A geometrically nonlinear (GNL) dynamic model, for functionally graded triply periodic minimal surface (FGTPMS) plates influenced by moving loads on a Pasternak foundation, is developed in this paper. The FGTPMS core is described by Primitive, Gyroid, and I-graph/Wrap-Package (IWP) topologies with throughthickness relative-density gradation, enabling spatial tuning of effective elastic and shear modulus. Plate kinematics follow Mindlin theory. Within a Total Lagrangian framework, Green-Lagrange strains and second Piola-Kirchhoff stresses are used to formulate the governing equations. Geometric stiffness terms are included to capture large-displacement effects. Mesh-load relocation and domain-size limitations of the Finite Element Method (FEM) are circumvented by a load-attached coordinate transformation within the Moving Element Method (MEM). Nine-node isoparametric elements are used, with the time integration and stepwise nonlinear equilibrium are achieved via Wilson and Newton-Raphson schemes. The formulation accommodates foundation normal/shear stiffnes, and a concentrated moving load with general velocity. The approach is designed to quantify the influence of density-gradation parameters, TPMS topology, plate thickness, and load velocity on the GNL dynamic response, and to benchmark FG-TPMS plates. The resulting framework provides an efficient and robust tool for analyzing lightweight architected plates under realistic moving-load conditions.
Dang et al. (Wed,) studied this question.