Consistent derivation of stress-based generalized models in elastodynamics: Application to layerwise plate models

The derivation of some class of generalized mechanical models relies on a specific stress expansion without any a priori assumption on the corresponding kinematics. In such situations, their extension to a dynamic setting is not easy, especially when deriving the corresponding generalized inertias since the kinematics is unknown. This paper shows how consistent generalized inertias can be obtained through the use of a complementary energy principle in elastodynamics. The methodology is then applied to extend a stress-based layerwise plate model in the dynamic setting. This approach is finally validated through modal analysis of various anisotropic composite laminates.