摘要：A finite element formulation to deal with friction contact between an elastic
body and a rigid obstacle is presented. Contact between flexible solids or
between a flexible and a rigid solid is defined using a non-penetration
condition which is based on a representation of the interacting
deforming surfaces. A large number of contact algorithms based on the
imposition of inequality constraints were developed in the past to represent
the non penetration condition. We can mention penalty methods,
Lagrange multiplier methods, augmented Lagrangian methods and many others. In
this work, we developed an augmented Lagrangian method using a slack
variable, which incorporates a modified Rockafellar Lagrangian to solve non
linear contact mechanics problems. The use of this method avoids the
utilization of the well known Hertz-Signorini-Moreau conditions in contact
mechanics problems (coincident with Kuhn-Tucker complementary conditions in
optimization theory). The contact detection strategy makes use of a
node-surface algorithm. Examples are provided to demonstrate the robustness and
accuracy of the proposed algorithm. The contact element we present can be
used with typical linear 3-D elements. The program was written in C++ under
the OOFELIE environment. Finally, we present several applications of
validation.
