"Relative Rigidity" of structures and Saint Venant's Principle.

Abstract

Stress and strain of structures can be calculated precisely today by numerical methods. It is also important, however, to obtain a macroscopic view of force flow in structures. In this paper, the definition of Relative Rigidity was introduced, and using this concept, the expression of force flow in structures was derived. As a relative has a tensor value which has positive principal values, it can be designated by a proper ellipsoid which can be called rigidity ellipsoid. Moreover, Saint Venant's Principle was interpreted by the decay of above mensioned force flow, and an example and a counter example of this principle were presented numerically.