Isogeometric 3D optimal designs of functionally graded triply periodic minimal surface

Recent research attention has been drawn to the interdisciplinary engineering applications of functionally graded triply periodic minimal surface (FG-TPMS) lattice structures due to their lightweight yet high mechanical properties. These features are especially important in the dynamic structural behaviors yet the TPMS gradation has not been studied in multi -dimensions. This paper presents the establishment of the optimization problem finding the 3D optimal designs of FG-TPMS plates under free vibration by assigning the relative density to each control point and applying the concept of NURBS-based interpolation for the continuous effective mechanical properties. The general 3D case of the constraint on total material volume is derived from the existing 1D case, which is required for the 3D optimization problem. Isogeometric analysis and generalized shear deformation theory are utilized to analyze the free vibration behavior of the FG-TPMS plates. Verification with the 1D case and a parametric study of the 3D FG-TPMS plate are conducted. Optimization examples include both basic and complex geometries. Unseen -before optimal 3D FG-TPMS designs with significantly elevated natural frequencies are obtained. The physical meaning of the optimal solutions can be explained by the similarity to porous structures in nature: less dense in the center or at free end, and more dense at the constrained boundaries and surfaces.