Conservative semidiscrete difference schemes for Timoshenko systems

We present a parameterized family of finite-difference schemes to analyze the energy properties for linearly elastic constant-coefficient timoshenko systems considering shear deformation and rotatory inertia. we derive numerical energies showing the positivity,and the energy conservation property and we show how to avoid a numerical anomaly known as locking phenomenon on shear force. our method of proof relies on discrete multiplier techniques. © 2014 d. s. almeida júnior.