5. Conclusions

that an important reduction of the computational cost is achieved by increasing the difference between Lmax and Luni. Similar tendencies are observed for case of study II, where the reductions of computational cost are even more remarkable due to the presence of finite dimensions.

In this section, the performance of the proposed approach when adaptive refinement is also performed inside the true contact area is illustrated. To do so, the contact problems defined by cases of study I and II are solved under several configurations of the approach, in which wmax has been varied, keeping Luni < Lmax (setting 3 in Section 3.1). Figures 10e, f and 12b show examples of the resulting contact area and pressure element mesh that have been obtained for

The contact pressure distributions along the principal axes of the contact area of the solutions shown in Figure 10d-f are shown in Figure 11b. The contact pressure distributions along the principal axes of the contact area of the solutions shown in Figure 12a, b are shown in Figure 13. It both cases, it can be observed that increasing the value selected for wmax implies that a coarser mesh is used in those regions of the true contact area where the contact pressure

Figure 12. Axisymmetric representation of the resulting contact area and pressure element mesh obtained for CoSII

Figure 13. Contact pressure distribution for CoSII under several configurations of the approach.

4.3. Performance of the approach when adaptive mesh refinement is performed

both inside and outside the true contact area

76 Contact and Fracture Mechanics

under two different configurations of the approach.

cases of study I and II under this setting of the approach.

A new semi-analytical approach has been developed to solve frictionless elastic contact problems using adaptive mesh refinement. Starting from a coarse initial uniform mesh (whose density is defined by the parameter Luni), a mesh refinement is performed based on two different criteria: (i) the maximum allowed rate of change of a physical magnitude (the contact pressure), defined by the parameter wmax and (ii) the maximum degree of mesh refinement, defined by the parameter Lmax.

The configuration of the approach is defined by a unique combination of values for Luni, Lmax, and wmax. The performance of the proposed approach has been illustrated with several cases of study solved under different configurations of the approach, and the obtained results enable us to draw the following conclusions:


A further discussion on this topic can be found in Ref. [11].
