Use of penalty variable in finite element analysis of contacting objects

In this paper, we investigate the solution to a subset of contact problems where the finite element systems are positive semidefinite resulting from insufficient supports to the objects at the onset of the analysis. A finite element algorithm, which incorporates a penalty variable defined as a function of the constraint condition, is developed to solve these kinds of contact problems. The solution algorithm employs an iterative technique to calculate the deformation of the object while enforcing compatibility through a modified penalty function. The new method is applied to example problems having the above characteristics. The method accurately predicts the contact zones and deformed configurations of the objects.