Formulation of an adaptive sandwich beam

Zhang, X D; Sun, C. T.

doi:10.1088/0964-1726/5/6/012

Cited by 138 publications

(163 citation statements)

References 5 publications

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“…Validation. In order to validate the new FE formulation and the computer program developed, cantilever plane strain beams (a) and (b) made of aluminum substrate with surface-bonded and embedded PZT-5H layers, respectively, are considered, which have been analyzed in [Zhang and Sun 1996;Benjeddou et al 1999]. The configurations and the dimensions of the beams are shown in Figure 5 and the material properties are selected as in the references mentioned above:…”

Section: Finite Element Modelmentioning

confidence: 99%

“…The shear mode piezoelectric layer in beam (a) is divided into two sublayers and those in beam (b) are modeled as one sublayer for the discretization of potential φ. The present results for the deflection profile of the centerline (z = 0) are compared in Figure 6 with the FE FSDT results of Benjeddou et al [1999] for beam (a) and with the analytical FSDT solution of Zhang and Sun [1996] for beam (b). It is found that the present results are in excellent agreement with the reference results in both cases.…”

Section: Finite Element Modelmentioning

confidence: 99%

“…The results showed that the shear actuators are subjected to much lower stresses compared to the extension actuators under the same electric field. Zhang and Sun [1996] presented a three layer sandwich beam theory for the shear actuated laminate by modeling the face layers as classical Euler-Bernoulli beams and the central core as a Timoshenko beam, without considering the two-way electromechanical coupling. Benjeddou et al [1997] presented a finite element (FE) formulation based on this uncoupled three-layer beam model for analysis of adaptive sandwich beams with elastic/EAM piezoelectric faces and SAM piezoelectric/elastic core.…”

Section: Introductionmentioning

confidence: 99%

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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: Finite Element Modelmentioning

confidence: 99%

Section: Finite Element Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Kapuria

Hagedorn

2007

JOMMS

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“…those of Zhang and Sun [54,55], Benjeddou et al [56]. Some results are given varying the actuator position along the x-axis, the deflection at the free edge is investigated for each position of the piezoelectric patch, see Figure 15, and compared with the literature solutions [54,56], here named Sun & Zhang, and Benjeddou et al, respectively.…”

Section: Sandwich Cantilever Plate Shear-actuated In Mode-15mentioning

confidence: 99%

Multilayered plate elements with node-dependent kinematics for electro-mechanical problems

Carrera

Valvano

Куликов

2017

International Journal of Smart and Nano Materials

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In the present work, a new class of finite elements (FEs) for the analysis of composite and sandwich plates embedding piezoelectric skins and patches is proposed. By making use of node-by-node variable plate theory assumptions, the new finite element allows for the simultaneous analysis of different subregions of the problem domain with different kinematics and accuracy, in a global/local sense. As a consequence, the computational costs can be reduced drastically by assuming refined theories only in those zones/nodes of the structural domain where the resulting strain and stress states, and their electro-mechanical coupling present a complex distribution. The primary advantage is that no ad-hoc techniques and mathematical artifices are required to mix the fields coming from two different and kinematically incompatible adjacent elements, because the plate structural theory varies within the finite element itself. In other words, the structural theory of the plate element is a property of the FE node in this present approach, and the continuity between two adjacent elements is ensured by adopting the same kinematics at the interface nodes. The finite element arrays of the generic plate element are formulated in terms of fundamental nuclei, which are invariants of the theory approximation order and the modeling technique (Equivalent-Single-Layer, Layer-Wise). In this work, the attention is focused on the use of Legendre polynomial expansions to describe the through-the-thickness unknowns to develop advanced plate theories. Several numerical investigations, such as composite and sandwich multilayered plates embedding piezoelectric skins and patches with various load, boundary conditions, and piezoelectric material polarizations, are carried out to validate and demonstrate the accuracy and efficiency of the present plate element, including comparison with various closed-form and FE solutions from the literature. ARTICLE HISTORY

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“…However, all these models based on classical theory neglect transverse shear and hence are inadequate for shorter and thick beams (Benjeddou et al, 1999). Zhang and Sun (1996) proposed a classical Sandwich Beam Theory (SBT) based analytical solution in which the thick core is modeled as Timoshenko beam and the relatively thin faces as Euler-Bernoulli beam. Based on SBT, Raja et al (2002) proposed beam finite element to study the behaviour of piezoelectric smart beams.…”

Section: Introductionmentioning

confidence: 99%

An accurate novel coupled field Timoshenko piezoelectric beam finite element with induced potential effects

Sulbhewar

Raveendranath

2014

Lat. Am. j. solids struct.

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An accurate coupled field piezoelectric beam finite element formulation is presented. The formulation is based on First-order Shear Deformation Theory (FSDT) with layerwise electric potential. An appropriate through-thickness electric potential distribution is derived using electrostatic equilibrium equations, unlike conventional FSDT based formulations which use assumed independent layerwise linear potential distribution. The derived quadratic potential consists of a coupled term which takes care of induced potential and the associated change in stiffness, without bringing in any additional electrical degrees of freedom. It is shown that the effects of induced potential are significant when piezoelectric material dominates the structure configuration. The accurate results as predicted by a refined 2D simulation are achieved with only single layer modeling of piezolayer by present formulation. It is shown that the conventional formulations require sublayers in modeling, to reproduce the results of similar accuracy. Sublayers add additional degrees of freedom in the conventional formulations and hence increase computational cost. The accuracy of the present formulation has been verified by comparing results obtained from numerical simulation of test problems with those obtained by conventional formulations with sublayers and ANSYS 2D simulations.

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Formulation of an adaptive sandwich beam

Cited by 138 publications

References 5 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

Multilayered plate elements with node-dependent kinematics for electro-mechanical problems

An accurate novel coupled field Timoshenko piezoelectric beam finite element with induced potential effects

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