Finite deformation of thin shells in the context of analytical mechanics of material surfaces

Елисеев, В. В.; Vetyukov, Yury

doi:10.1007/s00707-009-0154-7

Cited by 42 publications

(50 citation statements)

References 10 publications

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“…Each particle can be interpreted as a material unit normal (a needle), such that no virtual work is produced on its "drilling" rotations. This determines the equation of virtual work and the resulting theory in the purely elastic case; see [36,37]. The complete system of equations of the electromechanically coupled problem at hand is again provided by a variational principle after assigning an electrical variable ϕ, which has the meaning of the potential difference over the thickness, to each particle of the material surface.…”

Section: Finite Deformations Of Piezoelastic Shells As Materials Surfacesmentioning

confidence: 99%

“…For a presentation with coordinates on the surface, see [13,36] as well as the finite element implementation in Sect. 5.2.…”

Section: Finite Deformations Of Piezoelastic Shells As Materials Surfacesmentioning

confidence: 99%

“…Like in the purely mechanical case [26,36], we consider the variational formulation (33) for a shell, undergoing a rigid body motion with preserved electric potentials. The enthalpy shall remain constant under the following constraints:…”

Section: Finite Deformations Of Piezoelastic Shells As Materials Surfacesmentioning

confidence: 99%

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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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Section: Finite Deformations Of Piezoelastic Shells As Materials Surfacesmentioning

confidence: 99%

“…For a presentation with coordinates on the surface, see [13,36] as well as the finite element implementation in Sect. 5.2.…”

Section: Finite Deformations Of Piezoelastic Shells As Materials Surfacesmentioning

confidence: 99%

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

2017

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“…Für weitere Details verweisen wir auf Eliseev and Vetyukov [20]. δA i ist die virtuelle Arbeit der inneren Kräfte pro Flächeneinheit in der Referenzkonfiguration.…”

Section: Schalengleichungenunclassified

Modellierung, Simulation und Schwingungsreduktion dünner Schalen mit piezoelektrischen Wandlern

Krommer

Pieber

Vetyukov

2015

Elektrotech. Inftech.

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In diesem Beitrag wird zuerst eine elektromechanisch gekoppelte Theorie für dünne Schalen mit piezoelektrischen Wandlern im Rahmen einer geometrisch nichtlinearen Formulierung vorgestellt. Hierbei wird eine Schale als materielle Fläche mit mechanischen und elektrischen Freiheitsgraden modelliert. Eine Finite Elemente Implementierung beschließt den ersten Teil der Arbeit. Im zweiten Teil des Beitrags wird die vorgestellte Theorie mit Hilfe von Vergleichsrechnungen mit dem kommerziell erhältlichen Finite Elemente Programm ABAQUS sowie mit Ergebnissen aus der Literatur verifiziert, um dann im dritten Teil der Arbeit zur Schwingungsreduktion zur Anwendung gebracht zu werden. Der vorliegende Beitrag endet mit einer experimentellen Untersuchung der passiven Schwingungsreduktion einer dünnen Schale mit piezoelektrischen Wandlern unter Verwendung der Methode des passiven Shunt Dampings.Schlüsselwörter: smarte Strukturen; dünne piezoelektrische Schalen; effiziente numerische Modellierung; passive Schwingungsreduktion Modeling, simulation and vibration reduction of thin shells with piezoelectric transducers. In the present paper a geometrically nonlinear electromechanically coupled theory for thin shells with piezoelectric transducers is presented. Within this theory the shell is modelled as a material surface with mechanical and electrical degrees of freedom. A FiniteElement implementation completes the first part of the paper. In the second part of the paper the shell theory is verified by a comparison to results computed with the commercially available Finite Element code ABAQUS as well as to results from the literature. In the third part of the paper the theory is applied to the problem of vibration reduction in thin shells with piezoelectric transducers. Simulation results and experimental results are presented, in which the method of passive shunt damping is used.

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“…The equations of the theory of shells as material surfaces with particles having five degrees of freedom are used [11,12]. Important role is played by the conditions of compatibility for the corresponding strain tensors, which allow us to solve the problem in two stages: firstly, the asymptotics for the field of stresses is determined, and only afterwards the displacements are analyzed.…”

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confidence: 99%

The Theory of Thin-Walled Rods of Open Profile as a Result of Asymptotic Splitting in the Problem of Deformation of a Noncircular Cylindrical Shell

Vetyukov

2009

J Elast

Self Cite

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A new asymptotic approach to the theory of thin-walled rods of open profile is suggested. For the problem of linear static deformation of a noncircular cylindrical shell we consider solutions, which are slowly varying along the axial coordinate. A small parameter is introduced in the equations of the modern theory of shells. Conditions of compatibility for the shell strain measures are employed. The principal terms of the series expansion of the solution are determined from the conditions of solvability for the minor terms. We conclude the procedure with the subsequent solution for the field of displacements. The analysis shows that the known equations of thin-walled rods, which were previously obtained with some approximate methods using hypotheses and approximations of displacements, are asymptotically exact. The presented semi-numerical analysis of the shell equations allows us to estimate the accuracy of the obtained solution. The results of the paper constitute a sound basis to the equations of the theory of thin-walled rods and provide trustworthy information concerning the distribution of stresses in the cross-section.

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Finite deformation of thin shells in the context of analytical mechanics of material surfaces

Cited by 42 publications

References 10 publications

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

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

Modellierung, Simulation und Schwingungsreduktion dünner Schalen mit piezoelektrischen Wandlern

The Theory of Thin-Walled Rods of Open Profile as a Result of Asymptotic Splitting in the Problem of Deformation of a Noncircular Cylindrical Shell

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