Exact piezothermoelastic solution of simply-supported orthotropic flat panel in cylindrical bending

Dube, G.; Kapuria, S.; Dumir, P.C.

doi:10.1016/0020-7403(96)00020-3

Cited by 80 publications

(56 citation statements)

References 8 publications

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“…It is important to note that all the publications reported above use a three layer beam model, which is rather restrictive for modeling general laminates with EAM and SAM actuators to be placed at any arbitrary location across the thickness. It has been observed from 2D piezoelasticity solutions that the electric potential follows a nearly quadratic variation across the thickness in extension mode piezoelectric elements [Dube et al 1996] and a nearly cubic variation in shear mode elements [Parashar et al 2005]. It is also well established that the assumption of a linear electric potential along the thickness can cause a significant error in the computed response [Bisegna and Caruso 2001;Sze et al 2004;Parashar et al 2005].…”

Section: Introductionmentioning

confidence: 99%

Unified efficient layerwise theory for smart beams with segmented extension/shear mode, piezoelectric actuators and sensors

Kapuria

Hagedorn

2007

JOMMS

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A unified coupled efficient layerwise theory is presented for the dynamics of smart laminated beams with surface-mounted and embedded piezoelectric actuators and sensors with arbitrary poling directions, acting in extension or shear mode. The theory considers a global third-order variation across the thickness combined with a layerwise linear variation for the axial displacement, expressed in terms of only three primary variables, and accounts for the transverse normal strain due to the electric field in the approximation for the transverse displacement. The electric potential is approximated as piecewise quadratic across sublayers. A finite element is developed which has two physical nodes with mechanical and some electric potential degrees of freedom (DOF), and an electric node for the electric potentials of the electroded surfaces of the piezoelectric patches. The electric nodes eliminate the need for imposition of equality constraints of the electric DOF on the equipotential electroded surfaces of the segmented piezoelectric elements and result in significant reduction in the number of electric DOF. The electric DOF associated with the physical nodes allow for the inplane electric field that is induced via a direct piezoelectric effect. The accuracy of the formulation is established by comparing the results with those available in literature and the 2D piezoelasticity solutions for extension and shear mode actuators, sensors and adaptive beams. The effect of segmentation of the electroded surface on the deflection, sensory potential and natural frequencies is illustrated for both extension and shear mode cases. The influence of the location of extension and shear mode actuators and sensors on the response is investigated for a hybrid mode composite beam. The effect of actuator thickness on the actuation authority is studied.

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Section: Introductionmentioning

confidence: 99%

Unified efficient layerwise theory for smart beams with segmented extension/shear mode, piezoelectric actuators and sensors

Kapuria

Hagedorn

2007

JOMMS

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“…Simply-supported, electrically grounded and zero temperature edge boundary conditions for each layer [4][5][6][7][8]21]…”

Section: (I)mentioning

confidence: 99%

“…Three-dimensional analytical solutions for simplysupported plates continue to attract investigators' attention [1][2][3][4][5][6][7][8][9]. Various techniques including the asymptotic expansion scheme [7], the state space formulation [4,7], the Stroh formalism [6], the pseudo-Stroh formalism [8,9], and the transfer matrix (or propagator matrix) [2,[7][8][9] have been proposed in these studies.…”

Section: Introductionmentioning

confidence: 99%

“…Various techniques including the asymptotic expansion scheme [7], the state space formulation [4,7], the Stroh formalism [6], the pseudo-Stroh formalism [8,9], and the transfer matrix (or propagator matrix) [2,[7][8][9] have been proposed in these studies. The materials studied encompass purely elastic [1,2], piezoelectric [3,6,7], piezothermoelastic [4,5], and multiferroic [8,9] materials. One common assumption in most of the aforementioned works is that the extended displacement and traction vectors (see [8] for a detailed definition) are continuous across the interface between two adjacent layers.…”

Section: Introductionmentioning

confidence: 99%

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Exact Solutions for Simply Supported and Multilayered Piezothermoelastic Plates with Imperfect Interfaces

Wang¹,

Pan²

2007

TOMECHJ

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Exact solutions are derived for three-dimensional, orthotropic, linearly piezothermoelastic, simply-supported, and multilayered rectangular plates with imperfect interfaces under static thermo-electro-mechanical loadings. In this research the imperfect interface is described as thermally weakly (or highly) conducting, mechanically compliant and dielectrically weakly (or highly) conducting. While the homogeneous solutions for one layer are obtained in terms of the socalled pseudo-Stroh formalism, solutions for multilayered plates are expressed in terms of the transfer matrices for both the layer and the imperfect interface. Due to the fact that the thermal effect is incorporated, we adopt a special form of the transfer matrix, resulting in a very concise solution structure for piezothermoelastic multilayered plates. Numerical results are presented to validate the developed formulas and to demonstrate the influence of the interface imperfection on the distributions of the field variables.

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“…In w x particular, Xu et al 16, 17 have used a transfer matrix approac h to study the w x thermo-electro-mechanical characteristics of laminated plates. Dube et al 18 have presented an exact solution for a simply supported single-layer piezothermoelastic plate with its edges grounded.…”

Section: A Three-dimensional Asymptotic Scheme That Combines the Tranmentioning

confidence: 99%

Three-Dimensional Asymptotic Scheme for Piezothermoelastic Laminates

Cheng¹

2000

Journal of Thermal Stresses

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Exact piezothermoelastic solution of simply-supported orthotropic flat panel in cylindrical bending

Cited by 80 publications

References 8 publications

Unified efficient layerwise theory for smart beams with segmented extension/shear mode, piezoelectric actuators and sensors

Unified efficient layerwise theory for smart beams with segmented extension/shear mode, piezoelectric actuators and sensors

Exact Solutions for Simply Supported and Multilayered Piezothermoelastic Plates with Imperfect Interfaces

Three-Dimensional Asymptotic Scheme for Piezothermoelastic Laminates

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