A meshfree approach using naturally stabilized nodal integration for multilayer FG GPLRC complicated plate structures

• Published in: Engineering analysis with boundary elements Vol. 117; pp. 346 - 358
• Main Authors: Thai, Chien H., Phung-Van, P.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2020
• Subjects: Graphene platelets (GPLs); Graphene platelets reinforced composite (GPLRC); Higher-order shear deformation plate theory (HSDT); Moving Kriging meshfree method; Naturally stabilized nodal integration (NSNI); Graphene platelets reinforced composite (GPLRC); Naturally stabilized nodal integration (NSNI); Graphene platelets (GPLs); Higher-order shear deformation plate theory (HSDT); Moving Kriging meshfree method
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/j.enganabound.2020.04.001

In this study, a meshfree approach using a naturally stabilized nodal integration (NSNI) integrated with a higher-order shear deformation theory (HSDT) for free vibration analysis of multilayer functionally graded graphene platelets reinforced composite (FG GPLRC) plates with complicated shapes is presented. Four different patterns of graphene platelets (GPLs) including uniform and functionally graded distributions are exampled. The rule of mixtures and modified Halpin–Tsai model are respectively used to compute the Poisson's ratio, density and Young's modulus. Based on the principle of virtual work, discretize governing equations of FG GPLRC plates are derived. These equations are solved by a moving Kriging (MK) meshfree method to determine natural frequencies of the FG GPLRC plates. The advantage of moving Kriging shape function is content with the Kronecker delta function property, thus essential boundary conditions are simply imposed as in the finite element method. In addition, the present meshfree approach uses the direct nodal integration with an additional augmentation of stability components to reduce the computational cost as compared to the high-order Gauss quadrature scheme. As observed in numerical examples, natural frequencies of FG GPLRC plates are impressed by the geometries, boundary conditions and distributed patterns of GPLs. It is also seen that the present approach is simply, stable and good predictions for FG GPLRC plates.