Abstract: Contact problem is one of the most important problems frequently ncountered in engineering structures and processing technology.Collar rotary shouldered connection, contact between drillstring and hole, and between bit and rock as in petroleum engineering, and the quasi-static contact between bridge and concrete base and rolling contact between train wheel and track as in rail engineering are some special examples of contact problems. The most difficult and crucial issue in solving such problems is to establish contact varia-
tional function and solution method. In this paper, the current literature related to the theories and methods of variational principles of contact mechanics is reviewed, analyzed and compared, which sets a foundation for the establishment of variational principles specific to the rotary shouldered connection problem.

Key words: Contact mechanics, Variational principle, Lagrange equation, Finite element, Nonlinearity