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I have recently generated a code based on 8-node Hexahedral (tri-linear) element that gives the response of a hyperelastic material. However, now I have found out that with 20-node serendipity (bi-quadratic) element, maybe I can achieve better responses. My question is how to transfer the code that is written for "SMSTopology" -> "H1" to a code with "SMSTopology" -> "H2S".

As an example, the shape functions should be changed. But since for Serendipity elements, there is no unique equation for all the shape functions (corner and median nodes have different equations for shape functions), how can I program different shape function equation for different nodes?

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The equation of the shape functions for the corner nodes ($j = 1,...,8$) is written as,

$N_j = \frac{1}{8} (1 + \xi_j \xi)(1 + \eta_j \eta)(1 + \zeta \zeta_i)(\xi_j \xi + \eta_j \eta + \zeta_j \zeta -2).$

For mide-side nodes $j = 10,12,14,16$, the equation of the shape functions is written as,

$N_j = \frac{1}{4} (1 - \xi^2) (1 + \eta_j \eta)(1 + \zeta_j \zeta).$

For mide-side nodes $j = 9,11,13,15$, the equation of the shape functions is written as, $N_j = \frac{1}{4} (1 - \eta^2) (1 + \xi_j \xi)(1 + \zeta_j \zeta).$

For mide-side nodes $j = 17,18,19,20$, the equation of the shape functions is written as,

$N_j = \frac{1}{4} (1 - \zeta^2) (1 + \xi_j \xi)(1 + \eta_j \eta).$

Thanks in advance.

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  • $\begingroup$ Can you provide some real code demonstrating your problem? People will be much more willing to help if there's a clear problem with code demonstrating it that can easily be copied. $\endgroup$ – b3m2a1 Mar 22 '18 at 19:12
  • $\begingroup$ You can find examples of serendipity element code in online library of AceShare. This is the link to the "homepage" for 3D hyperelastic element, the one you are looking for. Does this already answers your question? $\endgroup$ – Pinti Mar 22 '18 at 19:18
  • $\begingroup$ @Pinti Thanks for the link. I don't know yet If it answers or not. By the way, that was a big help for me. $\endgroup$ – KratosMath Mar 23 '18 at 13:47

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