In this work concerning steady-state radiative-transfer calculations in plane-parallel media, the equivalence between the discrete ordinates method and the spherical harmonics method is proved. More specifically, it is shown that for standard radiative-transfer problems without the imposed restriction of azimuthal symmetry the two methods yield identical results for the radiation intensity when...

Laminated composite plates are widely used in modern structures. Resins of composites are almost made of polymers which show time dependent and and in some cases stress dependent behaviour. In this paper, a laminated composite plate is analysed using a multiscale method. At first, material properties of a lamina is obtained using an analytical micromechanical approach called simplified unit cel...

In this paper, we propose a natural collocation method with exact imposition of mixed boundary conditions based on a generalized Gauss-Lobatto-Legendre-Birhoff quadrature rule that builds in the underlying boundary data. We provide a direct construction of the quadrature rule, and show that the collocation method can be implemented as efficiently as the usual collocation scheme for PDEs with Di...

In this study, based on nonlocal differential constitutive relations of Eringen, the first order shear deformation theory of plates (FSDT) is reformulated for vibration of nano-plates considering the initial geometric imperfection. The dynamic analog of the von Kármán nonlinear strain-displacement relations is used to derive equations of motion for the nano-plate. When dealing with nonlineariti...

where y(x) denotes the solution of the differential equation. The idea is to use a quadrature formula to estimate the integral of (1). This requires knowledge of the integrand at specified arguments x¿ in (xo, -To + h)—hence we require the values of y(x) at these arguments. A numerical integration method may be used to estimate y(x) for the required arguments. In this way a numerical integratio...

Graphene sheets are combined of Honeycombs lattice carbon-carbon bonds which have high natural frequencies, high strength, and high conductivity. Due to important applications of the graphene sheets particularly at higher frequencies, the study of their dynamic behavior is important in this frequency range. From Molecular Dynamics (MD) point of view as the dimensions of graphene sheet incline, ...