Transient thermal stress analysis of functionally graded materials

A Functionally Graded Material (FGM) is a material in which the composition and structure gradually change resulting in a corresponding change in the properties of the material. To design FGM architecture and analyze FGMs, the first step is to establish mathematical definitions and theories for the graded structures and properties. A micromechanical approach is used to semi-analytically obtain the transient thermal stress fields in FGMs. In this method, an approximate solution which satisfies homogeneous boundary conditions is substituted in the governing equation for transient heat transfer to yield an eigenvalue problem. The eigenvalues and the orthonormalized eigenfunctions obtained by solving this eigenvalue problem for the given homogeneous boundary conditions constitute the transient temperature field in the FGM. The eigenfunctions are approximated by a linear combination of permissible functions which satisfy the homogeneous boundary conditions for the given geometry. The Galerkin method is used to obtain the coefficients of eigenfunctions. The Galerkin method is an approximation method based on "the method of weighted residuals" which uses trial functions as the weighting function. This temperature distribution is used in the elastic equilibrium equation which is solved for the stress field, again by the Galerkin method.; As examples, this method is applied to plot the transient temperature distribution and the thermal stress distribution in a 2D rectangular, non-specific FGM subjected to the first type of homogeneous boundary conditions. The method is implemented utilizing a computer algebra system. The eigenvalues and eigenfunctions by the Galerkin method are compared with their corresponding values obtained by the analytical method and the results proved that the proposed approach is correct. Hence the method and the two programs developed here can be used for transient temperature and thermal stress distribution in any FGM. (Abstract shortened by UMI.)...