Faster on-line calculation of thermal stresses by time integration

The Green’s function technique (GFT) is largely used for on-line calculation of thermal stresses in machines and plants, because it allows turning parameters such as fluid temperatures, pressures and flow rates directly in thermal stresses. Recently the use of the GFT has been extended by the authors to thermo-mechanical models having variable convective coefficients. The novel methodology is made of two steps. First of all, boundary temperatures are evaluated by time integration of a reduced thermal model and then thermal stresses are calculated by means of the GFT using as inputs the boundary temperatures previously evaluated. The new approach implies a large number of convolution integrals to be solved for thermal stress calculation. In order to reduce computation time it is here proposed to replace the convolution integrals which characterise the GFT with a reduced model of uncoupled first order differential equations, whose coefficients are estimated fitting the Green’s functions of the thermo-mechanical model with a sum of exponential terms. Thermal stresses are obtained by time integration of the model.