On antiplane stress in an elastic solid

Abstract

1—It is usual to apply the term “plane stress” to a stress system in an elastic solid in which all the stress components other than those acting solely parallel to a fixed plane (which may be taken as that of x, y ) vanish identically. Thus the characteristic of plane stress is that x͡y = 0, y͡x = 0, z͡z = 0, but x͡x , y͡y , x͡y do not in general vanish. We may use the term “antiplane stress” to denote a stress system which is complementary to plane stress, that is, one in which x͡x = 0, y͡y = 0, x͡y = 0, (1) but x͡z , y͡z , z͡z do not in general vanish.