in this paper, the interface crack of two non-homogenous functionally graded materials is studied. subsequently, with employing the displacement method for fracture of mixed-mode stress intensity factors, the continuous variation of material properties are calculated. in this investigation, the displacements are derived with employing of the functional graded material programming and analysis o...

It is shown that under very general conditions there is a rigorous identity between the group velocity and the velocity of energy transport in nonhomogeneous media with or without anomalous dispersion. The medium is assumed nondissipative and the parameters such as density, rigidity, dielectric constant, etc., vary from point to point but are independent of the Cartesian coordinate lying in the...

We propose a discrete weighted Helmholtz decomposition for edge element functions. The decomposition is orthogonal in a weighted L inner product and stable uniformly with respect to the jumps in the discontinuous weight function. As an application, the new Helmholtz decomposition is applied to demonstrate the quasi-optimality of a preconditioned edge element system for solving a saddle-point Ma...

In this lecture we learn to solve nonhomogeneous equations of the form ay′′ + by′ + cy = g(t) using the “method of undetermined coefficients”. In previous lectures we learned to how to solve any equation of the form ay′′ + by′ + cy = 0. We will apply these techniques to help us solve the nonhomogeneous equation ay′′ + by′ + cy = g(t) by understanding the connection between solutions to homogene...

Solutions of 3D multi-domain transient thermal analysis with variable sources in nonhomogeneous media are separated into homogeneous and special solutions by an efficient boundary meshfree computational approach, namely virtual Galerkin method. Homogeneous expressed the element The source functions unknowable coefficients can be formed radial basis function interpolation. Considering control eq...

In this paper we are going to study the Hyers{Ulam{Rassias typesof stability for nonlinear, nonhomogeneous Volterra integral equations with delayon nite intervals.