Complementary energy principle for elastodynamics: Free of volumetric locking

This paper proposes a complementary energy principle for elastodynamic problems. In doing so, the stresses and the inertial forces, that satisfy the equilibrium equations a priori, are chosen as basic variables and then, the complementary variational formulation is established by weakly enforcing the kinematic constraints. The eventual formulation is posed to be an integral equation with respect to the time dimension and can be easily applied to free and forced vibration analysis. In addition, the volumetric locking-free property inherent in the complementary energy principle is addressed. Numerical study on a rectangular plate is performed to validate the proposed complementary energy principle as well as to verify the featured locking-free property. Moreover, extensions of the dynamic complementary energy principle to tackle visco-elastodynamics and Stokes flows are also presented.