Asymptotic analysis of plates in static and dynamic strain gradient elasticity

We study the steady-state and transient responses of a second-order elastic plate by implementing an asymptotic analysis three-dimensional equations with respect to two geometric characteristics seen as parameters: thickness inner material length. Depending on their ratio, four different models arise. Conditions under which Reissner–Mindlin kinematics may appear are discussed while influence crystalline symmetries is studied. The situation solved through Trotter’s theory approximation semi-groups operators acting variable spaces.