In 1892, Boussinesq solved the radial stress distribution in a semi infinite body as shown in Fig. 6.2. He used polar coordinates instead of rectangular coordinates. When there is no shear stress on the surface, the solution of radial stress is

2fcos0r

Frm equation (6.16), it can be seen that when R approaches 0, O becomes infinite. Obviously, this situation is impossible, because the surface material will yield or fail seriously at this time. HRX's explanation for this is that a small contact area will be formed to replace point or line contact, and the load will be distributed to the whole contact surface, relieving infinite stress from the surface. Hea proposed the following assumptions in the analysis: 1) all the deformations are within the elastic range and do not exceed the proportional limit of the material. 2) The load is perpendicular to the surface, ignoring the shadow of the surface shear stress. 3) compared with the radius of curvature of the loaded object, the radius of the contact area is very small. 4) compared with the radius of the contact area, the radius of curvature of the contact area is very large. The solution of the elastic theoretical problem is based on the assumed stress function. These stress functions must be filled in Figure 6.2 individually or in combination The Boussinesq analysis model has sufficient compatibility equations and boundary conditions. For the stress distribution of a semi infinite elastic body, the assumption adopted by hert is

Where B is any fixed length, x, y and Z are parameters with the measurement network of 1. Set up:

These hypotheses come partly from intuition, partly from experience, and are combined with elastic relations (Eq. (6.7), Eq. (6.10) and

Fomula (612) to formula (6, 14), and

O.av Ou s AV