Nonlinear Dynamic FE Simulation of Smart Piezolaminated Structures Based on First- and Third-Order Transverse Shear Deformation Theory

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Nonlinear Dynamic FE Simulation of Smart Piezolaminated Structures Based on First- and Third-Order Transverse Shear Deformation Theory

Journal Article•DOI•

Nonlinear Dynamic FE Simulation of Smart Piezolaminated Structures Based on First- and Third-Order Transverse Shear Deformation Theory

Ruediger Schmidt¹, Thang Duy Vu¹•Institutions (1)

RWTH Aachen University¹

01 Aug 2009-Advanced Materials Research (Trans Tech Publications Ltd)-pp 1313-1316

TL;DR: In this article, two geometrically nonlinear finite plate elements incorporating piezoelectric layers are applied based either on first- or third-order transverse shear deformation theory.

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Abstract: This paper deals with nonlinear finite element analysis of smart structures with integrated piezoelectric layers. Two geometrically nonlinear finite plate elements incorporating piezoelectric layers are applied based either on first- or third-order transverse shear deformation theory. Nonlinear strain-displacement relations are used that are valid for small strains and moderate rotations. Numerical tests are performed for the time histories of the tip displacement and sensor output voltage of a thin beam with a piezoelectric patch bonded to the surface.

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Journal Article•DOI•

Active vibration control of piezoelectric bonded smart structures using PID algorithm

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Shun-Qi Zhang¹, Shun-Qi Zhang², Rüdiger Schmidt², Xian-Sheng Qin¹•Institutions (2)

Northwestern Polytechnical University¹, RWTH Aachen University²

01 Feb 2015-Chinese Journal of Aeronautics

TL;DR: In this paper, an electro-mechanically coupled finite element (FE) model of smart structures is developed based on first-order shear deformation (FOSD) hypothesis, and a PID control is implemented to damp both the free and forced vibrations.

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61 citations

Journal Article•DOI•

Static and dynamic FE analysis of piezoelectric integrated thin-walled composite structures with large rotations

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Shun-Qi Zhang¹, Rüdiger Schmidt¹•Institutions (1)

RWTH Aachen University¹

01 Jun 2014-Composite Structures

TL;DR: In this article, a geometrically nonlinear finite element (FE) model based on large rotation shell theory is developed for static and dynamic analysis of piezoelectric integrated thin-walled structures with cross-ply or angle-ply laminates.

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46 citations

Cites background or methods from "Nonlinear Dynamic FE Simulation of ..."

...Additionally, von Kármán type nonlinear FE models have been developed by Panda and Ray [29], Varelis and Saravanos [30] based on FOSD hypothesis, by Kapuria and Alam [31] based on first-order zigzag hypothesis, by Icardi [32] based on third-order zigzag hypothesis, and by Schmidt and Vu [23] based on both FOSD and TOSD hypotheses for plates and shells....
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...For large amplitude dynamic analysis, von Kármán type nonlinear theories are mostly used in modeling of smart structures as well, based on FOSD [33], TOSD [23,34] and first-order zigzag [35]...
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...higherorder shear deformation (HOSD) [20–23] and zigzag shear deformation hypotheses [24–26] have been proposed and developed....
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Journal Article•DOI•

A review on modeling techniques of piezoelectric integrated plates and shells

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Shun-Qi Zhang¹, Shun-Qi Zhang², Guozhong Zhao¹, Mekala Narasimha Rao³, Rüdiger Schmidt³, Ying-Jie Yu² - Show less +2 more•Institutions (3)

Dalian University of Technology¹, Shanghai University², RWTH Aachen University³

15 Mar 2019-Journal of Intelligent Material Systems and Structures

TL;DR: In this paper, piezoelectric materials embedded into plates and shells make the structures being capable of sensing and actuation, usually called smart structures, which are frequently used for shape and vibratio...

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Abstract: Piezoelectric materials embedded into plates and shells make the structures being capable of sensing and actuation, usually called smart structures, which are frequently used for shape and vibratio...

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39 citations

Cites methods from "Nonlinear Dynamic FE Simulation of ..."

...For dynamic analysis, von Kármán–type nonlinear theories are mostly used in modeling of smart structures as well, based on FOSD (Mukherjee and Chaudhuri, 2005), TOSD (Cheng et al., 2005; Schmidt and Vu 2009), and first-order zigzag (Ray and Shivakumar, 2009; Sarangi and Ray, 2011) hypotheses....
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...For dynamic analysis, von Kármán–type nonlinear theories are mostly used in modeling of smart structures as well, based on FOSD (Mukherjee and Chaudhuri, 2005), TOSD (Cheng et al., 2005; Schmidt and Vu 2009), and first-order zigzag (Ray and Shivakumar, 2009; Sarangi and Ray, 2011) hypotheses....
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...In order to deal with thick structures and present strain distribution more precisely, thirdorder shear deformation (TOSD) or higher order shear deformation (HOSD) hypothesis was first proposed by Reddy (1984a, 1984b) for composite structures....
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...Schmidt and Vu (2009) developed nonlinear FE models based on both the FOSD and TOSD hypotheses for plates and shells, and Shen and Yang (2015) and Singh et al. (2016) developed nonlinear model using higher order hypothesis....
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...Employing fully geometrically nonlinear strain– displacement terms with the assumption of moderate rotations, fully geometrically nonlinear FE models were developed by Moita et al. (2002) based on the Kirchhoff-Love theory for static analysis, by Kundu et al. (2007) based on the FOSD hypothesis for buckling and postbuckling analysis, by Gao and Shen (2003) based on the FOSD hypothesis for dynamic analysis, and by Dash and Singh (2009) based on the TOSD hypothesis for dynamic analysis....
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Journal Article•DOI•

Disturbance rejection control for vibration suppression of piezoelectric laminated thin-walled structures

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Shun-Qi Zhang¹, H.N. Li¹, Rüdiger Schmidt¹, Peter C. Müller²•Institutions (2)

RWTH Aachen University¹, University of Wuppertal²

28 Feb 2014-Journal of Sound and Vibration

TL;DR: In this article, a disturbance rejection (DR) control with proportional-integral (PI) observer using step functions as the fictitious model of disturbances is developed for vibration suppression of smart structures.

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31 citations

Journal Article•DOI•

Large rotation FE transient analysis of piezolaminated thin-walled smart structures

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Shun-Qi Zhang¹, Shun-Qi Zhang², Rüdiger Schmidt¹•Institutions (2)

RWTH Aachen University¹, Northwestern Polytechnical University²

10 Sep 2013-Smart Materials and Structures

TL;DR: In this paper, a geometrically nonlinear large rotation shell theory is proposed for dynamic finite element (FE) analysis of piezoelectric integrated thin-walled smart structures.

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Abstract: A geometrically nonlinear large rotation shell theory is proposed for dynamic finite element (FE) analysis of piezoelectric integrated thin-walled smart structures. The large rotation theory, which has six independent kinematic parameters but expressed by five nodal degrees of freedom (DOFs), is based on first-order shear deformation (FOSD) hypothesis. The two-dimensional (2D) FE model is constructed using eight-node quadrilateral shell elements with five mechanical DOFs per node and one electrical DOF per piezoelectric material layer with linear constitutive equations. The linear and nonlinear dynamic responses are determined by the central difference algorithm (CDA) and the Newmark method. The results are compared with those obtained by simplified nonlinear theories, as well as those reported in the literature. It is shown that the present large rotation theory yields considerable improvement if the structures undergo large displacements and rotations.

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28 citations

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References

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Journal Article•DOI•

Use of piezoelectric actuators as elements of intelligent structures

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Edward F. Crawley¹, Javier de Luis¹•Institutions (1)

Massachusetts Institute of Technology¹

01 Oct 1987-AIAA Journal

TL;DR: In this paper, a scaling analysis is performed to demonstrate that the effectiveness of actuators is independent of the size of the structure and evaluate various piezoelectric materials based on their effectiveness in transmitting strain to the substructure.

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Abstract: This work presents the analytic and experimental development of piezoelectric actuators as elements of intelligent structures, i.e., structures with highly distributed actuators, sensors, and processing networks. Static and dynamic analytic models are derived for segmented piezoelectric actuators that are either bonded to an elastic substructure or embedded in a laminated composite. These models lead to the ability to predict, a priori, the response of the structural member to a command voltage applied to the piezoelectric and give guidance as to the optimal location for actuator placement. A scaling analysis is performed to demonstrate that the effectiveness of piezoelectric actuators is independent of the size of the structure and to evaluate various piezoelectric materials based on their effectiveness in transmitting strain to the substructure. Three test specimens of cantilevered beams were constructed: an aluminum beam with surface-bonded actuators, a glass/epoxy beam with embedded actuators, and a graphite/epoxy beam with embedded actuators. The actuators were used to excite steady-state resonant vibrations in the cantilevered beams. The response of the specimens compared well with those predicted by the analytic models. Static tensile tests performed on glass/epoxy laminates indicated that the embedded actuator reduced the ultimate strength of the laminate by 20%, while not significantly affecting the global elastic modulus of the specimen.

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2,719 citations

Journal Article•DOI•

The application of a finite shell element for composites containing piezo-electric polymers in vibration control

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R. Lammering

01 Jan 1991-Computers & Structures

TL;DR: In this article, a finite element analysis of shell structures with thin piezo-electric layers bonded to the surfaces is presented and a finite shell element is presented, allowing for the computation of these advanced composite structures.

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122 citations

Journal Article•DOI•

A Refined Small Strain and Moderate Rotation Theory of Elastic Anisotropic Shells

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R. Schmidt¹, J. N. Reddy²•Institutions (2)

University of Wuppertal¹, Virginia Tech²

01 Sep 1988-Journal of Applied Mechanics

TL;DR: In this article, a general refined shell theory that accounts for the transverse deformation, small strains, and moderate rotations is presented, which can be reduced to various existing shell theories including: the classical (i.e., linear Kirchhoff-love) shell theory, the Donnell-Mushtari-Vlasov shell theory and the moderate rotation shell theory.

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Abstract: A general refined shell theory that accounts for the transverse deformation, small strains, and moderate rotations is presented. The theory can be reduced to various existing shell theories including: the classical (i.e., linear Kirchhoff-Love) shell theory, the Donnell-Mushtari-Vlasov shell theory, the Leonard-Koiter-Sanders moderate rotations shell theory, the von Karman type shear-deformation shell theory and the moderate-rotation shear-deformation plate theory developed by Reddy. The present theory is developed from an assumed displacement field, nonlinear strain-displacement equations that contain small strain and moderate rotation terms, and the principle of virtual displacements. The governing equations exhibit strong coupling between the membrane and bending deformations, which should alter the bending, stability, and post-buckling behavior of certain shell structures predicted using the presently available theories.

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82 citations

Journal Article•DOI•

Piezoelectric induced bending and twisting of laminated composite shallow shells

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Hazem Kioua¹, Shaukat Mirza•Institutions (1)

University of Ottawa¹

01 Aug 2000-Smart Materials and Structures

TL;DR: In this article, a simple and efficient method has been developed for the static analysis of shallow shells under mechanical, thermal, and piezoelectric fields, and approximate solutions have been obtained using the conventional Ritz analysis for different boundary conditions.

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Abstract: The piezoelectric induced bending and twisting deformation of laminated shallow shells has been presented in this report. A simple and efficient method has been developed for the static analysis of shallow shells under mechanical, thermal, and piezoelectric fields. The governing equations are based on the linear theory of piezoelectricity and the classical thin shallow shell assumptions. Approximate solutions have been obtained using the conventional Ritz analysis for different boundary conditions. Comparisons of degenerate cases with published analytical and experimental results show good agreement. Several cases have been reported here, investigating the effects of material stiffness coupling, shell shallowness, and actuator geometric parameters on the bending and twisting deformation of piezoelectric laminated structures. It is shown that the desired shape could be better controlled by a proper selection of the lay-up configuration and geometric characteristics of the structure such as the thickness, size, and location of the piezoelectric actuators.

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81 citations

Finite Elements Based on a First-Order Shear Deformation Moderate Rortation Shell Theory with Applications to the Anarysis of Composite Structures

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I. Kreja

01 Jan 1997

70 citations