A hierarchy of dynamic equations for micropolar plates

AbstractThis work considers homogeneous isotropic micropolar plates adopting a power series expansion method in the thickness coordinate. Variationally consistent equations of motion and end boundary conditions are derived in a systematic fashion up to arbitrary order for extensional and flexural displacement cases. The plate equations are asymptotically correct to all studied orders. Numerical results are presented for various orders of the present method, other approximate theories as well as the exact three dimensional theory. The results illustrate that the present approach may render benchmark solutions provided higher order truncations are used, and act as engineering plate equations using low order truncation