A THREE-DIMENSIONAL AIRY STRESS FUNCTION

The most general stress function in three dimensions is given by the symmetric Beltrami tensor, which consists of six scalar functions. In this brief communica-tion, we explore the possibility of expressing a three-dimensional state of stress by means of a single scalar function, in the spirit of the Airy stress function in two dimensions. The price to pay for such a severe restriction is a loss of generality, in the sense that not every divergence-free stress field can be derived from the single stress function. Clearly, any such single scalar function gives rise to a particular case of the Beltrami tensor. One of these particular cases exhibits an interesting analogy with the tensor of inertia of a rigid body.