Design of nonlinear gradient sheet-based TPMS-lattice using artificial neural networks

Gradient triply periodic minimal surface (TPMS) structures are renowned for lightweight design and enhanced performance, but their complex and nonlinear configurations pose challenges in achieving targeted design goals. A new design methodology for the nonlinear gradient structure was proposed in this study, with the aim of achieving efficient and accurate modeling of complex and gradient sheet-based TPMS structures under specific performance objectives. This method utilized automated finite element (FE) simulations to obtain structure topology element densities under various boundary conditions. An artificial neural network (ANN) was then employed to efficiently predict the correspondence between these boundary conditions and topology element densities. A mapping was established between topology element densities and TPMS structural parameters, and the gradient structure was accurately constructed by using the voxel modeling technique. Taking a typical cantilever beam TPMS structure as an example of nonlinear gradient design, the results indicate that the error between the ANN-predicted and FE-simulated structure topology element densities is only 2.73 %, with prediction time being only 0.15 % of the simulation time. The thin regions of the gradient structure align with those geometrically removed in regular topology optimization scheme, achieving up to 65.45 % weight reduction, a 28.72 % improvement over the regular scheme, along with uniform structural stress transition and maximum stress reduction. TC4 alloy nonlinear gradient TPMS structures, printed by metal selective laser melting (SLM) technique, confirm the practical application value of this design method.