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I am wondering what are the appropriate shape/interpolation functions for the B21 element since it has 3 DoF per node, but is stated as linear interpolation element.

Update: (as per duffymo's comment)

I know there is a distinction between nodal DoF and interpolation order and I am looking for the relation between the two. For example the standard Euler-Bernoulli beam element (B23) has a 3rd order polynomial interpolation and uses the four nodal DoF (2 displacements and 2 rotations) two determine the displacement field. This interpolation is still linear in the coefficients, but cubic in length. How is the interpolation kept linear in length for B21? Does it have separate first order polynomials for each DoF?

My end goal here is to calculate stresses from displacements, obtained by my own solver.

Any help is appreciated.

Peter Hristov
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  • It's a planar beam. That means displacements (u, v) and rotation (theta) about the z-axis at each node. It's still a linear interpolation along the length of the beam. Don't confuse DOF with interpolation order. – duffymo Apr 07 '20 at 10:55
  • @duffymo I know there is a distinction between the two, but I thought they are dependent. For example the Euler-Bernoulli beam element uses a 3rd order polynomial interpolation to take into account the four unknowns (2 at each node - v, theta). This interpolation is still linear in the coefficients, but cubic in length. So, in order to maintain the interpolation linear in length, I should have three separate first order polynomials for each dof? That is, something like - u = a_u + b_u x; v = a_v + b_v x; etc. Is that right? Thanks. – Peter Hristov Apr 08 '20 at 08:17

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