An asymptotic theory of thin micropolar plates

The asymptotic expansion technique is used to obtain the two-dimensional dynamic equations of thin micropolar elastic plates from the three-dimensional dynamic equations of micropolar elasticity theory. To this end, all the field variables are scaled via an appropriate thickness parameter such that it reflects the expected behavior of the plate. A formal power series expansion of the three-dimensional solution is used by considering the thickness parameter as a small parameter. Without any a priori assumption on the form of the field variables, it is shown that the zeroth-order approximation simultaneously includes both the plate equations previously presented in the literature and the standard assumptions on the specific forms of the field variables. Some aspects of the present asymptotic plate equations are also discussed.