The Effect of Laminate Kinematic Assumptions on the Global Response of Actuated Plates

The effects of accurately accounting for transverse shear strain, transverse normal strain, and discrete layer kinematics on the computed global response of actuated plates are investigated using a hierarchical displacement-based, two-dimensional (2-D) finite element model that is developed specifically for composite laminates. The hierarchical model is used to obtain the first-order shear deformation model, a higher-order cubic equivalent-singlelayer model, a type-I layerwise model, and a type-II layerwise model as special cases. Each of the first three models uses a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the models differ significantly in their assumed distribution of transverse shear strain. The type-II layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects. The scope of the study is restricted to homogeneous plates with surface-mounted actuators covering a wide range of span-to-thickness ratios. The results clearly demonstrate that as the span-to-thickness ratio of the actuated region decreases, discrete layer kinematics become very important for accurately characterizing the global response of the actuated plate. The set of laminate kinematic assumptions utilized by a particular model influence the predicted global response primarily through the so-called local kinematic effect where a portion of the available actuation energy is diverted to the production of localized transverse shear deformation and localized transverse normal deformation in the vicinity of the actuator edges, thereby reducing the amount of actuation energy that is available for producing the intended global deformation mode.