Conservation equations stiffness

The theoretical and measured results for E, are shown in Figure 3-41 as a function of resin content by weight. Theoretical results from Equation (3.64) are shown for C = 0,. 2,. 4, and 1, and the data are bounded by the curves for C = 0 and C =. 4. The theoretical curve labeled glass-resin connected in series is a lower, lower bound than the C = 0 curve and is an overly conservative estimate of the stiffness. 

The decision process of putting together models based the above methods is helped by some observations about timescale and solution stiffness. The modeler should decide on a timescale of interest. The characteristic times, or first order time constants, for a typical flow and a pressure element based on lumped momentum and mass conservation respectively are shown in the following equations [7, 8] ... 

In the equation above, bend is the stiffness parameter, while and 0 stand for the instantaneous and the average angles between consecutive bonds, respectively. Apart from the two conservative interactions, DPD particles experience pairwise dissipative forces, depending on the relative speed of the particles, and pairwise random forces that depend on their relative distances. The properties of the dissipative and the stochastic forces are chosen to ensure local momentum conservation and that the equilibrium states of the system comply with the Boltzmann distribution of the ensemble [96],... 

I ests have shown that this equation is too conservative because the maximum stress can be many feet away from the junction where the pressure is reduced and the stiffness of the second course becomes significant. Accordingly, the equation for the design of the bottom course is modified to read... 

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