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depending on the type of non linear analysis you used, then conceptually the analysis takes the following steps (again depending on the type on analysis you use): An iterative process starts: A small increment of the load $\Delta F$ is applied (typically a percentage between 1% and 10%) For those small load increments the displacements $\delta_i$ are ...

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I am not aware there is such an analysis method called "transient analysis" for civil/structural engineering, I think you mean the analysis of structure with the "transient loads. By definition, the transient load is temporary and brief in nature. In structural engineering, except for the dead weight, almost everything else can be called a ...

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You haven't given enough information to answer this exactly, but I am assuming from your equations that you are solving mesh-centered equations and the assumption is that the flux is linear in each cell. In that case, the average value of the flux in each cell is taken as the midpoint, and your integration just becomes a sum k^n=k^{n-1}\frac{\sum h(\nu_1\...

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