Shakedown occurs when the (elastically) calculated thermal plus mechanical stress range (primary plus secondary stress range) is within twice yield, whereupon the stresses cycle within the elastic range. I presume in that that the mechanical stresses alone must be within yield. To study this you'd need to have perfectly plastic material behaviour in your model, and loads that included secondary stresses from applied temperatures.
Have a look in pressure vessel design standards such as BS5500 or EN13445, or ASME something, for the definition. It's not so simples.
Tata but not yet tara