Grid structures have found widespread use in civil and mechanical engineering owing to their ability of covering long spans with an outstanding strength-to-weight ratio. However, their shallow structural depth and slender members make them susceptible to buckling failures. Therefore, it is crucial to enhance the stability of grid structures. An under-explored way to achieve this is by optimally configuring enhancement materials. This paper addresses the challenges of identifying the optimal enhancement layouts for grid structures by solving a density-based topology optimisation problem. The problem formulation is based on the SIMP approach, minimising compliance while satisfying constraints on material volume and structural stability. The stability constraint is expressed using buckling load factors obtained from a linear eigenvalue analysis. Two types of enhancement schemes, involving in-plane and out-of-plane elements, are developed for the single-layer base grid structures. The efficiency of the proposed method is evaluated by performing enhancement layout optimisation for a flat and three curved square grid structures, subject to a uniformly distributed vertical load and a half-span load. The optimisation results shed light on the impact of in-plane and out-of-plane enhancements on the stability of grid structures, providing insights on optimally configuring enhancement materials to achieve desired stability. In addition, comparative analysis between the case studies indicates that for curved structures, a higher curvature normally leads to greater achievable stability. In contrast, the flat grid structure exhibits the broadest range of customisable stability due to its primarily bending-dominant load-carrying mechanism. Furthermore, the outcomes of geometric non-linear analysis confirm the load-carrying capacity of the optimal structures, with non-linear critical loads typically showing a positive correlation with linear buckling loads.
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