Relaxation methods applied to engineering problems. X. The graphical representation of stress

A convenient representation of a vector quantity (e.g. the shear stress on a specified plane) is by contours which exhibit its resultant magnitude and by ‘trajectories’ which have its direction at every point. But it sometimes happens that only its components in two perpendicular directions are known, and then, while the contours are easy to construct, derivation of the ‘trajectories’ presents a special problem. If this can be solved, tensor quantities also will be representable, e.g. a state of plane stress. By orthodox methods the problem would appear to be difficult, but in this paper it is shown to yield to ‘relaxational’ attack.