Mechanical Performance-Enhanced Parabolic Curved-Beam Lattice Structures: Multi-Objective Optimization and Theoretical Modeling

Lattice structures offer superior mechanical properties, including lightweight design and performance tailorability, due to their unique geometric configurations and porous characteristics. This study proposes a novel lattice structure, namely the parabolic curved-beam (PCB) lattice structure, in which the struts within the unit cells are designed in a parabolic shape. Based on the principle of minimum potential energy, a theoretical model for the mechanical behavior of the proposed structure under compressive loading was derived. The influence of structural parameters on mechanical performance was systematically analyzed, and the accuracy and validity of the theoretical model were verified through experimental design. Additionally, the advantages of the structure were explored through comparison with the traditional body-centered cubic (BCC) lattice structure. Subsequently a response surface surrogate model was constructed using orthogonal experimental design, yielding quadratic regression equations for key mechanical indicators, including Young’s modulus, specific energy absorption (SEA), and yield strength. The results demonstrate that optimal mechanical performance is achieved with a strut curvature of 0.55 mm−1, a cross-sectional area of 1.22 mm2, and a unit cell size of 5 mm. Under these design parameters, the structure exhibits a Young’s modulus of 4152.85 MPa, an SEA of 3.86 J/g, and a yield strength of 17.02 MPa. The findings demonstrate that the present study employs theoretical analysis and optimization design to achieve mechanical characterization and performance optimization of the designed lattice structure. It shows broad application prospects in fields such as aerospace, vehicle engineering, and protective equipment, where there is an urgent demand for lightweight and high-strength materials. This work provides new insights and a theoretical basis for the design and performance optimization of multi-functional integrated structures in engineering practice.