Simultaneous optimization of piezoelectric actuator topology and polarization

Gonçalves, Juliano F.; Leon, Daniel M. De; Perondi, Eduardo André

doi:10.1007/s00158-018-1957-8

Cited by 16 publications

(12 citation statements)

References 39 publications

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“…Afterwards, other approaches including SIMP (Kögl and Silva 2005), BESO (de Almeida 2019) or level set method (Chen et al 2010) are also explored. By defining proper objective functions, TO methodology is applied to piezoelectric actuators (Moretti and Silva 2019;Gonċalves et al 2018), sensors (Menuzzi et al 2018) and energy harvesters (Homayouni-Amlashi et al 2020b;Homayouni-Amlashi 2019;Townsend et al 2019). The publications considered different types of system modeling including the static (Zheng et al 2009), dynamic (Noh and Yoon 2012;Wein et al 2009), modal (Wang et al 2017) and electrical circuit coupling (Salas et al 2018;Rupp et al 2009).…”

Section: Introductionmentioning

confidence: 99%

2D topology optimization MATLAB codes for piezoelectric actuators and energy harvesters

Homayouni-Amlashi

Schlinquer

Mohand-Ousaid

et al. 2020

Struct Multidisc Optim

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In this paper, two separate topology optimization MATLAB codes are proposed for a piezoelectric plate in actuation and energy harvesting. The codes are written for one-layer piezoelectric plate based on 2D finite element modeling. As such, all forces and displacements are confined in the plane of the piezoelectric plate. For the material interpolation scheme, the extension of solid isotropic material with penalization approach known as PEMAP-P (piezoelectric material with penalization and polarization) which considers the density and polarization direction as optimization variables is employed. The optimality criteria and method of moving asymptotes (MMA) are utilized as optimization algorithms to update the optimization variables in each iteration. To reduce the numerical instabilities during optimization iterations, finite element equations are normalized. The efficiencies of the codes are illustrated numerically by illustrating some basic examples of actuation and energy harvesting. It is straightforward to extend the codes for various problem formulations in actuation, energy harvesting and sensing. The finite element modeling, problem formulation and MATLAB codes are explained in detail to make them appropriate for newcomers and researchers in the field of topology optimization of piezoelectric material.

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Section: Introductionmentioning

confidence: 99%

2D topology optimization MATLAB codes for piezoelectric actuators and energy harvesters

Homayouni-Amlashi

Schlinquer

Mohand-Ousaid

et al. 2020

Struct Multidisc Optim

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“…where i and i are the design variables related to the ith element, k is the eigenvalue associated to the kth vibration mode, V i is the volume of the ith element, and C P is a threshold for the actuators' volume. Compared to the optimization problem presented in the work of Gonçalves et al, 39 there is a modification in the objective function that is proposed to overcome some problems that occurred when including void areas in the fixed domain. Faster convergence and less gray areas in the final solution were achieved when including the term − n k √ T in the objective function.…”

Section: Actuator Design By Maximizing the Controllabilitymentioning

confidence: 99%

“…For the initial S iterations, only the structural and polarization design variables ( i and i ) are calculated (Marker 5) in order to avoid starting the piezoelectric distribution with null-polarization elements. 39 The stopping criteria (Marker 6) are based on tolerance thresholds and take into account the values of design variables in the current (k) and previous iteration (k − 1):…”

Section: Optimization Problem Implementationmentioning

confidence: 99%

A simultaneous approach for compliance minimization and piezoelectric actuator design considering the polarization profile

Gonçalves

Leon

Perondi

2019

Numerical Meth Engineering

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Summary This article addresses the compliance problem along with the piezoelectric actuator design for active vibration control. The topology structural design is obtained by solving a compliance minimization problem with volume constraint, whereas the actuator design is carried out by the maximization of a control performance index written in terms of the controllability Gramian. This measure describes the ability of the actuator to move the structure from an initial condition to a desired final state, at rest for instance, in a finite time interval. The actuator design is also characterized by the polarization profile, which is defined according to the distribution of an additional design variable. Therefore, the actuators can yield both tensile and compressing fields at different points of the structure using the same applied control voltage. To achieve this goal, a material interpolation scheme based on the solid isotropic material with penalization and the piezoelectric material with penalization and polarization (PEMAP‐P) models is employed, and both the optimum structure/actuator layout and polarization profile are obtained simultaneously. The sensitivities with respect to the polarization and design variables are calculated analytically. Numerical examples are presented considering the design and vibration control for a cantilever beam, a beam fixed at both ends, and an L‐bracket structure to show the efficiency of the proposed formulation. The control performance of the designed structures are analyzed employing a linear‐quadratic regulator simulation, and these results are compared to verify the influence of the optimized polarization profiles.

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“…Topology optimization is employed to find an optimal distribution of piezoelectric material in a multi-layer plate or shell structure to provide the maximum displacement δpre or generated forces in a given direction at a given point of the domain [19,20,21]. Simultaneous topology and polarization optimization, which uses the Piezoelectric Material with Penalization and Polarization (PEMAP-P) and works to find the optimum actuator layout and polarization profile simultaneously [22,23,24]. For this method, in addition to the pseudo-density ρ1, a new design variable ρ2 is introduced for the polarization of the piezoelectric material.…”

Section: Introductionmentioning

confidence: 99%

“…Simultaneous topology and polarization optimization, which uses the Piezoelectric Material with Penalization and Polarization (PEMAP-P) and works to find the optimum actuator layout and polarization profile simultaneously [22,23,24]. For this method, in addition to the pseudo-density ρ1, a new design variable ρ2 is introduced for the polarization of the piezoelectric material.…”

Section: Introductionmentioning

confidence: 99%

Optimal Design of Piezoelectric Cantilevered Actuators for Charge-Based Self-Sensing Applications

Liseli

Agnus

Lutz

et al. 2019

Sensors

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Charge-based Self-Sensing Actuation (SSA) is a cost and space-saving method for accurate piezoelectric based-actuator positioning. However, the performance of its implementation resides in the choice of its geometry and the properties of the constituent materials. This paper intends to analyze the charge-based SSA’s performances dependence on the aforementioned parameters and properties for a piezoelectric cantilever. A model is established for this type of Piezoelectric Actuator (PEA), and a multi-objective function is defined. The multi-objective function consists of the weighted actuator and sensor objective functions of the PEA. The analytical optimization approach introduced herein aims to assess the evolution of the defined multi-objective function across a defined set of geometrical parameters and material properties and highlights the existence of a subset of solutions for an optimal charge-based SSA’s implementation. The commercially-available finite element analysis software, COMSOL Multiphysics, is used on the parametric model of the given structure to validate the analytical model. Then, experiments are conducted to corroborate the numerical and analytical modeling and analysis.

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Simultaneous optimization of piezoelectric actuator topology and polarization

Cited by 16 publications

References 39 publications

2D topology optimization MATLAB codes for piezoelectric actuators and energy harvesters

2D topology optimization MATLAB codes for piezoelectric actuators and energy harvesters

A simultaneous approach for compliance minimization and piezoelectric actuator design considering the polarization profile

Optimal Design of Piezoelectric Cantilevered Actuators for Charge-Based Self-Sensing Applications

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