Stress transformation in plane stress and plane strain. Consider a point in a continuum under a state of plane stress, or plane strain, with stress components (,,) and all other stress components equal to zero (Figure 8.1). From static equilibrium of an infinitesimal material element at (Figure 8.2), the normal stress and the shear stress on any plane perpendicular to the -plane passing ...

The quotient map from the sphere onto the real projective plane is in fact a two sheeted (i.e. two-to-one) covering map. It follows that the fundamental group of the real projective plane is the cyclic group of order 2; i.e., integers modulo 2. One can take the loop AB from the figure above to be the generator. The projective hemisphere