Numerical Study on the Buckling Behavior of FG Porous Spherical Caps Reinforced by Graphene Platelets

The buckling response of functionally graded (FG) porous spherical caps reinforced by graphene platelets (GPLs) is assessed here, including both symmetric and uniform porosity patterns in the metal matrix, together with five different GPL distributions. The Halpin-Tsai model is here applied, together with an extended rule of mixture to determine the elastic properties and mass density of the selected shells, respectively. The equilibrium equations of the pre-buckling state are here determined according to a linear three-dimensional (3D) elasticity basics and principle of virtual work, whose solution is determined from classical finite elements. The buckling load is, thus, obtained based on the nonlinear Green strain field and generalized geometric stiffness concept. A large parametric investigation studies the sensitivity of the natural frequencies of FG porous spherical caps reinforced by GPLs to different parameters, namely, the porosity coefficients and distributions, together with different polar angles and stiffness coefficients of the elastic foundation, but also different GPL patterns and weight fractions of graphene nanofillers. Results denote that the maximum and minimum buckling loads are reached for GPL-X and GPL-O distributions, respectively. Additionally, the difference between the maximum and minimum critical buckling loads for different porosity distributions is approximately equal to 90%, which belong to symmetric distributions. It is also found that a high weight fraction of GPLs and a high porosity coefficient yield the highest and lowest effects of the structure on the buckling loads of the structure for an amount of 100% and 12.5%, respectively.

Automated summary

The buckling response of functionally graded porous spherical caps reinforced by graphene platelets is studied in this research. The study considers both symmetric and uniform porosity patterns and five different graphene platelet distributions. The elastic properties and mass density of the shells are determined using the Halpin-Tsai model and an extended rule of mixture. The buckling load is obtained using the nonlinear Green strain field and generalized geometric stiffness concept. Parametric investigations reveal the sensitivity of the natural frequencies to various parameters such as porosity coefficients, distributions, polar angles, stiffness coefficients, graphene platelet patterns, and weight fractions. The results show that the maximum buckling load is obtained for the GPL-X distribution, while the minimum load is obtained for GPL-O distribution. The difference between the maximum and minimum critical buckling loads for different porosity distributions is approximately 90%, indicating significant variations. High weight fractions of graphene platelets and porosity coefficients have the highest and lowest effects on the buckling loads, respectively.