Improving the efficiency of the shifted penalty method

The method presented here is a variation of the classical penalty one, widely used in Contact Mechanics. The modification is suited to reduce the pathological penetration among the contacting surfaces, and could be used also to deal with the fictitious sliding in stick phase for frictional problems. The solution is achieved without introducing any additional set of forces or new unknowns into the global stiffness matrix. Also, the result is then achieved without any increase of the penalty parameters.