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Fuel assembly finite-element dynamic models are developed to perform the core seismic analysis. The fuel assembly is modeld by a single vertical beam, which represents the cross-sectional inertias of the fuel rods, guide thimbles and instrument thimble, and a series of rotational springs. The rotational springs are located at the intermediate spacer grid locations. Benchmarking to fuel assembly natural frequencies determined by testing is accomplished by adjusting the moment of inertia and the grid rotational stiffness to find their effective values. Most often these models are linear and are appropriate for the small amplitude stiffness representation of the fuel assembly. Large deflection problems are approximated by choosing a fuel assebly stiffness value appropriate to the average deflection range. Some loss of accuracy will naturally result from this approach. This paper presents a nonlinear model to approximate the hysterisis and free vibration response for large amplitudes fuel assembly motion. The force required to impose the initial displacement (pluck) and the free vibration responses are used to compare the nonlinear model’s behavior with the test data. This model correctly predicts fuel assembly deflection shapes as a function of axial position for various lateral loads for several fuel assembly designs. Displacement hysterisis is primarily due to fuel assembly to grid slippage, which is a strong function of grid preload. “Tight” and “relaxed” prototypes were tested to account for grid preload effect. The model correctly analyzes the grid preload effect. A nonlinear fuel assembly model provides better matching of grid impact loads determined by fuel assembly lateral impact testing and also prvides better matching of all of the initial conditions (initial deflection, initial force, initial energy and impact velocity). In this test, the fuel assembly impacts a test wall to determine grid internal stiffness. This value is used in the core model for seismic analyses.

The objective of this paper is to develop a purely mechanistic fuel assembly structural model that will predict the fuel assembly’s static and dynamic characteristics from the knowledge of the fuel assembly’s geometry and component properties. This model provides a method for analyzing the static and dynamic lateral and axial properties of the fuel assembly. A comparison of various in-air fuel assembly test data such as lateral and axial stiffnesses and lateral natural frequencies is provided to demonstrate the analytical model. The fuel assembly model developed by Shah, Brenneman, etc. (1), achieved very good agreement with assembly lateral impact test data by utilizing a “3-beam” model. In that model, the fuel rod-to-spacer grid interfaces were represented by spring and friction elements. The fuel assembly was restrained at each grid position by means of rotational springs, which were benchmarked to the test frequencies. This newly developed model eliminates the need for using rotational springs at the grid locations. Hence, it fully simulates the fuel assembly lateral and axial behavior based on the fuel assembly geometric properties. The fuel assembly model is a 2-D planar model of beams in both lateral and axial directions. The grids are modeled with plate elements. At each grid location there are springs, preload, and frictional sliders representing the lateral and axial connectivity characteristics to the fuel assembly beam model. As the Zircaloy grid preloads relax from irradiation, they can be easily simulated by removing the preload. Hence, this model can represent the fuel assembly structural properties for all aspects of fuel assembly cycles. This model can be used to analyze the fuel assembly lateral static stiffness, first mode and higher order lateral natural frequencies, mode shapes, axial stiffness, in-grid stiffness, through-grid stiffness, and fuel assembly lateral and axial seismic and LOCA response. The model will also estimate the fuel rod frequencies and mode shapes. This model may eliminate the need for some expensive prototype fuel assembly testing.

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This study reports on relation between bicycle frame and rider comfort. It involves developing a theory on interdependence of vertical compliance or stiffness of bicycle frame and induced human comfort. The factors affecting vertical stiffness/compliance are identified and varied to observe their influence. A standard diamond type bicycle frame is modelled and analysed which is generally used for on-road bikes, applying different materials to the frame to note its deflection on application of load, considering the structural and material properties. The results of the analysis confirm with stiffness trend associated with Young's modulus of the material. i.e., for the same structure and loading conditions, material with lesser Young's modulus offer more compliance. Reducing thickness of tubing is also observed to be increasing compliance of the frame, which can be achieved either by reducing the outer diameter or increasing the inner diameter, the former being more beneficial according to manufacturing standpoint. This is verified by generating a series of supplementary equations. An experimental analysis is performed to discern the most influential tube out of every other tubings forming the frame structure, wherein their thicknesses are decreased by 10% one at a time, keeping the rest as it is. The study accomplishes that as compared to rest of the tubes, more rider comfort can be achieved by making least changes to the seat tube cross-sectional thickness, to decrease vertical stiffness and therefore, comfort. The obtained conclusions can serve as a base for further studies involving cyclist comfort and bicycle frame design.