Mesh original and displaced coordinates

I am trying to use Global ODEs and DAEs equations,.....

equation is that u(X,Y,Z)=0 where X,Y and Z are original coordinates of mesh nodes,.....

u is the displacement of the nodes in x direction ( so unequal displacement of every node of mesh),..... so I want to model this deformed sphere ,........ Do anyone have any idea how can i do this?,.......... Thanx in advace!