A nonlocal isogeometric model for buckling and dynamic instability analyses of FG graphene platelets-reinforced nanoplates

The current study aims to propose an effective and robust computational approach that combines the nonlocal elasticity theory, refined plate theory (RPT) with only four independent unknowns and an isogeometric analysis (IGA) framework for buckling and dynamic instability of functionally graded graphene nanoplatelet reinforced composite (FG-GNPRC) nanoplates. To accomplish this purpose, the structural displacement field is estimated via the four-variable RPT model and a non-uniform rational B-splines (NURBS)-based IGA approach. Meanwhile, the size-dependent effect of FG nanoplates can be captured effectively by applying the nonlocal theory of elasticity. Dynamic instability regions of small-scale structures under periodic in-plane compressions can be approximated by employing Bolotin's method. Three different dispersions of graphene nanoplatelets (GNPs) in the matrix materials, specifically uniform and two non-uniform distributions, are investigated in this study. The effect of several crucial parameters on the static as well as dynamic instability characteristics for FG-GNPRC nanoplates is thoroughly examined for the first time. We explore that the distribution and the weight fraction of GNPs have a remarkable influence on the buckling and dynamic instability characteristics of the nanoplates. The present results reveal that the FG-X model always provides the best performance for both static and dynamic problems. Furthermore, an increase in the nonlocal parameter or the static load factor results in a decrease in the instability performance while the wider instability regions can be observed when the dynamic load factor gradually increases. Finally, the outcomes of the present study could be assigned as noteworthy benchmark results for intensive studies on the engineering structures at the small-scale level with GNPs reinforcement in the future.

Automated summary

The current study proposes a computational approach that combines nonlocal elasticity theory, refined plate theory, and isogeometric analysis for buckling and dynamic instability analysis of functionally graded graphene nanoplatelet reinforced composite nanoplates. The effects of distribution and weight fraction of graphene nanoplatelets on the instability characteristics are examined, and the results demonstrate that the FG-X model provides the best performance. The outcomes of this study can serve as important benchmark results for future research on engineering structures at the small-scale level with graphene nanoplatelet reinforcement.