Optimal pressure and ambient temperature profiles are calculated to allow the rapid heating and cooling of pressure vessels during startup and shutdown. The ordinates of the ambient temperature and pressure at equally spaced time intervals are chosen as the design variables. Cubic splines are fitted through the ordinates to describe the ambient temperature profile required for the convective heat transfer analysis, and the pressure profile required during the structural analysis. Response surface methodology is used to construct approximations to temperature and stress in the transient thermoelastic nonlinear analysis. Linear response surfaces were found to be sufficiently accurate, thereby minimizing the number of finite element analyses. Three problems are solved to illustrate the methodology.

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