Piezolaminated beams with large deformations

Mukherjee, Abhijit; Chaudhuri, Arup Saha

doi:10.1016/s0020-7683(02)00341-4

Cited by 51 publications

(33 citation statements)

References 13 publications

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“…Here, the stresses S b and the electric displacements D are determined by the non-linear material law (15). The linearized beam strains E b = A E with E = [ e, j, a, a ] T are formally obtained from Equation (41) by replacing the operator by .…”

Section: Linearization Of the Virtual Work Expressionsmentioning

confidence: 99%

A geometrically and materially non‐linear piezoelectric three‐dimensional‐beam finite element formulation including warping effects

Butz

Klinkel

Wagner

2008

Numerical Meth Engineering

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This paper is concerned with a three-dimensional piezoelectric beam formulation and its finite element implementation. The developed model considers geometrically and materially non-linear effects. Ail eccentric beam formulation is derived based on the Timoshenko kinematics. The kinematic assumptions are extended by three additional warping functions of the cross section. These functions follow from torsion and piezoelectrically induced shear deformations. The presented beam formulation incorporates large displacements and finite rotations and allows the investigation of stability problems. The finite element model has two nodes with nine mechanical and five electrical degrees of freedom. It provides ail accurate approximation of the electric potential, which is assumed to be linear in the direction of the beam axis and quadratic within the cross section. The mechanical degrees of freedom are three displacements, three rotations and three scaling factors for the warping functions. The latter are computed in a preprocess by solving a two-dimensional in-plane equilibrium condition with the finite element method. The gained warping patterns are considered within the integration through the cross section of the beam formulation. With respect to material non-linearities, which arise in ferroelectric materials, the scalar Preisach model is embedded in the formulation. This model is a mathematical model for the general description of hysteresis phenomena. Its application to piezoelectric materials leads to a phenomenological model for ferroelectric hysteresis effects. Here, the polarization direction is assumed to be constant, which leads to unidirectional constitutive equations. Some examples demonstrate the capability of the proposed model

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Section: Linearization Of the Virtual Work Expressionsmentioning

confidence: 99%

A geometrically and materially non‐linear piezoelectric three‐dimensional‐beam finite element formulation including warping effects

Butz

Klinkel

Wagner

2008

Numerical Meth Engineering

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“…Icardi and Sciuva [9] presented large deflection and stress analysis of multilayered plates with induced strain actuators. Geometrically nonlinear static behavior of PVDF bimorph has been investigated by Mukherjee and Saha Chaudhuri [10].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic response of piezolaminated smart beams

Mukherjee

Chaudhuri

2005

Computers & Structures

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“…Concerning static analysis of smart structures, the von Kármán nonlinearity has been taken into account for interlaminar stress analysis of multilayered plates with induced-strain actuators by Icardi and Di Sciuva [29] in the framework of third-order shear deformation theory, and for the analysis of the sensed voltage of a PVDF bimorph cantilever beam by Mukherjee and Chaudhuri [30] adopting first-order shear deformation theory. Sensor output voltage analysis, deflection analysis, and shape control of smart isotropic or composite laminated beams, plates, and shells with integrated piezoelectric actuator and sensor layers have been considered in recent papers (Lentzen and Schmidt [31][32][33][34][35], Vu et al [36], Nguyen et al [37], Zhang et al [38][39][40][41]) accounting for moderate rotations in the framework of first-and third-order shear deformation theories.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

Chróścielewski

Schmidt

Eremeyev

2018

Continuum Mech. Thermodyn.

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This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.

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Piezolaminated beams with large deformations

Cited by 51 publications

References 13 publications

A geometrically and materially non‐linear piezoelectric three‐dimensional‐beam finite element formulation including warping effects

A geometrically and materially non‐linear piezoelectric three‐dimensional‐beam finite element formulation including warping effects

Nonlinear dynamic response of piezolaminated smart beams

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

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