The transient response of a functionally graded half-space heated by a laser pulse based on the generalized thermoelasticity with memory-dependent derivative

Based on the generalized thermoelasticity with memory-dependent derivative, the transient response of a half-space heated by a non-Gaussian laser beam on its boundary is investigated. The coupled governing equations containing thermal time-delay factor and thermal kernel function, which can be chosen to adapt to specific problems, are formulated and solved by the Laplace transform technique and its numerical inversion. For the functionally graded half-space, its material properties are assumed to exponentially vary with material coordinate. In calculation, the non-dimensional temperature, displacement as well as stress under different thermal time-delay factor, thermal kernel function and functionally graded parameter are obtained and illustrated graphically. The results show that: with the decrease of thermal time-delay factor or the increase of exponent of thermal kernel function, the peak value of the non-dimensional temperature, displacement and the absolute value of peak value of stress increase; negative temperature value, positive displacement and stress values will appear when functionally graded parameter is less than zero. It is hoped that the obtained results would be helpful in designing the functionally graded materials heated by a non-Gaussian laser beam in engineering.

Automated summary

The transient response of a half-space heated by a non-Gaussian laser beam is investigated based on generalized thermoelasticity. Coupled governing equations with thermal time-delay factor and thermal kernel function are formulated and solved using Laplace transform technique. The study reveals that the peak values of non-dimensional temperature, displacement, and stress increase with decreasing thermal time-delay factor or increasing exponent of thermal kernel function. Negative temperature values, positive displacement, and stress values occur when the functionally graded parameter is less than zero.