In this article, the effect of size-dependent on the buckling and vibration analysis of functionally graded (FG) double-layer boron nitride plate based on classical plate theory (CPT) under electro-thermo-mechanical loadings which is surrounded by elastic foundation is examined. This subject is developed using modified couple stress theory. Using Hamilton's principle, the governing equations of...

We investigate the asymptotic behavior, as ε tends to 0+, of the transverse displacement of a Kirchhoff-Love plate composed of two domains Ωε ∪ Ω − ε , contained in the (x1, x2)-coordinate plane and depending on ε in the following way. The first domain Ωε is a thin strip with vanishing height hε (in direction x2), as ε tends to 0+. The second one Ωε is a comb with fine teeth, having small cross...

A fast multipole boundary element method (BEM) for solving large-scale thin plate bending problems is presented in this paper. The method is based on the Kirchhoff thin plate bending theory and the biharmonic equation governing the deflection of the plate. First, the direct boundary integral equations and the conventional BEM for thin plate bending problems are reviewed. Second, the complex not...

Graphene is an ultimate membrane that mixes both flexibility and mechanical strength, together with many other remarkable properties. A good knowledge of the elastic properties of graphene is prerequisite to any practical application of it in nanoscopic devices. Although this two-dimensional material is only one atom thick, continuous-medium elasticity can be applied as long as the deformations...

We investigated an unsteady elastic diffusion vibration of a simply supported rectangular isotropic Kirchhoff-Love plate. The plate is under the action distributed transverse load. A model that describes coupled processes in multicomponent continuum used for mathematical problem formulation. taking into account fluxes relaxation. equations with were obtained from using d'Alembert variational pr...

We develop a new paradigm for thin-shell finite-element analysis based on the use of subdivision surfaces for: i) describing the geometry of the shell in its undeformed configuration, and ii) generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the Kirchhoff-Love theory of thin shells. The particular subdivision strategy adopted here is Loo...

In this work, an attempt is done to apply the Kirchhoff plate theory find out vibrational analyses of a nanoplate incorporating surface irregularity effects. The effects on natural frequency vibration nanomaterials, especially for nanoplates, have not been investigated before, and most previous research carried regular nanoplates. Therefore, it must be emphasized that vibrations irregular are n...

This paper is the second in a series of two in which we care about the asymptotics of the three-dimensional displacement field in thin elastic plates as the thickness tends to zero. In Part I we have investigated four types of lateral boundary conditions when the transverse component is clamped. In this Part II we study four other types of lateral conditions when the transverse component is fre...