Elbow strike is one of the basic secondary techniques in tai chi, and represents one of the 8 fundamental “energies” or dimensions of martial applications.
While this particular movement is archetypal, it is not the only way in which elbows can be applied. Any number of elbow strike, press, throw or joint control techniques can be used that conform to tai chi principles.
The knee strike is also and expression of the “elbow” energy, the knee being the elbow of the leg.
An important thing to remember is that the power for the elbow strike comes from the legs, and not from movement of the shoulder or arm. It can be very tempting to try to add shoulder muscle to the action. But this would be counterproductive. The arm holds the shape. It does not contribute to the motion.
Elbow Right: (Front view and follow view)