Transient response of a thermoelastic half-space to mechanical and thermal buried sources

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 95; no. 4; pp. 354 - 376
• Main Authors: Raoofian Naeeni, M., Eskandari-Ghadi, M., Ardalan, A.A., Sture, S., Rahimian, M.
• Format: Journal Article
• Language: English
• Published: Weinheim Blackwell Publishing Ltd 01.04.2015; Wiley Subscription Services, Inc
• Subjects: buried source; Coupled thermoelasticity; Finite element analysis; Half spaces; Hankel transforms; Heat flux; Heat transfer; Integral transforms; Integrals; Laplace transform; Mathematical analysis; Mathematical models; scalar potential functions; Traction; Transient responses; transient wave
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201300055

With the aid of a complete set of two scalar potential functions, the transient responses of an isotropic thermoelastic half‐space subjected to time dependent tractions and heat flux applied to a finite patch at an arbitrary depth below a free surface are derived. Using the displacements‐ and temperature‐potential function relationships, the coupled equations of motion and energy equation are uncoupled, resulting in two (6th and 2nd order) partial differential equations in the cylindrical coordinate system, which are solved with the aid of Fourier series expansion and joint Hankel‐Laplace integral transforms. The solutions are also investigated in details for tractions varying with time in terms of a Heaviside step function and heat flux as a Dirac delta function, which may be used as a kernel in any integral based method for more complicated thermoelastodynamic initial‐boundary value problems. Due to the complexity of the integrands involved in the general case, the integrals cannot be resolved analytically and thus an appropriate numerical algorithm is used for the inversion of the Laplace and Hankel integral transforms. To demonstrate the pattern of deformations as well as the distribution of change of temperature at the free surface of the half‐space, numerical evaluations for these functions are presented for an isotropic material. With the aid of a complete set of two scalar potential functions, the transient responses of an isotropic thermoelastic halfspace subjected to time dependent tractions and heat flux applied to a finite patch at an arbitrary depth below a free surface are derived…. To demonstrate the pattern of deformations as well as the distribution of change of temperature at the free surface of the half‐space, numerical evaluations for these functions are presented for an isotropic material.