buckling instabilities. Results are rigorously verified against analytical solutions or published benchmarks. This work provides a powerful, accessible, and symmetry-preserving approach within the ubiquitous Abaqus environment, enabling systematic explorations of complex post-buckling landscapes. By enabling precise critical point identification and automated branch switching, our framework fundamentally advances the understanding of post-buckling behaviour, leading to more robust lightweight load-bearing structures while unlocking transformative potential for next-generation designs where strategically controlled instabilities enable multifunctional performance.