Geometrically nonlinear finite element simulation of smart piezolaminated plates and shells

Lentzen, S.; Kl̵osowski, Pawel̵; Schmidt, Romy

doi:10.1088/0964-1726/16/6/029

Cited by 41 publications

(40 citation statements)

References 38 publications

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“…The second Piola-Kirchhoff stress and Green-Lagrange strain are chosen to express the mechanical part of the internal virtual work. Consequently, the electric variables are defined as referring to the initial undeformed configuration [17].…”

Section: Structural Modelmentioning

confidence: 99%

See 1 more Smart Citation

Genetically optimised placement of piezoelectric sensor arrays: linear and nonlinear transient analysis

Rao¹,

Lentzen²,

Schmidt³

2006

WIT Transactions on the Built Environment, Vol 85

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In modern structural control the application of discrete modal sensor arrays is a commonly used technique to obtain the modal state vectors. In this paper, a genetic algorithm is used to find the optimal positions to place modal sensor arrays on simple structures such as beams, plates and shells. The performance criterion is taken as the steady state observability Grammian of the system and includes spillover prevention as well. The performance of optimally placed modal sensors in the linear range is discussed. The variation in the performance of these modal sensors in the nonlinear range is investigated.

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Section: Structural Modelmentioning

confidence: 99%

“…where the above matrices are found in Lentzen et al [17]. There, M is the mass matrix, K qq is the linear elastic stiffness matrix, K qφ = K φq are the linear electromechanical coupling matrices and K φφ is the piezoelectric capacitance matrix.…”

Section: Performance Criterionmentioning

confidence: 99%

Genetically optimised placement of piezoelectric sensor arrays: linear and nonlinear transient analysis

Rao¹,

Lentzen²,

Schmidt³

2006

WIT Transactions on the Built Environment, Vol 85

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“…In these theories, a priori assumptions concerning the mechanical displacements and the electrical field in certain directions are made to reduce the three-dimensional continuum to a lower-order one. With respect to nonlinear formulations for piezoelectric plates and shells, we refer to the rich literature, e.g., Zheng et al [8], Tan and Vu-Quoc [9], Klinkel and Wagner [10], Marinković et al [11] and Lentzen et al [12]. In this paper, we develop a novel hybrid approach to the modeling of the nonlinear behavior of piezoelectric shells, which is here presented in a holistic form for the first time; the approach is illustrated by two numerical examples.…”

Section: Introductionmentioning

confidence: 99%

Hybrid asymptotic–direct approach to finite deformations of electromechanically coupled piezoelectric shells

2017

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We present a novel multistage hybrid asymptotic-direct approach to the modeling of the nonlinear behavior of thin shells with piezoelectric patches or layers, which is formulated in a holistic form for the first time in this paper. The key points of the approach are as follows: (1) the asymptotic reduction in the threedimensional linear theory of piezoelasticity for a thin plate; (2) a direct approach to geometrically nonlinear piezoelectric shells as material surfaces, which is justified and completed by demanding the mathematical equivalence of its linearized form with the asymptotic solution for a plate; and (3) the numerical analysis by means of an FE scheme based on the developed model of the reduced electromechanically coupled continuum. Our approach is illustrated by examples of static and steady-state analysis and verified with three-dimensional solutions computed with the commercially available FE code ABAQUS as well as by comparison with results reported in the literature.

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“…References [1,2,3], and classical formulations, which model the shell by a reference surface, see e.g. References [4,5,6,7,8,9,10,11]. Some of these element formulations are restricted to shallow shell structures, [5,6,9,11], where the initial shell curvature is assumed to be small.…”

Section: Introductionmentioning

confidence: 99%

“…In order to consider laminated structures, the above mentioned formulations include a more or less sophisticated laminate theory. References [5,10,12,13,14] point out that geometrically nonlinear characteristics can significantly influence the performance of piezoelectric systems, especially for the sensor usage. A geometrically nonlinear theory that incorporates large rotations is presented in References [1,5,6,12].…”

Section: Introductionmentioning

confidence: 99%

A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

Schulz

Klinkel

Wagner

2011

Numerical Meth Engineering

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In this paper we present a nonlinear finite element formulation for piezoelectric shell structures. Based on a mixed multi field variational formulation, an electro-mechanical coupled shell element is developed considering geometrically and materially nonlinear behavior of ferroelectric ceramics. The mixed formulation includes the independent fields of displacements, electric potential, strains, electric field, stresses, and dielectric displacements. Besides the mechanical degrees of freedom, the shell counts only one electrical degree of freedom. This is the difference of the electric potential in thickness direction of the shell. Incorporating nonlinear kinematic assumptions, structures with large deformations and stability problems can be analyzed. According to a Reissner-Mindlin theory, the shell element accounts for constant transversal shear strains. The formulation incorporates a three-dimensional transversal isotropic material law, thus the kinematic in thickness direction of the shell is considered. The normal zero stress condition and the normal zero dielectric displacement condition of shells are enforced by the independent resultant stress and resultant dielectric displacement fields. Accounting for material nonlinearities, the ferroelectric hysteresis phenomena are considered using the Preisach model. As a special aspect, the formulation includes temperaturedependent effects and thus the change of the piezoelectric material parameters due to the temperature. This enables the element to describe temperature dependent hysteresis curves.

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Geometrically nonlinear finite element simulation of smart piezolaminated plates and shells

Cited by 41 publications

References 38 publications

Genetically optimised placement of piezoelectric sensor arrays: linear and nonlinear transient analysis

Genetically optimised placement of piezoelectric sensor arrays: linear and nonlinear transient analysis

Hybrid asymptotic–direct approach to finite deformations of electromechanically coupled piezoelectric shells

A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

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