Mechanical contact conditions implementation in FEM algorythms with different basis functions sets: one-dimensional case

The one-dimensional axisymmetric approximation for the elastic contact problem is considered. Finite element method algorythms with Lagrange and Hermite basic functions are used. In the first case the Lagrange multiplier method for contact conditions implementation is used. In the second case the contact conditions are implemented in the natural way. Test contact problems with analitical solutions are solved. The tests showed that FEM algorythm with Hermite basis functions is more accurate, than Lagrange one. On the other hand, algorythm with Hermite basis functions has a much higher computational complexity.