An asymptotically exact theory of functionally graded piezoelectric shells

Le, Khanh Chau

doi:10.1016/j.ijengsci.2016.12.001

Cited by 40 publications

(7 citation statements)

References 44 publications

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“…It is necessary to highlight the works [23][24][25][26], which present fundamental results on the use of the variational-asymptotic method for piezoelectric shells, plates and rods. The advantage of this approach is that, in contrast to the classical approach, which uses power series expansions in the normal coordinate, it allows one to construct high-order approximations.…”

Section: Introductionmentioning

confidence: 99%

Non‐stationary bending of a finite electromagnetoelastic rod

2021

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The related problem of non-stationary bending of a finite electromagnetoelastic rod is considered. It is assumed that the material of the rod is a homogeneous isotropic conductor. The problem statement takes into account the initial electromagnetic field, the Lorentz force, Maxwell's equations and the generalized Ohm's law. The unknown functions are assumed to be bounded, and the initial conditions are assumed to be zero. It has noted that it is difficult to construct a solution analytically for a general model. Therefore, a transition is made to simplified equations corresponding to the Bernoulli-Euler rod and the electromagnetic field is considered quasi-stationary. For a rod with hinged ends, trigonometric series expansions and the Laplace transform in time are used. The solution of the problem is constructed in integral form with kernels in the form of influence functions. Images of kernels are found in the space of transformations and Fourier in the spatial coordinate. Their original functions are found explicitly.The present study presents examples of calculations for a concentrated load.

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Section: Introductionmentioning

confidence: 99%

Non‐stationary bending of a finite electromagnetoelastic rod

2021

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“…[28] also proposed an efficient computational approach based on isogeometric analysis for dynamic control of smart piezoelectric composite plates. Le [29] present an asymptotically exact two-dimensional theory for elastic-piezoceramic sandwich shells [30] and functionally graded piezoelectric shells [31] using the variational-asymptotic method.…”

Section: Introductionmentioning

confidence: 99%

Study of the effects of shear piezoelectric actuators on the performance of laminated composite shells by an isogeometric approach

Nikoei

Hassani

2020

Jnl of Sandwich Structures & Materials

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This paper presents an isogeometric approach based on the Non-Uniform Rational B-Splines (NURBS) to investigate static and free vibration responses of smart composite shells integrated with shear piezoelectric actuators. The degenerated shell formulation according to the Mindlin-Reissner shell theory is combined with the isogeometric approach. To model the laminated smart shells, the Equivalent Single Layer (ESL) theory is used. To consider the electric potential in the shear piezoelectric actuator layers, a sub-layer approach is adopted that assumes linear variation in the thickness direction of the sub-layer. The effect of different mechanical and electrical boundary conditions on transverse deformation and natural frequencies of laminated smart shells by applying the electric field have been investigated. In the case studies, two parallel edges of the considered shell structures are assumed simply supported and the other two with an arbitrary combination of boundary conditions including clamped, free or simply supports. Also, open-circuit and closed-circuit conditions are used as electric boundary conditions. Investigation of the effects of the shear piezoelectric actuator layers on various factors, including the simultaneous mechanical and electrical loadings as well as the radius of curvature of the shell are amongst the objects of this paper. Also, several numerical examples are presented to demonstrate the efficiency and accuracy of the isogeometric approach in the study of shear effects of the piezoelectric actuator layers. The obtained results indicate the reliability and desirability of the proposed approach.

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“…Le and Nguyen [14,15] developed the analytical formulations for beams. Further, Le and Yi [16] and Le [17,18] have established the error estimate of the approximate laminated and functionally graded plates and shells showing the accuracy of variational asymptotic method.…”

Section: Introductionmentioning

confidence: 99%