Generalized variational principles for micromorphic magnetoelectroelastodynamics

Zheng, Chengbo; Liu, Bin; Wang, Zuojun; Lu, Hongshi

doi:10.1016/j.camwa.2010.09.015

Cited by 8 publications

(3 citation statements)

References 25 publications

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“…According to the presented variational principle, the solution of the linear elastodynamic problem can be characterized as the stationary point of functional (71) over the space of all vector fields u k , φ s and all a priori non-symmetric tensor fields σ k , satisfying the kinematic equations (5), the inverse velocity-momentum relations of (6), the inverse stress-strain relations of (7) and the traction boundary conditions (16), as well as the compatibilities (26).…”

Section: Three-field Functional and Variational Principlementioning

confidence: 99%

See 1 more Smart Citation

Multi-field Dual-Mixed Variational Principles Using Non-symmetric Stress Field in Linear Elastodynamics

Tóth

2015

J Elast

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Three types of multi-field dual-mixed variational principles using a priori non-symmetric stress field will be derived for dynamic problems of linearly elastic solids. Starting from the functional of complementary Hamilton's principle it is shown how this variational formulation is modified with applying the Lagrange multiplier technique, to obtain a new four-field dual-mixed functional. The independent fields of this functional will be the displacement vector, the non-symmetric stress tensor, the skew-symmetric rotation tensor and the momentum vector. Then we present how to treat appropriately the six different types of initial conditions in a weak and/or strong sense by adding a new integral expression to the four-field functional. Modifying this functional through a Legendre transformation results in a new complementary energy-based five-field dual-mixed functional which allows the momentum-and velocity vectors to be independently approximated. A complementary energy-based three-field dual-mixed variational formulation is obtained by eliminating the momentum-and velocity fields through the strong enforcement of the kinematic equation and the impulse-velocity relation from the five-field principle.

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Section: Three-field Functional and Variational Principlementioning

confidence: 99%

“…Without completeness unified variational principles were reported in electro-and/or magnetoelasticity by [37,65,66,69,71], as well as further generalized variational formulations were elaborated on thermo-and/or piezoelectricity problems by [3, 16, 19, 21, 26-28, 38, 45, 47, 58, 70].…”

Section: Introductionmentioning

confidence: 99%

Multi-field Dual-Mixed Variational Principles Using Non-symmetric Stress Field in Linear Elastodynamics

Tóth

2015

J Elast

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“…We have to note that the field equations of the micromorphic electromagnetic theory (see [2]) have been utilized previously in [10] to study the wave propagation in ferroelectric perovskites and in [11] to establish a generalized variational principle for micromorphic magnetoelectroelastodynamics.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Partition of Energy in Micromorphic Thermopiezoelectricity

Galeş

Ghiba

Ignătescu

2011

Journal of Thermal Stresses

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On the bending of plates in the electromagnetic theory of microstretch elasticity

Galeş¹,

Baroiu

2013

Z Angew Math Mech

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This paper deals with the electromagnetic theory of microstretch elasticity. The full dynamic theory, which describes the interaction of electromagnetic fields with piezoelectric bodies, called piezoelectromagnetism, is considered. First, we derive the equations governing the bending theory of thin piezoelectromagnetic microstretch plates. Then, the boundary‐initial value problem is formulated and a uniqueness result is presented. Finally, the effects of a concentrated charge density in an infinite plate are studied.

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Generalized variational principles for micromorphic magnetoelectroelastodynamics

Cited by 8 publications

References 25 publications

Multi-field Dual-Mixed Variational Principles Using Non-symmetric Stress Field in Linear Elastodynamics

Multi-field Dual-Mixed Variational Principles Using Non-symmetric Stress Field in Linear Elastodynamics

Asymptotic Partition of Energy in Micromorphic Thermopiezoelectricity

On the bending of plates in the electromagnetic theory of microstretch elasticity

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