The present work studies an axisymmetric rotating truncated cone made of functionally graded (FG) porous materials reinforced by graphene platelets (GPLs) under a thermal loading. The problem is tackled theoretically based on a classical linear thermoelasticity approach. The truncated cone consists of a layered material with a uniform or non-uniform dispersion of GPLs in a metal matrix with open-cell internal pores, whose effective properties are determined according to the extended rule of mixture and modified Halpin–Tsai model. A graded finite element method (FEM) based on Rayleigh–Ritz energy formulation and Crank–Nicolson algorithm is here applied to solve the problem both in time and space domain. The thermo-mechanical response is checked for different porosity distributions (uniform and functionally graded), together with different types of GPL patterns across the cone thickness. A parametric study is performed to analyze the effect of porosity coefficients, weight fractions of GPL, semi-vertex angles of cone, and circular velocity, on the thermal, kinematic, and stress response of the structural member.

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.

In this work, a numerical 3D finite element method is developed to investigate the natural frequencies and static responses of saturated FG porous annular elliptical sector plate. 3D elasticity theory is utilized to model the problem. Three various porosity patterns are assumed along the thickness direction such as porosity nonlinear symmetric distribution (PNSD), porosity nonlinear nonsymmetric distribution (PNND), and porosity uniform distribution (PUD). Biot theory of poroelasticity instead of the simple Hooke’s law is applied to describe the relation between stress and strain. To derive the governing equations, finite element approach according to Rayleigh-Ritz energy formulation is applied. A thorough investigation studies the sensitivity of the static behavior and natural frequencies of the plate to different parameters, including the Skempton and porosity coefficients, geometric parameters, and various patterns of porosity.