The Finite Element Method for the Analysis of Non-Linear and ...

Definitions used in Contact Analysis
Let t f IJ : vector of contact surface traction on body I due to contact with
body J then t f IJ = − t f JI . Hence, the virtual work due to the contact
traction can be written:
∫
δu I
S IJ i fi IJ dS IJ +
∫
δu J
S IJ i fi JI dS JI =
∫
δu IJ
S IJ i fi
IJ dS IJ
where
where
δu IJ
i = δu I i − δu J i
We call the pair of surfaces S IJ , S IJ a contact surface pair.
S IJ is named the ”contactor surface” and
S JI is named the ”target surface”
Hence, the right hand side of the previous eqn represents the virtual work
of the contact tractions over the relative virtual displacements δu I i , δuJ i
Institute of Structural Engineering Method of Finite Elements II 36