Abstract: This paper explores the optimization design method for continuously variable periodic TPMS structures, which are highly regarded in functionally graded structure design due to their light weight and excellent energy absorption characteristics. To address the issue of distortion in TPMS with equal thickness and var-iable periods, a novel optimization method is proposed. This method utilizes a target structural frequency distribution function as input and constructs a phase field function through axial integration. Subsequently, the phase field reference points are set as design variables to develop an optimization model aimed at minimizing global average curvature. Utilizing a global optimization algorithm for iterative solving, the method ultimately enhances the distribution of average curvature in the structure, significantly reducing geometric distortion during period changes. Compared to distortion optimization methods based on local orthogonality criteria, this approach demonstrates greater numerical stability, reducing computational time from hours to minutes. Systematic mechanical tests conducted on monotonic continuously variable period-ic fused deposition modeling specimens indicate that under quasi-static compression conditions, the energy absorption efficiency for optimized Schwarz P and Schwarz D type TPMS structures is increased by 35% and 239% respectively compared to traditional methods that directly modify periodic parameters, with no apparent inter-layer defects evident.