Mechanical contact is encountered whenever two or more bodies physically interact along their boundaries. The formulation presented in this chapter deals with the static and dynamic stress analysis of two or more bodies when they come into contact with each other under the action of external loads. The formulation is not restricted to the special case of an unanchored tank resting on the ground, rather it handles the general contact problem in two and three dimensions.
In many engineering problems, externally applied forces are considered independently from their source. This assumption simplifies the analysis significantly and, on many occasions, does not seriously affect the accuracy of the solution. In contact analysis, the contact forces that arise from the inequality constraints over the contact area are unknowns. In addition, the contact area and deformation status of the bodies in contact are also unknowns. These unknowns associated with any contact problem render the resulting problem nonlinear. Hence, analytical solutions are obtained for very few of relatively simple problems. As it almost invariably happens in these cases, complicated practical problems are simulated by numerical methods. The numerical algorithm used in this study is adapted from the work done by Chaudhary and Bathe (, ).