Analytical study of free vibration, buckling, and bending behaviors of functionally graded triply periodic minimal surface beams using higher-order shear deformation theory

This study explores the free vibration, buckling, and bending behaviors of functionally graded triply periodic minimal surface (FG-TPMS) beams using a combination of higher-order shear deformation theory (HSDT) and the Ritz method. The aim is to address gaps in understanding how FG-TPMS beams respond to factors, such as shear effects, slenderness ratios, and boundary conditions. Three architectures, Primitive, Gyroid, and I-graph with Wrapped Package-Graph, are analyzed, each with six different volume fraction distribution patterns. A numerical fitting approach is used to determine the material properties, and governing equations are derived using Lagrange’s principle, with solutions based on Ritz approximations and Laguerre polynomials. The study examines the natural frequencies, critical buckling loads, and deflections of the beams, providing a detailed analysis of how different TPMS architectures, porosity distributions, and boundary conditions affect structural performance. The results offer valuable insights and a reference point for future research in this area.