Thermal Stress in a Nonhomogeneous Curved Beam

Abstract

The thermoelastic stress field in a functionally graded curved beam, where the elastic stiffness varies in the radial direction, is considered. An analytical solution is obtained where the radial variation of the stiffness is represented by a fairly general form. The stress fields corresponding to two different cases for the elastic properties are examined: first, the elastic properties representing a coating on the outer surfaces of the curved beam; secondly, the elastic properties obtained from experimental data. The flexural stress in the curved beam is then compared with that of a solid ring. Finally, a relatively simple approximate solution is developed and this is shown to be in good agreement with the analytical results.

Influence of the spatial variation of Poisson’s ratio upon the elastic field in nonhomogeneous axisymmetric bodies

“…(19) analytically, two substitutions are used and the governing equation is transformed into Kummer's equation, and the two linearly independent solutions to the homogeneous differential equation can be obtained (Dryden, 2007;Mohammadi and Dryden, 2008) / 1 ðqÞ ¼ q n 1 Mða 1 ; b 1 ; cq s Þ; ð20Þ / 2 ðqÞ ¼ q n 2 Mða 2 ; b 2 ; cq s Þ;…”

“…Less analysis has been done on examining the stress field induced by mechanical and thermal loads in circular curved bars (see e.g. Dryden, 2007;Mohammadi and Dryden, 2008). In these investigations only Young's modulus has been considered to vary with position and Poisson's ratio was taken as being constant.…”

Stress analysis in a functionally graded disc under mechanical loads and a steady state temperature distribution

“…Chen et al (2007) have presented three-dimensional analytical solution for a rotating disc made of transversely isotropic functionally graded materials. Mohammadi & Dryden (2008) have examined the role of non-homogeneous stiffness on the thermoelastic stress field. Tutuncu (2007) has obtained power series solutions for stresses and displacements in functionally-graded cylindrical vessels subjected to internal pressure by using the small deformation theory.…”

Micromechanics for a long fibre reinforced composite model with a functionally graded interphase

“…Consisting of two or more phases, functionally graded materials (FGMs) are nonhomogeneous composites, which have superior mechanical and thermal properties for specific applications compared to traditional composites [22]. The composition and the morphology of FGMs change as a function of position over the volume.…”