Optimized dynamic design of laminated piezocomposite multi-entry actuators considering fiber orientation
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© 2018 Elsevier B.V. Laminated piezocomposite actuators (LAPA) are structures composed of piezoelectric and non-piezoelectric materials layers. Due to several parameters and the multiphysics domain involved in the design of LAPA, simple forms are commonly found in industrial applications. However, its design can be systematized by using the topology optimization method (TOM) that permits the solution of complex problems. The design of LAPA with TOM has traditionally considered the optimization of piezoelectric materials over an isotropic substrate, yet some previous researches suggest that LAPA including fiber-reinforced composite layers can increase the performance of these transducers. In addition, works dealing with fiber-based composite focus on static or harmonic analysis with sinusoidal excitations, although other signal inputs are used in practice. In fact, the design of fiber-based LAPA in transient regime has not been assessed before. Thus, a methodology is proposed here to design LAPA with TOM. The actuator is electrically excited with a combined waveform: a sine wave treated as a harmonic problem and a step excitation addressed as a transient problem. Both waves have the same frequency, however they are not applied at the same time. This approach allows the development of a multi-entry actuator since it generates the same level of output displacement independently of the type of excitation input. Consequently, the optimization problem is formulated with the purpose of distributing the material in all layers, the polarization sign in piezoelectric layers and the fiber orientation angle in composite layers, in which the objective function simultaneously seeks for the maximization of the vibration amplitude at certain points of the actuator and its response speed. Eight-node shell elements taking into account the piezoelectric effects are used in the finite element method (FEM) and the “layer wise theory is adopted to model the laminated structure. The Generalized-α method is used to solve the transient problem. In order to optimize the material distribution and the polarization sign, the classical SIMP and PEMAP-P models are used respectively, while to optimize the fiber orientation angles in the composite material, a novel self-penalizable interpolation model is proposed. This optimization problem is solved by using the sequential linear programming (SLP) technique with the CVX solver and the sensitivity analysis is performed with the adjoint method. Discrete signal processing concepts are applied to solve the adjoint problem involving specific points of curves obtained by time integration methods in transient analysis. Numerical techniques are implemented to avoid TOM instabilities. Finally, the potential of this approach is demonstrated with two numerical examples.
author list (cited authors)
Salas, R. A., Ramírez-Gil, F. J., Montealegre-Rubio, W., Silva, E., & Reddy, J. N.