Abstract: In this paper any symmetric tensor is decomposed into the sum of two tensors. One of them is a "type of stress" tensor, and another is a "type of strain" tensor. The inner product space of symmetric tensor is decomposed into the sum of two orthogonal subspaces. The geometric meaning of several principles in the theory of elasticity, is given.

Key words: temperature, rotating cylinder, pressure, angular velocity, functionally graded piezoelectric (FGP) material, sensor