# Solving a system on non-linear equations

For a structural analysis problem having to do with finite element analysis I have a book that sets up a system of equations starting with nodal displacements called Ue1 (for the displacement of element 1) and Ue2 (for the displacement of element 2 respectively forward.). The whole system is:

[Ue1] = [v1]= [1, 0, 0, 0][alpha1]
[Uphi1] = [phi1]= [0, -1, 0, 0][alpha2]
[Ue2] = [v2]= [1, l, l^2, l^3][alpha3]
[Uphi2] = [phi2]= [0, -1, -2l, -3l^2][alpha4]

The alpha values come from a type of Hermite polynomial series and are known and relate to shape functions that are written of to be developed. The length l is known. A value for phi2 is declared as known and also phi1 is known to be 0 at the boundary condition.

So, I am being given enough to solve the system. So, from what I take it this would be a non-linear system given the powers of l taken. So, I am aware that there is a way to solve manually the system by graphing each equation and finding overlapping points.

Is there some way that the Fenics API has to readily plug in the system and have Fenics solve it for me based on the plugging in of known values?

Hi Phillip, the tutorials and demos might be a place to start.
You can find some at
https://jsdokken.com/dolfinx-tutorial/
and
https://docs.fenicsproject.org/dolfinx/v0.6.0/python/demos.html

They include some examples of nonlinear systems.

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