4. METHOD OF SOLUTION
FRANCO uses two-dimensional finite element theory and applications for mechanical deformation and heat conduction, and determines the temperature distribution from the fuel center to the coolant adjacent to the clad at a position along the fuel rod axis. FRANCO calculates the average temperature of each radial division, the nodal displacement, and strain and stress within the fuel pellet and clad. The principal stresses, which represent maximum and minimum stresses within an element, result from Mohr's circle relationship between normal stresses. FRANCO is capable of predicting the thermo-mechanical behavior in the radial direction of a single fuel rod for both boiling water reactors (BWR's) and pressurized water reactors (PWR's). The cross sectional plane geometry of fuel rod is modeled using three-node constant strain triangular finite elements, and both thermal and mechanical solutions are computed with the same finite element configurations. The local linear heat generation rate is modeled as a uniform heat source in a fuel pellet, and the coolant temperature and heat transfer coefficient are applied as known boundary conditions at the boundary of the cladding surface. The total load to form the global force vector consists of the thermal load that results from thermal expansion of the material and the mechanical load exerted by pressure. FRANCO assumes the fuel-cladding gap region to be conductive material in order to simplify the analysis, and this gap is simulated by either an open gap or a closed gap model. A time- dependent problem can be simulated by FRANCO using quasi-static analysis when time-dependent parameters are provided. FRANCO can treat a steady-state or mild transient condition as a time-dependent problem, where time-dependent parameters are input as "snap shots". Consequently, the FRANCO code is able to run faster and easier compared to other industrial codes with comparable results; and hence, FRANCO is useful in analyzing the fuel element performance as a first cut or scoping tool.