Extended Kantorovich method for coupled piezoelasticity solution of piezolaminated plates showing edge effects

Kapuria, S.; Kumari, Poonam

doi:10.1098/rspa.2012.0565

Cited by 25 publications

(4 citation statements)

References 22 publications

(32 reference statements)

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“…The six roots of the characteristic Equation (28) has been solved and the general solution of Equation (7) should be written in the format as Equation (37).…”

Section: Modified Rayleigh-rita Methods and Closed-form Solutionsmentioning

confidence: 99%

“…Except those, researchers also proposed some other theories and models, such as trigonometric shear deformation theory [33], new higher order shear deformation theory [34,35], and so on. Then, the methods to solve the different partial differential equations are also developed by many researchers [36][37][38]. However, in many of those works, the boundary conditions of the plates are only simply-supported for four edges since it is easier to solve the equations and get solutions.…”

Section: Introductionmentioning

confidence: 99%

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Experimental and Theoretical Research on Bending Behavior of Photovoltaic Panels with a Special Boundary Condition

Zhang

Xie

et al. 2018

Energies

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Currently, the photovoltaic (PV) panels widely manufactured on market are composed of stiff front and back layers and the solar cells embedded in a soft polymeric interlayer. The wind and snow pressure are the usual loads to which working PV panels need to face, and it needs the panels keep undamaged under those pressure when they generate electricity. Therefore, an accurate and systematic research on bending behavior of PV panels is important and necessary. In this paper, classical lamination theory (CLT) considering soft interlayer is applied to build governing equations of the solar panel. A Rayleigh–Rita method is modified to solve the governing equations and calculate the static deformation of the PV panel. Different from many previous researches only analyzing simply supported boundary condition for four edges, a special boundary condition which consists of two opposite edges simply supported and the others two free is studied in this paper. A closed form solution is derived out and used to do the numerical calculation. The corresponding bending experiments of PV panels are completed. Comparing the numerical results with experiment results, the accuracy of the analytical solutions are verified.

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“…The six roots of the characteristic Equation (28) has been solved and the general solution of Equation (7) should be written in the format as Equation (37).…”

Section: Modified Rayleigh-rita Methods and Closed-form Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Experimental and Theoretical Research on Bending Behavior of Photovoltaic Panels with a Special Boundary Condition

Zhang

Xie

et al. 2018

Energies

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“…Besides the electromechanical response of a multilayer piezoelectric structure to dynamic loading conditions, the response to static loading is also discussed in couple of works (e.g. Ballas, 2007; Edery-Azulay and Abramovich, 2008; Her and Lin, 2010; Kapuria and Kumari, 2012; Shiyekar and Kant, 2011; Vel and Batra, 2000).…”

Section: Current State Of the Artmentioning

confidence: 99%

Modeling of electromechanical response and fracture resistance of multilayer piezoelectric energy harvester with residual stresses

Machů

Ševeček

Hadaš

et al. 2020

Journal of Intelligent Material Systems and Structures

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The article focuses on a modeling and subsequent optimization of a novel layered architecture of the vibration piezoceramic energy harvester composed of ZrO2/Al2O3/BaTiO3 layers and containing thermal residual stresses. The developed analytical/numerical model allows to determine the complete electromechanical response and the apparent fracture toughness of the multilayer vibration energy harvester, upon consideration of thermal residual stresses and time-harmonic kinematic excitation. The derived model uses the Euler–Bernoulli beam theory, Hamilton’s variational principle, and a classical laminate theory to determine the first natural frequency, steady-state electromechanical response of the beam upon harmonic vibrations, and also the mechanical stresses within particular layers of the harvester. The laminate apparent fracture toughness is computed by means of the weight function approach. A crucial point is the further optimization of the layered architecture from both the electromechanical response and the fracture resistance point of view. Maximal allowable excitation acceleration of the harvester upon which the piezoelectric layer will not fail is determined. It makes possible to better use the harvester’s capabilities in a given application and simultaneously guarantee its safe operation. Outputs of the derived analytical model were validated with finite element method simulations and available experimental results, and a good agreement between all approaches was obtained.

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“…It is well known from earlier studies on piezoelectric actuators that the interfacial stresses at the actuator-host structure interface are far from being concentrated at the actuator edges [62] and the stress distributions are highly sensitive to the adhesive layer stiffness [63]. The interfacial stress profiles, in turn, have significant effects on the actuator performance [64,65].…”

Section: Introductionmentioning

confidence: 99%

A flexoelectric actuator model with shear-lag and peel stress effects

Rout

Kapuria

2023

Proc. R. Soc. A.

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Flexoelectric materials are being extensively studied in recent years for potential sensing, actuation, energy harvesting and structural health monitoring applications. However, no analytical model exists in the literature to predict the stress transfer between a flexoelectric transducer and the host structure, considering bonding compliance. In this article, we present an analytical model for the interfacial stresses and deformations of flexoelectric patch actuator(s) bonded to an isotropic host plate considering both shear-lag and peel stress effects at the interface(s). The model is valid for both piezoelectric and flexoelectric effects. The system’s one-dimensional governing equations are derived consistently from the three-dimensional equations for linear dielectric solids obtained using the bulk electric Gibbs energy density function and extended Hamilton’s principle. The transducer and substrate, modelled as classical Kirchhoff plates, undergo both extension and bending deformations. The formulation produces a seventh-order differential equation for the interfacial shear stress, which is solved analytically, satisfying all boundary conditions. The solution is validated by comparing with the available results for piezoelectric actuators with a non-rigid interface and those of flexoelectric actuators based on the pin-force-moment model assuming a rigid interface. Detailed numerical studies are presented to show the effect of the plate, actuator and adhesive parameters on the interfacial stresses and deformations. Finally, the size effect of the actuators at the micro-scale is illustrated.

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Extended Kantorovich method for coupled piezoelasticity solution of piezolaminated plates showing edge effects

Cited by 25 publications

References 22 publications

Experimental and Theoretical Research on Bending Behavior of Photovoltaic Panels with a Special Boundary Condition

Experimental and Theoretical Research on Bending Behavior of Photovoltaic Panels with a Special Boundary Condition

Modeling of electromechanical response and fracture resistance of multilayer piezoelectric energy harvester with residual stresses

A flexoelectric actuator model with shear-lag and peel stress effects

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