Symplectic duality system on plane magnetoelectroelastic solids

Hamiltonian dual equation of plane transversely isotropic magnetoelectroelastic solids is derived from variational principle and mixed state Hamiltonian elementary equations are established. Similar to the Hamiltonian formulation in classic dynamics, the z coordinate is treated analogous to the time coordinate. Then the x-direction is discreted with the linear elements to obtain the state-vector governing equations, which are a set of first order differential equations in z and are solved by the analytical approach. Because present approach is analytic in z direction, there is no restriction on the thickness of plate through the use of the present element. Using the propagation matrix method, the approach can be extended to analyze the problems of magnetoelectroelastic laminated plates. Present semi-analytical method of mixed Hamiltonian element has wide application area.

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Cracks in Magnetoelectroelastic Solids under Impact Loading

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.417-418.377 ◽

2009 ◽

Vol 417-418 ◽

pp. 377-380

Author(s):

Michael Wünsche ◽

Andrés Sáez ◽

Felipe García-Sánchez ◽

Chuan Zeng Zhang

Keyword(s):

Boundary Integral Equations ◽

Domain Boundary ◽

Crack Opening ◽

Fundamental Solutions ◽

Boundary Integral ◽

Dynamic Crack ◽

Time Stepping ◽

Convolution Integrals ◽

Magnetoelectroelastic Solids ◽

Dynamic Loading Conditions

In this paper, transient dynamic crack analysis in two-dimensional, linear magnetoelectroelastic solids is presented. For this purpose, a time-domain boundary element method (BEM) is developed and the elastodynamic fundamental solutions for linear magnetoelectroelastic and anisotropic materials are derived. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the discrete boundary data and the generalized crack-opening-displacements. To show the effects of the coupled fields and the different dynamic loading conditions on the dynamic intensity factors, numerical examples will be presented and discussed.

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An iterative approach for analysis of cracks with exact boundary conditions in finite magnetoelectroelastic solids

Smart Materials and Structures ◽

10.1088/1361-665x/ab0eb0 ◽

2019 ◽

Vol 28 (5) ◽

pp. 055025 ◽

Cited By ~ 1

Author(s):

MingHao Zhao ◽

QiaoYun Zhang ◽

XinFei Li ◽

YaGuang Guo ◽

CuiYing Fan ◽

...

Keyword(s):

Boundary Conditions ◽

Iterative Approach ◽

Exact Boundary ◽

Magnetoelectroelastic Solids

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Saint Venant Solutions in Symmetric Deformation for Rectangular Transversely Isotropic Magnetoelectroelastic Solids

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.284-286.2243 ◽

2011 ◽

Vol 284-286 ◽

pp. 2243-2250 ◽

Cited By ~ 2

Author(s):

Xiao Chuan Li

Keyword(s):

Separation Of Variables ◽

Electric Displacement ◽

Transversely Isotropic ◽

Rectangular Domain ◽

Generalized Variational Principle ◽

Hamiltonian Matrix ◽

Operator Matrix ◽

Zero Eigenvalue ◽

Symmetric Deformation ◽

Magnetoelectroelastic Solids

Hamiltonian system used in dynamics is introduced to formulate the transversely isotropic magnetoelectroelastic solids plane problem in rectangular domain and symplectic dual equation is derived corresponding to the generalized variational principle of the magnetoelectroelastic solids. The equation is expressed with displacements, electric potential and magnetic potential, as well as their duality variables--lengthways stress, electric displacement and magnetic induction in the symplectic geometry space. Since the x-coordinate is treated as time variable so that z becomes the independent coordinate in the Hamiltonian matrix operator. The symplectic dual approach enables the separation of variables to work and all the Saint Venant solutions in the symmetric deformation are obtained directly via the zero eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian operator matrix and the boundary condition. An example is presented to illustrate the proposed approach.

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