Abstract This article re-examines the nonlinear vibration and bending responses of porous sandwich cylindrical panels reinforced by graphene platelets resting on elastic foundations in thermal environments. The platelet-reinforced composite (GPLRC) core is assumed to be multilayers, each layer may have different porosity coefficient values achieve a piece-wise functionally graded pattern. By in...

Primarily, two models are commonly used to describe rocking of rigid bodies; the Housner model, and the Winkler foundation model. The first deals with the motion of a rigid block rocking about its base corners on a rigid foundation. The second deals with the motion of a rigid block rocking and bouncing on a flexible foundation of distributed linear springs and dashpots (Winkler foundation). The...

In this paper, it is tried to find an approximate single layer equivalent for multi-layer graphene sheets based on third order non-local elasticity theory. The plates are embedded in two parameter Winkler-Pasternak elastic foundation, and also the thermal effects are considered. A uniform transverse load is imposed on the plates. Applying the non-local theory of Eringen based on third order she...

In present study, thermo-elastic buckling analysis of multi-layer orthotropic annular/circular graphene sheets is investigated based on Eringen’s theory. The moderately thick and also thick nano-plates are considered. Using the non-local first and third order shear deformation theories, the governing equations are derived. The van der Waals interaction between the layers is simulated for multi-...

Based on the nonlocal Timoshenko beam theory, the dynamic stability of functionally gradded (FG) nanoeams under axial load is studied in thermal environment, with considering surface effect. It is used power law distribution for FGM and the surface stress effects are considered based on Gurtin-Murdoch continuum theory. Using Von Karman geometric nonlinearity, governing equations are derived bas...

In this article, dynamic modeling of double walled cylindrical functionally graded (FG) microshell is studied. Size effect of double walled cylindrical FG microshell are investigated using modified couple stress theory (MCST). Each layer of microshell is embedded in a viscoelastic medium. For the first time, in the present study, has been considered, FG length scale parameter in double walled c...

The main aim of this paper is to investigate bending behavior in sandwich plates with functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets with considering the effects of carbon nanotube (CNT) aggregation. The sandwich plates are assumed resting on Winkler-Pasternak elastic foundation and a mesh-free method based on first order shear deformation theory (FSDT) is devel...

The nonlinear bending behavior of sector graphene sheets is studied subjected to uniform transverse loads resting on a Winkler-Pasternak elastic foundation using the nonlocal elasticity theory. Considering the nonlocal differential constitutive relations of Eringen theory based on first order shear deformation theory and using the von-Karman strain field, the equilibrium partial differential eq...

In his book “Mathematical Mind-Benders”, Peter Winkler poses the following open problem, originally due to the first author: “[In the game Peer Pressure,] two players are dealt some number of cards, initially face up, each card carrying a different integer. In each round, the players simultaneously play a card; the higher card is discarded and the lower card passed to the other player. The play...