Bending and vibration analysis of porous-elastic bilayer microplate using case-based reasoning with size effects

Abstract Classical theory without material length-scale parameters fails to explain size effects, and thus constrains the case-based reasoning (CBR) in the forward/inverse design of mechanical response for microcomponent. In this paper, the case-based reasoning (CBR) and the classical couple stress theory (CST) with material length-scale parameters are combined to establish the size-dependent porous-elastic bilayer Kirchhoff microplate model. The classical couple stress theory (CST) and modified couple stress theory including the symmetric/anti-symmetric couple stress theory are applied to describe size effects. Hamilton's principle is applied to derive the governing equation, boundary conditions, and initial condition. Static bending and free vibration analyses of porous-elastic bilayer microplates are performed to construct case base with classical couple stress. Subsequently, forward and inverse design analyses are conducted based on CBR. For the forward design, compared with CBR with the symmetric/anti-symmetric couple stress, the deflection and axial displacement of microplate based on the CBR with classical couple stress are the minimum while the natural frequency is maximum. The influences of the classical couple stress, porosity coefficient and porosity distribution pattern on deflection, axial displacement, and natural frequency of microplates are systematically investigated. For the inverse design, the plate length-to-thickness ratio and porosity coefficient are determined according to the prescribed bending deflection. Furthermore, the porosity distribution pattern is further predicted by combining forward and inverse design results. Thus, case-based reasoning (CBR) incorporated with the classical couple stress theory can appropriately capture the size-dependent bending and vibration behaviors of porous-elastic bilayer microplates.