Analysis of laminated piezoelectric composite plates using an inverse hyperbolic coupled plate theory

Joshan, Yadwinder Singh; Santapuri, Sushma; Grover, Neeraj

doi:10.1016/j.apm.2020.01.050

Cited by 28 publications

(13 citation statements)

References 51 publications

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“…However, higher-order correction terms need to incorporated for thicker beams [57]. These higher-order terms are modeled as quadratic or other non-polynomial functions in literature [58,59].…”

Section: Variation Of the Electric Potential Across The Thickness Of ...mentioning

confidence: 99%

A gradient electromechanical theory for thin dielectric curved beams considering direct and converse flexoelectric effects

Joshan

Santapuri

2022

Z. Angew. Math. Phys.

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This work presents the development of a unified gradient electromechanical theory for thin flexoelectric beams considering both direct and converse flexoelectric effects. The two-way coupled electromechanical theory is developed starting from 3D variational formulation by considering an electric field-strain based free energy function. The formulation incorporates mechanical as well as electrical size effects. The coupled 3D theory is specialized to isotropic materials and a 1D beam theory for composite flexoelectric curved beams is derived using the classical Kirchhoff assumptions. The beam theory is solved using a novel C 2 continuous finite element framework for different loading and boundary conditions. Our finite element results are verified with analytical solutions for a simply-supported flexoelectric beam operating in both actuator and sensor modes. The results are also compared with existing literature for the special case of a passive micro-beam. Our computational framework is subsequently used to perform various parametric studies to analyze the effect of electrical and mechanical length scale parameters, geometric parameters like the radius of curvature, flexoelectric layer thickness etc., on the response of the beam. Also, contribution of converse flexoelectricity in the overall response of the flexoelectric beam is compared with that of the direct effect. Our simulation results predict that the converse effect is significant (≈ 10-25% of the direct effect) for a wide range of thickness and length scale parameter values. It is also observed that the effective electromechanical coupling coefficient, calculated in terms of the voltage developed across the flexoelectric layer thickness, is higher in flexoelectric materials compared to piezoelectric materials at smaller length scales (thickness of the order of a few microns). Our simulation results also agree well with the trends observed in recent experimental work [1].

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Section: Variation Of the Electric Potential Across The Thickness Of ...mentioning

confidence: 99%

A gradient electromechanical theory for thin dielectric curved beams considering direct and converse flexoelectric effects

Joshan

Santapuri

2022

Z. Angew. Math. Phys.

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“…(2022) obtained the governing equations of the Sandwich plate under uniform in-plane mechanical loading by taking the Mindlin plate theory and Von Karman assumptions into account. Josha et al. (2020) presented a non-polynomial coupled plate theory for smart composite structures employing inverse hyperbolic displacement and electric potential functions.…”

Section: Introductionmentioning

confidence: 99%

“…Gughari et al (2022) obtained the governing equations of the Sandwich plate under uniform in-plane mechanical loading by taking the Mindlin plate theory and Von Karman assumptions into account. Josha et al (2020) presented a non-polynomial coupled plate theory for smart composite structures employing inverse hyperbolic displacement and electric potential functions. Andakhshideh et al (2019) derived the governing equations and boundary conditions of the piezoelectric plate using the principle of minimum total potential energy, and they obtained the inter laminar stresses using the three-dimensional multi-term extended Kantorovich method.…”

Section: Introductionmentioning

confidence: 99%

The actuation performance of a piezoelectric laminated plate actuator via Galerkin method

Mao

Zhou

Xue

2022

MMMS

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PurposePiezoelectric materials are widely used as actuators, due to the advantages of quick response, high sensitivity and linear strain-electric field relationship. The previous work on the piezoelectric material plate structures is not enough; however, such structures play a very important role in the practical design. In this paper, the actuation performance of piezoelectric laminated plate actuator (PLPA) is analyzed based on Galerkin method to parametric study the shape control.Design/methodology/approachIn this paper, the actuation performance of PLPA is analyzed based on Galerkin method to parametric study the shape control. The stress components of the matrix plate are formulated based on electro-mechanical coupling theory and Kirchhoff's classical laminated plate theory. The effectiveness of the developed method is validated by the comparison with finite element method.FindingsThe actuation performance of PLPA and its influencing factors are numerically analyzed through the developed method. The deflection of PLPA is reasonably increased by optimizing the electric fields, the piezoelectric patch and the matrix plate.Originality/valueThe Galerkin method can be used for engineering applications more easily, and it does not require to rebuild the calculation model as finite element method during the calculation and analysis of PLPA. This paper is a valuable reference for the design and analysis of PLPAs.

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“…[17][18][19] In addition to these polynomial shear deformation theories (PSDTs), the theories with non-polynomial function of transverse coordinate are also developed and these theories are termed as non-polynomial shear deformation theories (NPSDTs). [20][21][22][23][24][25][26][27][28][29][30][31] NPSDTs do not require shear correction factor and satisfy transverse shear free conditions at the top and bottom surface of the plate. 32 However, these theories are generally applied for modelling and analysis of plate structures of composites, sandwich and functionally graded materials.…”

Section: Introductionmentioning

confidence: 99%

A non-polynomial axiomatic framework for modelling and bending analysis of doubly curved spherical and cylindrical shells: An analytical solution

Sharma

Grover

Purohit

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part L:

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In the present work, the doubly curved spherical and cylindrical laminated composite shells are modelled and analysed in the framework of non-polynomial axiomatic approach. The inverse hyperbolic shear deformation theory originally developed for the laminated composite plates is extended to model the deformation characteristics of laminated composite shells. The mathematical formulation is developed under the assumption of linear structural kinematics and linear-elastic-orthotropic material behaviour. The governing equations of the model are obtained using the principle of virtual work and solved in exact manner for simply supported boundary conditions following the Navier solution methodology. The bending response of thick and thin spherical and cylindrical shells subjected to different types of transverse loads such as point load, uniform load and sinusoidal load is analysed in the framework of developed methodology. The obtained results due to inverse hyperbolic shear deformation theory are compared with other shell theories and on the basis of this comparison, the validity and applicability of the inverse hyperbolic shear deformation theory for doubly curved spherical and cylindrical shells is ensured.

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Analysis of laminated piezoelectric composite plates using an inverse hyperbolic coupled plate theory

Cited by 28 publications

References 51 publications

A gradient electromechanical theory for thin dielectric curved beams considering direct and converse flexoelectric effects

A gradient electromechanical theory for thin dielectric curved beams considering direct and converse flexoelectric effects

The actuation performance of a piezoelectric laminated plate actuator via Galerkin method

A non-polynomial axiomatic framework for modelling and bending analysis of doubly curved spherical and cylindrical shells: An analytical solution

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