Saint-Venant's conditions of compatibility (contd...):

Let V be simply connected region occupied by a body. In this domain (x,y,z) is the current location of a point at which are given and we need to find out the deformations.

Let be any point in V and are the components of displacement at and are the components of rotation.

Let be any other point at V at which we want to find out the components of displacements. Let be a line that joins and and lies in V. Then if the partial derivatives are known, then the displacements can be found out as,

where

(1.37)

Hence,