Lightweight composite structures are widely employed across various engineering fields, due to their advantageous properties such as high specific strength/stiffness and low weight. Despite these benefits, many lightweight structures are prone to unstable post-buckling behaviour under compressive loads, often amplified by significant imperfection sensitivity, which can lead to potentially dangerous reductions in load-carrying capacity. However, this geometrically nonlinear response is not inherently undesirable. In specific contexts, particularly those requiring adaptive or morphing capabilities, nonlinear deformations and instabilities can be strategically harnessed to enable complex shape reconfigurations and facilitate the rapid deployment of structural systems. It is therefore of pivotal importance to develop and employ methods capable of accurately and efficiently predicting the geometrically nonlinear behaviour of lightweight composite structures. This mini-symposium seeks to bring together researchers engaged in the development of advanced methodologies for analysing, tracing, and optimising the nonlinear structural response of lightweight composites. Contributions may address, but are not limited to, the following topics: - Advanced computational methods and discretisation techniques for evaluating the stability of lightweight composite structures, while also accounting for multiphysics interactions. - The use of AI/ML techniques to construct surrogate models for accelerating the design and optimisation of lightweight nonlinear structures. - Optimisation algorithms to solve convex and non-convex problems with single or multiple objectives for composite structures dominated by geometrically nonlinear behaviour. - Uncertainty quantification techniques to assess the influence of parameter variability on structural performance in the nonlinear regime.