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Deformation zone infinitesimal element

In the derivation for von Karman equation for metal strip rolling, an infinitesimal element is chosen as shown in the picture above. The equilibrium equation for the element is as follows:

Balance equation

Upon further simplification and ignoring the product of small quantities, we obtain the von Karman equation:

Von Karman Equation

Notice that the parameters of the element are chosen such that there will be product of (σx+dσx) and (h+dh), i.e. (σx+dσx) acting on left face and height of element at left face is also (h+dh).

My confusion is: When we choose to keep (σx+dσx) on the right side face, keeping (h+dh) on the left face, the resulting equilibrium equation does not give us the von Karman equation. Why does this happen? Should'nt the final result be independent of the variable chosen? Is there a certain rule for this? Where am I making a mistake?

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  • $\begingroup$ Can someone please answer? $\endgroup$
    – Utility ZC
    Commented Jun 13 at 7:27

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