Closed-form expressions for higher order electroelastic tetrahedral elements

Moetakef, Mohammad; Lawrence, K. L.; Joshi, S. K.; Shiakolas, Panos S.

doi:10.2514/3.12343

Cited by 9 publications

(5 citation statements)

References 8 publications

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“…After the weighted integrals are calculated and the admissible solutions are found in elementary matrix form (superscript e), the global matrices for a dynamic system are given by the mass matrix M uu , the stiffness matrix K uu , the piezoelectric coupling matrix K K u u = f f and the dielectric permittivity matrix K ff [21,22]:…”

Section: Piezoelectric Constitutive Equationsmentioning

confidence: 99%

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Topology optimization of flextensional piezoelectric actuators with active control law

Moretti

Silva

Reddy

2019

Smart Mater. Struct.

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Flextensional actuators assembled in association with piezoceramics feature the amplification of nanometric displacements generated by the ceramics energy conversion. For applications that require high precision positioning or vibration response attenuation, such as hard disc reading or atomic force microscopy, a response tracking control needs to be implemented. Shell and plate piezoactuators with vibration control have been extensively studied in literature, however the design of controlled piezoelectric systems by means of the Topology Optimization Method (TOM) has not been fully explored in literature yet, and is generally focused on the frequency domain transient analysis, which employs a model reduction method for the sake of computational implementation. Dealing with transient analysis of flextensional piezoelectric actuators, an active closed loop control design is more suited for the positioning and vibration problem, which consists on measuring the outputs of the system by the closed loop sensor layer, whose signal is modified by a control gain and eventually inputted into the actuator layer so the system response signal is modulated. Aiming to enhance the active feedback control in piezoelectric actuators (PEAs), this work targets the design of the flextensional microstructure considering an active velocity feedback control (AVFC), where the active piezoelectric sensing and actuating cycles imply in an extra damping to the system. Therefore, the flextensional mechanism compliance shall be distributed within the design domain by the allocation of void regions where there should be the flexible hinges. Such a design can be accomplished by means of the TOM, which employs a systematic analysis of the dynamic model through the finite element method (FEM). In this work, the finite element (FE) system model takes into account the piezoelectric ceramics intermediate nodes, what is denominated as non-collapsed piezoelectric nodes model, and whose induced voltage during the time domain dynamic response contributes to the active control of the system. The topology optimization (TO) problem is formulated for the system vibration suppression at the restoring position and at the actuated position (positioner) subject to material volume and design variables constraints. The TOM implemented is based on the solid isotropic material with penalization (SIMP), the dynamic adjoint sensitivity, and on the optimization solver known as sequential linear programming (SLP). To illustrate the method, bidimensional examples of optimized topologies are numerically obtained by employing different velocity feedback control gains, and the topologies efficiency are compared and contrasted.

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Section: Piezoelectric Constitutive Equationsmentioning

confidence: 99%

“…Note that equation (22) can be used to calculate the prescribed electric charges at the actuator electrode, if this information is required. The feedback control system expressed by equation ( 23) is illustrated by blocks diagram in figure 3).…”

Section: Active Velocity Feedback Controlmentioning

confidence: 99%

Topology optimization of flextensional piezoelectric actuators with active control law

Moretti

Silva

Reddy

2019

Smart Mater. Struct.

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“…subdivided into free voltages, Φ f , and prescribed voltages, Φ p . Therefore, the dynamic FE equilibrium equations for the piezoelectric system are written [21]:…”

Section: Dynamic Piezoelectric Equationsmentioning

confidence: 99%

Topology optimization of piezoelectric bi-material actuators with velocity feedback control

Moretti

Silva

2019

Front. Mech. Eng.

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In recent years, the new technologies and discoveries on manufacturing materials have encouraged researchers to investigate the appearance of material properties that are not naturally available. Materials featuring a specific stiffness, or structures that combine non-structural and structural functions are applied in the aerospace, electronics and medical industry fields. Particularly, structures designed for dynamic actuation with reduced vibration response are the focus of this work. The bi-material and multifunctional concepts are considered for the design of a controlled piezoelectric actuator with vibration suppression by means of the topology optimization method (TOM). The bi-material piezoelectric actuator (BPEA) has its metallic host layer designed by the TOM, which defines the structural function, and the electric function is given by two piezo-ceramic layers that act as a sensor and an actuator coupled with a constant gain active velocity feedback control (AVFC). The AVFC, provided by the piezoelectric layers, affects the structural damping of the system through the velocity state variables readings in time domain. The dynamic equation analyzed throughout the optimization procedure is fully elaborated and implemented. The dynamic response for the rectangular four-noded finite element analysis is obtained by the Newmark's time-integration method, which is applied to the physical and the adjoint systems, given that the adjoint formulation is needed for the sensitivity analysis. A gradient-based optimization method is applied to minimize the displacement energy output measured at a predefined degree-of-freedom of the BPEA when a transient mechanical load is applied. Results are obtained for different control gain values to evaluate their influence on the final topology.

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“…Since none of the displacement and electric potential can be condensed from the principle, the formulation is irreducible [2]. Inheriting the work of Allik & Hughes, most of the finite element models in the literature are based on the irreducible formulation [3][4][5][6][7][8][9][10][11][12][13][14][15]. Unfortunately, they are often found to be inaccurate and susceptible to mesh distortion.…”

Section: Introductionmentioning

confidence: 99%

Stabilized plane and axisymmetric piezoelectric finite element models

Sze

Yang

Yao³

2004

Finite Elements in Analysis and Design

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This paper derives a four-node plane, a nine-node plane and a four-node axisymmetric stabilized elements for piezoelectric analysis. All elements are formulated by a stabilization approach founded on the generalized Hellinger-Reissner functional which employs stress, electric displacement, displacement and electric potential as the independent field variables. The lower and higher order stress and electric displacement are chosen to be orthogonal such that their coupling terms in the electromechanical flexibility matrices vanish. In the absence of the higher order modes, the elements are equivalent to their uniformly reduced integrated counterparts. Numerical examples are presented to illustrate that the stabilized elements are markedly more accurate than the standard fully integrated elements.

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Closed-form expressions for higher order electroelastic tetrahedral elements

Cited by 9 publications

References 8 publications

Topology optimization of flextensional piezoelectric actuators with active control law

Topology optimization of flextensional piezoelectric actuators with active control law

Topology optimization of piezoelectric bi-material actuators with velocity feedback control

Stabilized plane and axisymmetric piezoelectric finite element models

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