By L. I. Sedov, J. R. M. Radok
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Additional info for A course in continuum mechanics, vol. 1: Basic equations and analytical techniques
Jin (2002) employed a multi-layered material model and an asymptotic technique to investigate the 1-D temperature field in an FGM strip with continuous and piecewise differentiable material properties and obtained a simple closed-form short time asymptotic solution. This sub-section introduces this short time temperature solution. A multi-layered material model. 1 FGM strip of thickness b as shown in Fig. 9. The material properties are graded in the thickness direction (x-direction). The strip is initially at a constant temperature which can be assumed as zero without loss of generality.
15) The SIFs at the crack tip x = -a are the same as those at x = a due to symmetry. 3. Numerical results were given with crack faces subjected to uniform pressure P2 = Po and uniform shear PI = qo, respectively. 2 shows the SIFs (normalized by qoFa) under the uniform shearing load qo. More detailed results can be found in Delale and Erdogan (1988). Unlike the oscillatory nature of stress and displacement fields found in the sharp interface crack problems, the usual inverse squareroot singularity now prevails and the SIF is well defined for the crack in this composite system due to the continuous variations of material properties.
9. The material properties are graded in the thickness direction (x-direction). The strip is initially at a constant temperature which can be assumed as zero without loss of generality. The surfaces x = 0 and x = b of the strip are subjected to sudden temperature drops Ta and Tb, respectively. The initial and boundary conditions for the temperature field are T=O, t = O. T = -Ta, x =0, T=-n, x = b. 16), a multi-layered material model is first employed. In the discrete model, the FGM strip is divided into N + 1 homogeneous layers in the thickness direction, as shown in Fig.
A course in continuum mechanics, vol. 1: Basic equations and analytical techniques by L. I. Sedov, J. R. M. Radok