Asymptotic analysis of plates in static and dynamic strain gradient elasticity

Christian Licht, Thibaut Weller
2022 Comptes Rendus. Mécanique  
We study the steady-state and transient responses of a second-order elastic plate by implementing an asymptotic analysis of the three-dimensional equations with respect to two geometric characteristics seen as parameters: the thickness of the plate and an inner material length. Depending on their ratio, four different models arise. Conditions under which Reissner-Mindlin kinematics may appear are discussed while the influence of crystalline symmetries is studied. The transient situation is
more » ... d through Trotter's theory of approximation of semi-groups of operators acting on variable spaces.
doi:10.5802/crmeca.118 fatcat:sbqxgjh5xjeihk6gdgiku5kwuq