CONTACT PROBLEMS IN ORTHOTROPIC MATERIALS USING THE BOUNDARY ELEMENT METHOD

Resumo

The main objective of this work is the development of a boundary element formulation for the evalu-
ation of frictional contact problems in bodies of anisotropic materials under centrifugal loads. The fundamental

solution is obtained using the Lekhnitskii formulation. Centrifugal loads are treated as body forces and are not

included in the computation of the fundamental solution. Because of this, domain integrals arises in the formu-
lation. In order to avoid domain discretization, these integrals are transformed into boundary integrals using an

exact transformation. As a result, an elegant formulation is obtained where only boundaries need to be discretized.

Quadratic continuous boundary elements are used in order to discretize boundaries of contact bodies. As the con-
tact area is unknown, there is a non-linear problem in which the Newton’s method is used in order to compute

tractions and displacements. Problems with known analytical solutions are used in order to assess the accuracy of
the proposed formulation. A numerical analysis of a contact problem in a high pressure compressor of the turbojet
engine is carried out. This problem comprises of anisotropic monocristal blades in contact with an isotropic rotor.
Due to centrifugal and random loads, blades are subjected to stresses of fretting. They are attached at the rotor
by dovetail joints where occur severe contact. Fatigue due to fretting is the main cause of mechanical failure in
turbojet engines, what shows the relevance of this work. If compared to other traditional numerical methods, as
the finite element method, there are many advantages in the boundary element formulation, considering accuracy
in the computation of stress field and an easier mesh manipulation.