Laminated Piezocomposites Structures (LAPS) Designed for Topology Optimization Considering Simultaneously Harmonic and Transient Responses

Laminated Piezocomposites Structures (LAPS) Designed for Topology Optimization Considering Simultaneously Harmonic and Transient Responses

Salas, Ruben A.; Silva, Emilio C. N.; Reddy, J. N.

Abstract:

LAminated Piezocomposite Structures (LAPS) are primarily multi-layer structures composed by piezoelectric, metal and composite materials (epoxy matrix with carbon or glass fiber). This structures show superior features over conventional piezoelectric materials because their characteristics cannot be achieved by any of its components isolated, for example more strength and less weight. Thus, this work aims at the development of LAminated Piezocomposite Structures (LAPS) through the vibration modes and resonance frequencies design aiming at dynamic applications. Piezomotors, sonar devices and energy harvesters can be mentioned as potential applications. Therefore, LAPS dynamic design can be systematized by using the Topology Optimization Method (TOM), which is a method based on the distribution of material in a fixed design domain with the aim of extremizing a cost function subjected to constraints inherent to the problem. TOM combines the optimization algorithms and the finite element method (FEM). In this work, the TOM formulation aims to determine simultaneously the optimal topology of the materials for different layers, the polarization sign of the piezoelectric material and the fiber angle of the composite layer, in order to design a particular vibration mode by means of maximizing the vibration amplitude at certain points for a specified resonance frequency or the energy conversion aiming applications such as energy harvesters. The governing equations for modeling of LAPS are solved using the linear FEM based on three-dimensional eight-node isoparametric elements. The TOM formulation includes several material models as the Simple Isotropic Material with Penalization (SIMP) for isotropic materials, the PiezoElectric MAterial with Penalization and Polarization (PEMAP-P) in order to describe polarization in piezoelectric material and one based on the Discrete Material Optimization (DMO) for the purpose to take into account of fiber orientation in composite materials. The objective function combines harmonic and transient FEM analysis terms to deal with vibration amplitude maximization and rise time minimization with the purpose of improving the dynamic response. The transient problem is solved with the Cross Weighted-Residual (CWR) time integration scheme and Sequential Linear Programming (SLP) is used for solving the non-linear optimization problem. Results are shown in order to illustrate the method.

LAminated Piezocomposite Structures (LAPS) are primarily multi-layer structures composed by piezoelectric, metal and composite materials (epoxy matrix with carbon or glass fiber). This structures show superior features over conventional piezoelectric materials because their characteristics cannot be achieved by any of its components isolated, for example more strength and less weight. Thus, this work aims at the development of LAminated Piezocomposite Structures (LAPS) through the vibration modes and resonance frequencies design aiming at dynamic applications. Piezomotors, sonar devices and energy harvesters can be mentioned as potential applications. Therefore, LAPS dynamic design can be systematized by using the Topology Optimization Method (TOM), which is a method based on the distribution of material in a fixed design domain with the aim of extremizing a cost function subjected to constraints inherent to the problem. TOM combines the optimization algorithms and the finite element method (FEM). In this work, the TOM formulation aims to determine simultaneously the optimal topology of the materials for different layers, the polarization sign of the piezoelectric material and the fiber angle of the composite layer, in order to design a particular vibration mode by means of maximizing the vibration amplitude at certain points for a specified resonance frequency or the energy conversion aiming applications such as energy harvesters. The governing equations for modeling of LAPS are solved using the linear FEM based on three-dimensional eight-node isoparametric elements. The TOM formulation includes several material models as the Simple Isotropic Material with Penalization (SIMP) for isotropic materials, the PiezoElectric MAterial with Penalization and Polarization (PEMAP-P) in order to describe polarization in piezoelectric material and one based on the Discrete Material Optimization (DMO) for the purpose to take into account of fiber orientation in composite materials. The objective function combines harmonic and transient FEM analysis terms to deal with vibration amplitude maximization and rise time minimization with the purpose of improving the dynamic response. The transient problem is solved with the Cross Weighted-Residual (CWR) time integration scheme and Sequential Linear Programming (SLP) is used for solving the non-linear optimization problem. Results are shown in order to illustrate the method.

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Salas, Ruben A.; Silva, Emilio C. N.; Reddy, J. N.; "Laminated Piezocomposites Structures (LAPS) Designed for Topology Optimization Considering Simultaneously Harmonic and Transient Responses", p-75-75. In: Proceedings of the 13th International Symposium on Multiscale, Multifunctional and Functionally Graded Materials [=Blucher Material Science Proceedings, v.1, n.1]. São Paulo: Blucher, 2014.
ISSN 23589337, DOI