Generalized Thermoelastic Infinite Layer Subjected to Ramp-Type Thermal and Mechanical Loading under Three Theories—State Space Approach

A problem of thermoelastic interactions in an elastic infinite layer 0 ≤ x ≤ h with an elevated temperature field arising from ramp-type heating and loading has been constructed. The governing equations are written in a unified system from which the field equations for coupled thermoelasticity as well as for generalized thermoelasticity can be easily obtained as particular cases. Due attention has been paid to the finite rise times of temperature and stress. The problem has been solved analytically by using a state-space approach. Solutions from the derived analytical expressions have been computed for a specific situation. The solution for the half-space when (h → ∞) has been found also. Numerical results for the temperature distribution and thermal stress are represented graphically. A comparison was made among the results predicted by the theories.