Fundamental solution traction

Is determined provided that either the deformation or surface traction vector Is prescribed on the boundary. The fundamental solutions for the elastic deformation and surface traction are further discussed In Appendix 1. 

Here H and g are determined from the integral of the fundamental solutions. It is appropriate to mention here that both H and G are slngtilar operators. The uniform displacement vector V is mapped to the zero vector by H and the constant pressure surface traction vector t is mapped to zero by G. This is because both t and Hq are homogeneous solutions to the Stokes equations. In the present work the vectors W and are specified on different parts of the boundary. Complete mathematical details of this method and application are to be reported elsewhere. 

Soon after vinyl BR s were first introduced commercially, it was recognized that the vinyl structure imparted non-typical dynamic properties. In particular, their vulcanizates showed improved resistance to heat build-up when compared to emulsion SBR. j O Before relating the special contribution of the vinyl structure to properties, it is informative to first determine the influence of styrene content (at constant vinyl) on the two fundamental properties of interest Tg and tan 6, as shown in Figure 14. As expected, both Tg and tan 6 increase almost linearly with styrene content. Thus like a conventional tire tread rubber, the rolling resistance of solution SBR s prepared using lower amounts of styrene is accompanied by a decrease in the wet traction of the rubber. 

In order to describe how the various molecular structural features of solution rubbers influence rolling resistance and traction, it is necessary to relate these performance properties of tyres in terms of the fundamental material properties of rubbers (Fig. 23). The loss tangent of a tread rubber vulcanizate determined at about 100 Hz and at a temperature of 60°C is a significant material property that relates to the energy dissipated per cycle in a rolling tyre, i.e. the tyre s rolling resistance. The 7 of the rubber is a suitable physical material... 

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