This paper conducts an in-depth investigation into the stability and instability responses of a nanocomposite-reinforced concrete disk, analyzed under unconventional boundary conditions. The study centers on the dynamic behavior and critical buckling features, influenced by the integration of nanomaterials into the concrete matrix. By employing both analytical techniques and numerical simulations, the research assesses the impact of nanocomposite reinforcement on the disk's structural performance across a range of loading scenarios. The non-classical boundary conditions, characterized by atypical constraints and support systems distinct from standard fixed or simply supported conditions, are shown to play a pivotal role in determining the disk's critical load and stability thresholds. Such boundary conditions, which frequently arise in practical applications, significantly influence the disk's stability and load-bearing capacity. The paper also delves into the material properties of the nanocomposites, highlighting their improved stiffness, toughness, and mechanical performance, which contribute to enhancing the structure's overall strength. Through a parametric study, the research thoroughly examines the effects of variables such as nanomaterial volume fraction, disk geometry, and boundary support type. The results indicate a complex interaction between reinforcement, geometry, and boundary conditions, which may lead to instability in specific configurations. This investigation provides valuable insights for optimizing the design of nanocomposite-reinforced concrete structures and offers recommendations for enhancing their structural stability and integrity in practical applications. The findings advance the understanding of the mechanical behavior of nanocomposite materials under non-standard boundary conditions.