Systematic procedures are presented for reducing the order of a matrix differential equation governing transient heat conduction in solids. Two principal aspects of this development are a condensation of the set of gridpoint temperature degrees of freedom using steady-state relations and the introduction of generalized (modal) temperature degrees of freedom to achieve a further reduction. These processes are illustrated in an elementary one-dimensional transient heat conduction problem.
A finite element model of a nozzle in a cylindrical shell is analyzed for three cases; pressure, out-of-plane moment and combined pressure plus out-of-plane moment. The model uses three-dimensional finite elements and the analysis considers inelastic behavior at small displacements. Load versus displacement behavior is given for the three cases. Estimates of limit loads are obtained based upon extrapolation of load versus inverse displacement data curves. An interaction expression is used to show the effect of the combined loading for a case in which an internal pressure reduces the moment capability of the nozzle by 35 percent.
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