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In the formulation of Euler-Bernoulli Beam Theory, there are two degrees of freedom at a point, $w$ and $\frac{dw}{dx}$. Typically, the finite element model of this theory uses cubic polynomial for interpolation of $w$ using a two noded element as given in Chapter 5 of this book. This element is a subparametric because the geometry is represented by low-order elements than those used to approximate the dependent variable. I need a reference where I can find the FE model for this problem using isoparametric elements.

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  • $\begingroup$ Why do you need an isoparametric representation of it? Euler-Bernoulli beams are supposed to be straight lines in the undeformed configuration and hence are completely defined by the extreme nodes. $\endgroup$ – nicoguaro Feb 20 '19 at 15:24
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    $\begingroup$ @nicoguaro: that's not true. curved beams can also be analyzed with EB theory. $\endgroup$ – Biswajit Banerjee Feb 20 '19 at 21:26
  • $\begingroup$ @BiswajitBanerjee, I would not call that EB, but I suppose that you are referring to the hypotheses, and in that case you are right. Also, in that case an isoparametric formulation would make sense. $\endgroup$ – nicoguaro Feb 20 '19 at 21:29
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    $\begingroup$ What he is proposing is an isoparametric formulation because the displacement and geometry are represented by the same Hermite shape functions. What is unusual is requiring the slopes at the end points to represent the geometry. Typically, if you want a curved beam FE, you would introduce one or two intermediate points. $\endgroup$ – Bill Greene Feb 20 '19 at 23:37

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