The method of fundamental solutions for transient heat conduction in functionally graded materials: some special cases

Authors

  • F. M. Maalek Ghaini Department of Mathematics, Yazd University, Yazd, Iran
  • M. Arab Department of Mathematics, Yazd University, Yazd, Iran
  • M. Nili Ahmadabadi Department of Mathematics, Islamic Azad University, Najafabad Branch, Najafabad, Iran
Abstract:

In this paper, the Method of Fundamental Solutions (MFS) is extended to solve some special cases of the problem of transient heat conduction in functionally graded materials. First, the problem is transformed to a heat equation with constant coefficients using a suitable new transformation and then the MFS together with the Tikhonov regularization method is used to solve the resulting equation.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

The simple boundary element method for transient heat conduction in functionally graded materials

This paper presents a ‘‘simple’’ boundary element method for transient heat conduction in functionally graded materials, which leads to a boundary-only formulation without any domain discretization. For a broad range of functional material variation (quadratic, exponential and trigonometric) of thermal conductivity and specific heat, the non-homogeneous problem can be transformed into the stand...

full text

Fundamental Solutions and Functionally Graded Materials

A fundamental solution (or Green’s function) is a singular solution of a governing partial differential equation (PDE). They can be constructed easily when the PDE has constant coefficients. They are useful for reducing boundary-value problems to boundary integral equations (BIEs). We begin by describing simple properties of fundamental solutions, and then comment on the use and construction of...

full text

Analysis of Transient Heat Conduction in 3D Anisotropic Functionally Graded Solids, by the MLPG Method

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously nonhomogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for ...

full text

A method of fundamental solutions for two-dimensional heat conduction

Note: The following files were submitted by the author for peer review, but cannot be converted to PDF. You must view these files (e.g. movies) online. (Received) We investigate an application of the method of fundamental solutions (MFS) to heat conduction in two-dimensional bodies, where the thermal diffusivity is piecewise constant. We extend the MFS proposed in [15] for one-dimensional heat ...

full text

Simple Solutions for Buckling of Conical Shells Composed of Functionally Graded Materials

Using Donnell-type shell theory a simple and exact procedure is presented for linear buckling analysis of functionally graded conical shells under axial compressive loads and external pressure. The solution is in the form of a power series in terms of a particularly convenient coordinate system. By analyzing the buckling of a series of conical shells, under various boundary conditions and diffe...

full text

The Method of Fundamental Solutions for Stationary Heat Conduction Problems in Rotationally Symmetric Domains

We propose an efficient boundary collocation method for the solution of certain twoand three-dimensional problems of steady-state heat conduction in isotropic bimaterials. In particular, in two dimensions we consider the case where a circular region composed of one material is coated with an annular region of another material. In three dimensions, we examine the corresponding case for axisymmet...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 02  issue 02

pages  117- 127

publication date 2013-06-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023