An isogeometric analysis of functionally graded triply periodic minimal surface microplates

Abstract

In the current study, we present an efficient and straightforward numerical framework for exploring the responses of functionally graded triply periodic minimal surface (FG-TPMS) microplates. FG-TPMS structures including Primitive (P), Gyroid (G), and I-graph and Wrapped Package-graph (IWP) exhibit numerous potential applications in engineering due to their excellent stiffness-to-weight ratios. The behaviors of these structures at the microscale level, however, remain strongly unknown. For the first time, the static bending, free vibration and buckling characteristics of FG-TPMS microplates under various conditions are thoroughly presented in this study. To obtain this, this study employs the four-variable refined plate theory (RPT) with the support of the isogeometric analysis (IGA) to study these mechanical responses. Additionally, one material length scale parameter is utilized to account for the size effect with the modified couple stress theory. The two-phase fitting technique is adopted to predict the effective elastic properties of the FG-TPMS architectures. We in this research examine the two density distribution patterns in terms of the thickness for static bending, free vibration, uni-axial, and bi-axial buckling problems. The results of this investigation agree that as the material length scale parameter increases, the stiffness of microplate models improves significantly. It is explored that the effect of this size-dependent parameter also varies among different TPMS types. The FG microplates based on the P-type architecture have a trend of significant improvement in stiffness with a higher value of the material length scale ratio. With these findings, this research contributes to the development as well as the application of TPMS geometry in microscale structures in the future.