A Problem on Elastic Half Space Under Fractional Order Theory of Thermoelasticity

作者：Kothari Shweta^*; Mukhopadhyay Santwana

来源：Journal of Thermal Stresses, 2011, 34(7): 724-739.

DOI：10.1080/01495739.2010.550834

• Elastic half space
• Fractional calculus
• Generalized thermoelasticity
• State-space approach

The present work is concerned with the solution of a problem on fractional order theory of thermoelasticity for an elastic medium. We investigate the thermoelastic interactions inside the medium by employing the fractional order theory of thermoelasticity, recently advocated by Sherief et al. (Int. J. Solids Struct., 47, 269-275, 2010). State space approach together with the Laplace transform technique is used to obtain the general solution of the problem. The general solution is then applied to three specific problems on an elastic half space, whose boundary is subjected to (i) a thermal shock (i.e., a step input in temperature and zero stress), (ii) a normal load (i.e., a step input in stress and zero temperature change) and (iii) a ramp type increase in temperature and zero stress. To observe the variations of displacement, temperature and stress inside the half-space we compute the numerical values of the field variables for a particular material by utilizing a numerical method of Laplace inversion. The effects of fractional order parameter on the variations of different fields inside the medium are analyzed graphically.

• 出版日期2011