The treatment of contact problems as a non-linear complementarity problem

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:35842

Bjorkman, G

Contact and friction problems are of great importance in many engineering applications, for example in ball bearings, bolted joints, metal forming and also car crashes. In these problems the behavior on the contact surface has a great influence on the overall behavior of the structure. Often problems such as wear and initiation of cracks occur on the contact surface. Contact problems are often described using complementarity conditions, w {>=} 0, p {>=} 0, w{sup T}p = 0, which for example represents the following behavior: (i) two bodies can not penetrate each other, i.e. the gap must be greater than or equal to zero, (ii) the contact pressure is positive and different from zero only if the two bodies are in contact with each other. Here it is shown that by using the theory of non-linear complementarity problems the unilateral behavior of the problem can be treated in a straightforward way. It is shown how solution methods for discretized frictionless contact problem can be formulated. By formulating the problem either as a generalized equation or as a B-differentiable function, it is pointed out how Newton`s method may be extended to contact problems. Also an algorithm for tracing the equilibrium path of frictionless contact problems is described. It is shown that, in addition to the {open_quotes}classical{close_quotes} bifurcation and limit points, there can be points where the equilibrium path has reached an end point or points where bifurcation is possible even if the stiffness matrix is non-singular.

• OSTI ID: 35842
• Report Number(s): CONF-9408161--
• Country of Publication: United States
• Language: English

Related Subjects

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION
36 MATERIALS SCIENCE
99 GENERAL AND MISCELLANEOUS
BIFURCATION
COMPUTERIZED SIMULATION
FRICTION
NONLINEAR PROBLEMS
NUMERICAL SOLUTION