Steady-state response of thermoelastic half-plane with voids subjected to a surface harmonic force and a thermal source

• Study the steady-state response for a thermoelastic half-plane with voids.
• Present a semi-analytical method and get a semi-analytical solution for the problem.
• Develop a differential quadrature element method and obtain the numerical solution.
• Compare the numerical results obtained from the DQEM and the SAM.
• Consider the effect of parameters on the steady-state response of the half-plane.

In this paper, the steady-state response for a thermoelastic half-plane with voids is studied, in which, the surface of the half-plane is partly subjected to a surface harmonic force and a thermal source. The semi-analytical solutions and the numerical solutions of the half-plane problems with three different materials are obtained from a semi-analytical method and a developed differential quadrature element method in this paper, respectively. The corresponding numerical results are compared and the effects of parameters are considered as well. It can be seen that the semi-analytical solutions and corresponding numerical solutions coincide with each other. This means that the differential quadrature element method is a very efficient method for seeking the numerical solutions of the half-plane problems with discontinuity, and it has some advantageous properties, such as small computational amount, high accuracy, and better convergence.