Topology design is the most important method of obtaining optimal material distribution that is directly related to the mechanical properties of structural materials. Aimed at improving the accuracy and efficiency of topology design, this paper explores an innovative topological technique that integrates a sigmoid-rational approximation of material properties approach, with a modified optimality criteria algorithm. Furthermore, a three-dimensional (3D) star-shaped auxetic structure, based on the sigmoid-rational approximation of material properties approach and a modified optimality criteria technique is proposed. The unit cell structural parameters are extracted, and the mechanical properties of the 3D star-shaped structure, including the relative density, equivalent elastic modulus, and equivalent Poisson's ratio, are investigated using mechanical derivation, numerical, and experimental methods. The subsequent results demonstrate that the sigmoid-rational approximation of material properties approach and a modified optimality criteria technique provides a feasible novel idea for multicellular structure development and that the advantageous 3D star-shaped auxetic structure has great potential within the field of structural safety.
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