Is it possible to get a constant voltage using piezoelectric crystal by giving mechanical stress?
No.


  Piezoelectricity /piˌeɪzoʊˌilɛkˈtrɪsɪti/ is the electric charge that accumulates in certain solid materials (such as crystals, certain ceramics, and biological matter such as bone, DNA and various proteins) in response to applied mechanical stress. Wikipedia._


Note that the result of stressing the crystal is a charge and not a current. You can use the charge but once it's gone - it's gone.

The other way of thinking of it is by reasoning with the laws of thermodynamics. You are thinking of putting a one time stress energy into the material and getting a continuous stream of energy out of it. That would be free energy and that's impossible.