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Method and device for analyzing bending deformation of functionally gradient multilayer magnetoelectric elastic nano-plate

A functional gradient and bending deformation technology, applied in the field of bending deformation analysis of functionally graded multilayer magneto-elastic nanoplates, and bending deformation analysis devices of functionally graded multilayered magneto-elastic nanoplates, can solve problems such as low precision and achieve The effect of high solution accuracy

Active Publication Date: 2020-10-16
INNER MONGOLIA UNIV OF TECH
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  • Application Information

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Problems solved by technology

[0005] In order to solve the technical problem of low precision in the analysis of the static bending deformation of the functionally graded multilayer magnetoelectric elastic nanoplate by the existing analytical method, the present invention provides a bending deformation analysis method of the functionally graded multilayer magnetoelectric elastic nanoplate and its device

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Embodiment 1

[0055] see figure 1 , the present embodiment provides a bending deformation analysis method of a functionally graded multilayer magneto-electroelastic nanoplate, and the analytical method is used for the mechanical load and electric load on the surface of a functionally graded multilayer nanoplate composed of a magneto-electric-elastic material. The static bending deformation under the action is solved. In this embodiment, it is assumed that the functionally graded material is distributed exponentially along the thickness direction, and the interface displacement and stress of each layer are continuous, and the solution result of the multilayer board is obtained by using the transfer matrix method. Among them, the bending deformation analysis method includes the following four main steps.

[0056] (1) First establish the three-dimensional coordinate system of the functionally graded multilayer nanoplate, and then apply electroelastic loads on both ends of the functionally gra...

Embodiment 2

[0134] This embodiment provides a method for analyzing the bending deformation of a functionally graded multilayer magneto-electroelastic nanoplate, and this method adds a numerical example on the basis of Embodiment 1. In the numerical analysis, a BaTiO 3 (abbreviated as B) and Al-Ni-Co (abbreviated as F) composed of rectangular layered functionally graded sandwich nanoplates. z-independent material properties [36] They are listed in Table 1-2 respectively. Sandwich panels with two ply sequences namely B / F / B and F / B / F were investigated. The middle layer of the sandwich panel is uniform, and the top and bottom layers are functionally graded materials with symmetrical exponential changes, such as figure 2 shown. figure 2 η in represents the exponential factor of the top layer, and five different exponential factors, ie η=-10,-5,0,5,10, were studied.

[0135] The length and width of the nanoplate are Lx=Ly=100nm and height H=30nm. The material length scale parameter l is...

Embodiment 3

[0143] This embodiment provides a bending deformation analysis method of a functionally graded multilayer magnetoelectric elastic nanoplate, which is similar to that of Embodiment 2, the difference is that this embodiment studies the effect of non-local parameters on two functional gradients under the action of a force load. Effects of generalized displacement and generalized stress in sandwich nanoplates.

[0144] see Figure 9-14 , showing the displacement u of a functionally graded magnetoelectric sandwich panel under force loading for two different stacking orders x = u y and u z , potential Magnetic potential ψ, stress σ xz ,σ zz ,σ xx ,σ xy , Magnetic induction B x ,B z and electric displacement D x ,D z Variation law along the thickness direction with the non-local parameter l. From Figure 9 It can be found that when the exponent factor η=5 is taken, the displacement u x , u z The changing trends in the two kinds of functionally graded sandwich nanoshee...

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Abstract

The invention discloses a method and device for analyzing bending deformation of a functionally gradient multilayer magnetoelectric elastic nano-plate. The method comprises the following steps: establishing a three-dimensional coordinate system; establishing a coupling constitutive relation formula, an expansion strain-displacement relation formula and a balance equation; calculating an extended displacement vector of a functionally graded magnetic-electric-elastic nano-plate under a simply supported boundary condition, sequentially substituting the extended displacement vector into the expansion strain-displacement relation formula, the coupling constitutive relation formula and the balance equation to obtain a linear intrinsic equation set, and finally determining a general solution formula to calculate a general solution; determining a general solution expression, then applying a force load and an electric load to the top surface, then calculating an expansion displacement vector and a stress vector at any depth of each layer, and finally, calculating all quantities and corresponding in-plane components. The method is helpful for revealing small-scale mechanical behaviors, and provides a theoretical basis for the design and application of the functionally graded magnetoelectric elastic nano-multilayer board and the miniaturized design and manufacturing of an engineering intelligent structure.

Description

technical field [0001] The present invention relates to a bending deformation analysis method in the technical field of functionally gradient magneto-electric elastic nano-layer plate analysis, in particular to a bending deformation analysis method of functionally gradient multi-layer magneto-electric elastic nano-plates, and also relates to a functional gradient using the method Bending deformation analysis device for multilayer magneto-electroelastic nanoplates. Background technique [0002] With the development trend of device miniaturization, magnetoelectric elastic nanomaterials (such as BiFeO 3 , BiTiO 3 -CoFe 2 o 4 , NiFe 2 o 4 -PZT) and its nanostructures (such as nanowires, nanomembranes) have attracted extensive attention in the research field in recent years. Because magneto-electroelastic nanomaterials have good electrical, magnetic, and force properties and superior force-electromagnetic coupling effects, they have potential application prospects in nanoel...

Claims

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Application Information

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IPC IPC(8): G06F30/20G06F111/14G06F113/26G06F119/14G06F119/18
CPCG06F30/20G06F2111/14G06F2113/26G06F2119/14G06F2119/18Y02T90/00
Inventor 张丽李磊郭俊宏邢永明孙托娅
Owner INNER MONGOLIA UNIV OF TECH
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