In this paper, static and free vibrations behaviors of the orthotropic functionally graded material (FGM) plates resting on the two-parameter elastic foundation are analyzed by the a mesh-free method based on the first order shear deformation plate theory (FSDT). The mesh-free method is based on moving least squares (MLS) shape functions and essential boundary conditions are imposed by transfer...

this paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. a model problem with nonlinear kinetic law is considered. the main result is an existence theorem. the mathematical effects of the kinetic term are discussed

in this paper, free vibration of an Euler-Bernoulli beam with variable cross-section resting on elastic foundation and under axial tensile force is considered. Beam’s constant height and exponentially varying width yields variable cross-section. The problem is handled for three different boundary conditions: clamped-clamped, simply supported-simply supported and clamp-free beams. First, the equ...

free surface modeling plays an important role in some ocean structures design, especially in oscillating water column (owc) devices. boundary element method (bem) is a suitable method for free surface modeling due to its simplicity, quick solving, and low data storage requirement. in this paper, bem was used for free surface modeling in owc chamber and out of it. linear kinematic and dynamic bo...

In this paper, we provide a unified and self-consistent treatment of a functionally graded material (FGM) microbeam with varying thermal conductivity subjected to non-uniform or uniform temperature field. Specifically, it is our objective to determine the effect of the microscopic size of the beam, the electrostatic gap, the temperature field and material property on the pull-in voltage of the ...

In this section we will consider the general properties of the solution p(r, t) of the Smoluchowski equation in the case that the force field is derived from a potential, i.e., F (r) = −∇U(r) and that the potential is finite everywhere in the diffusion doamain Ω. We will demonstrate first that the solutions, in case of reaction-free boundary conditions, obey an extremum principle, namely, that ...

We consider the van der Waals’ free energy functional, with scaling parameter ε, in the plane domain R+ × R+, with inhomogeneous Dirichlet boundary conditions. We impose the two stable phases on the horizontal boundaries R+×{0} and R+×{∞}, and free boundary conditions on {∞}×R+. Finally, the datum on {0} ×R+ is chosen in such a way that the interface between the pure phases is pinned at some po...

This paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. A model problem with nonlinear kinetic law is considered. The main result is an existence theorem. The mathematical effects of the kinetic term are discussed

Let f , U and C represent, respectively, the free energy, the internal energy and the specific heat of the critical Ising model on the square M×N lattice with periodic boundary conditions, and f∞ represents f as M,N → ∞. We find that f , U and C can be written as: N(f −f∞) = ∑ ∞ i=1 fi/N 2i−1, U = − √ 2+ ∑ ∞ i=1 ui/N 2i−1 and C = 8 π lnN+ ∑ ∞ i=0 ci/N i andNf and U are well-defined odd function...