## General Mechanical

#### Userelem (USER300) Mixed u-p formulation

• m_soleimani
Subscriber
As an experienced person who has developed multiple Userelement in the USER300 platform, I have a very important suggestion for ANSYS to improve this amazing advanced feature.
Well, in User300 if you define the shape and the number of nodes using USRELEM command you need to define your DoFs afterward using USRDOF. Apparently, everything is fine! As long as "all nodes" bear "All DoFs" defined in USRDOF, there is no problem. However, if some nodes intentionally don't have some of the DoFs, the problem arises. Let me give you an example for more clarification:
Assume that the element shape is a 2D triangle enjoying 6 nodes (corners as well as mid sides) and we want to develop an element for incompressible material using mixed u-p formulation. It is known that in this case, all nodes (6 nodes) are allowed to have displacement DoF but only the corner nodes can bear pressure DoF. It naturally leads to a quadratic interpolation for displacements (UX, UY) while the pressure (HDSP) is interpolated linearly. It "MUST" be like this to have a stable element. I don't want to elaborate more on the theoretical ground (so-called LBB condition) for that.
Based on the current situation, there is no possibility to let ANSYS make a distinction between corner and mid-side nodes. It always assumes that "all nodes" bear "all DoFs". In our 2D example (triangle 6 nodes), I expect to have a stiffness matrix whose dimension is 15*15 (6*2+3*1=15) instead of 18*18 (6*3=18). This shortage needs to be remedied by ANSYS.

I hope to get feedback from ANSYS
Thanks
• David Weed
Ansys Employee
, thank you for your detailed post. I will check with development on this and get back to you soon.