Friction

A cubic block A with side equal to 0.5 m, is placed upon the upper face of a parallelepiped B with base equal to 0.7m • 4.0m and height 1.0m. Besides the gravitational force, a horizontal force His considered.

H magnitude is equal to 0.5 • Wa, where Wa is the absolute value of the gravitational force acting in A, and its direction is the same of the longer edge of B base.

Figure 8. Friction: (a) geometrical model; (b) forces and constraints; (c) node numbering of block A.

The geometrical configuration, forces and constraints and node numbering are summarize in Figure 8.

No damping is considered in this analysis.

This configuration is useful to check the behaviour of the shear force at contact.

At first the static frictional coefficient is set equal to 0.4. The force applied horizontally is higher than the elastic limit of the shear force and sliding is expected.

The horizontal distance covered in the time-interval (0, t) can be easily computed with where a = 0.1 • g.

The analytical result can be compared with the numerical one (Fig. 9).

Using the same configuration the static frictional coefficient is set equal to 0.6. The elastic limit of the shear force is therefore exceeding the applied force and

Nod« 10. X displacement

Nod« 10. X displacement

Figure 9. X displacement of node 10: comparison between the analytical and the numerical solution.

Node 10: X displacement

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