United elements method for general contact–impact problems Original Research Article

This work presents the details of a finite element-based numerical method to analyse general contact/impact problems, called united elements method (UEM). In contrast to usual methods, that is Lagrange Multipliers and Penalty Function, this method is conceptual, suitable for computer programming, and free from inherent deficiencies of those methods. The key points of this procedure are elimination of the normal degree of freedom of the contactor node from the system energy potential functional in terms of target surface motion, and proper calculation of target element unbalanced forces, to incorporate the contact constraints. After a review on classic formulations, the mathematical and matrix presentation of the united element stiffness matrix are discussed. Solution of some examples adopting a Newton–Raphson-based solution, together with a normal return scheme, support the capability and accuracy of the procedure in static and dynamic problems.