Stochastic transient analysis of thermal stresses in solids by explicit time-domain method

•A novel time-domain approach is proposed for non-stationary stochastic transient heat conduction and thermal response analysis.•The explicit expressions of temperatures and thermal displacements and stresses are established in terms of stochastic thermal excitations.•The dimension-reduced statistical moment analysis is conducted with high efficiency based on the explicit formulations. Stochastic heat conduction and thermal stress analysis of structures has received considerable attention in recent years. The propagation of uncertain thermal environments will lead to stochastic variations in temperature fields and thermal stresses. Therefore, it is reasonable to consider the variability of thermal environments while conducting thermal analysis. However, for ambient thermal excitations, only stationary random processes have been investigated thus far. In this study, the highly efficient explicit time-domain method (ETDM) is proposed for the analysis of non-stationary stochastic transient heat conduction and thermal stress problems. The explicit time-domain expressions of thermal responses are first constructed for a thermoelastic body. Then the statistical moments of thermal displacements and stresses can be directly obtained based on the explicit expressions of thermal responses. A numerical example involving non-stationary stochastic internal heat generation rate is investigated. The accuracy and efficiency of the proposed method are validated by comparison with the Monte-Carlo simulation.