Variational equations and application in FEM software

[frztrb]

Hi All

if the displacement is defined with a different variational equation than the conventional one in FEM , and I have to apply FEM on it , how should I do this to apply it in a commercial software ? starting from variational equation is not familiar for me , I mean if the equation changes

 

[frztrb]

Till now I know that I can use Orphan mesh in Abaqus

but any ideas please , how and where do I define the solution method for the orphan mesh and how do I put the results back on Abaqus output ?