CN112784460A - Method for analyzing stability of mechanical metamaterial compression bar - Google Patents

Method for analyzing stability of mechanical metamaterial compression bar Download PDF

Info

Publication number
CN112784460A
CN112784460A CN202110118958.0A CN202110118958A CN112784460A CN 112784460 A CN112784460 A CN 112784460A CN 202110118958 A CN202110118958 A CN 202110118958A CN 112784460 A CN112784460 A CN 112784460A
Authority
CN
China
Prior art keywords
metamaterial
target
finite element
element analysis
strain
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202110118958.0A
Other languages
Chinese (zh)
Other versions
CN112784460B (en
Inventor
孙伟福
林高建
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Institute of Technology BIT
Chongqing Innovation Center of Beijing University of Technology
Original Assignee
Beijing Institute of Technology BIT
Chongqing Innovation Center of Beijing University of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Institute of Technology BIT, Chongqing Innovation Center of Beijing University of Technology filed Critical Beijing Institute of Technology BIT
Priority to CN202110118958.0A priority Critical patent/CN112784460B/en
Publication of CN112784460A publication Critical patent/CN112784460A/en
Application granted granted Critical
Publication of CN112784460B publication Critical patent/CN112784460B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
    • G16C10/00—Computational theoretical chemistry, i.e. ICT specially adapted for theoretical aspects of quantum chemistry, molecular mechanics, molecular dynamics or the like
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
    • G16C60/00—Computational materials science, i.e. ICT specially adapted for investigating the physical or chemical properties of materials or phenomena associated with their design, synthesis, processing, characterisation or utilisation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Computing Systems (AREA)
  • General Physics & Mathematics (AREA)
  • Bioinformatics & Computational Biology (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • General Engineering & Computer Science (AREA)
  • Bioinformatics & Cheminformatics (AREA)
  • Mathematical Analysis (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Computational Mathematics (AREA)
  • Health & Medical Sciences (AREA)
  • General Health & Medical Sciences (AREA)
  • Spectroscopy & Molecular Physics (AREA)
  • Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)

Abstract

本发明提供一种力学超材料压杆稳定性分析方法，包括以下步骤：获取样本超材料压杆的样本周期单元，根据所述样本周期单元构建有限元分析模型；获取目标超材料压杆的目标周期单元，根据所述有限元分析模型对所述目标周期单元进行有限元分析，获取若干特征刚度参数；根据所述目标超材料压杆的变形协调条件，结合所述若干特征刚度参数得到目标超材料压杆的整体刚度矩阵；建立屈曲控制方程，将设定的压杆边界条件和所述整体刚度矩阵带入所述屈曲控制方程，求解获取临界失稳载荷；将设计负载与所述临界失稳载荷进行比较，判断所述目标超材料压杆的稳定性。本发明缩短了超材料压杆结构稳定性判断所需的时间，极大地提高了结构设计效率。

Figure 202110118958

The invention provides a method for analyzing the stability of a mechanical metamaterial pressure rod, comprising the following steps: obtaining a sample periodical unit of a sample metamaterial pressure rod, and constructing a finite element analysis model according to the sample periodical unit; obtaining a target of a target metamaterial pressure rod Periodic element, performing finite element analysis on the target periodic element according to the finite element analysis model, to obtain several characteristic stiffness parameters; according to the deformation coordination conditions of the target metamaterial compression rod, combining the several characteristic stiffness parameters to obtain the target superstructure The overall stiffness matrix of the material compression rod; the buckling control equation is established, the set boundary conditions of the compression rod and the overall stiffness matrix are brought into the buckling control equation, and the critical buckling load is obtained; The steady load is compared to judge the stability of the target metamaterial pressure rod. The invention shortens the time required for judging the structural stability of the metamaterial pressure rod, and greatly improves the structural design efficiency.

Figure 202110118958

Description

Method for analyzing stability of mechanical metamaterial compression bar
Technical Field
The invention relates to the technical field of metamaterial structure performance analysis, in particular to a method for analyzing the stability of a mechanical metamaterial compression bar.
Background
The metamaterial refers to a composite material which has an artificially designed structure and shows extraordinary physical properties which natural materials do not have, and the metamaterial breaks through the limitation of certain apparent natural laws so as to obtain extraordinary material functions. The metamaterial has wide application prospect and comprises the fields of electronic engineering, condensed state physics, microwave, optoelectronics, classical optics, material science, semiconductor science, nanotechnology and the like. The compression bar structure made of the metamaterial can be applied to the manufacturing industries of aircraft automobile manufacturing, engineering machinery manufacturing and the like.
In the prior art, for mechanical stability analysis of a compression bar structure constructed by using metamaterials, a 3D printing prototype experimental verification or a finite element analysis method based on a full-scale model is generally adopted. However, these two methods require a long time and have low working efficiency.
Disclosure of Invention
In view of the above, it is necessary to provide a method for analyzing the stability of a mechanical metamaterial compression bar.
A method for analyzing the stability of a mechanical metamaterial compression bar comprises the following steps: obtaining a sample period unit of a sample metamaterial compression bar, and constructing a finite element analysis model according to the sample period unit; acquiring a target period unit of a target metamaterial compression bar, and performing finite element analysis on the target period unit according to the finite element analysis model to acquire a plurality of characteristic stiffness parameters; obtaining an integral rigidity matrix of the target metamaterial compression bar by combining the characteristic rigidity parameters according to the deformation coordination condition of the target metamaterial compression bar; establishing a buckling control equation, substituting the set boundary condition of the compression bar and the integral rigidity matrix into the buckling control equation, and solving to obtain a critical buckling load; and comparing the design load with the critical instability load, and judging the stability of the target metamaterial compression bar.
In one embodiment, the target cycle unit for acquiring the target metamaterial compression bar specifically includes: the target metamaterial compression bar is formed by periodically arranging basic units, and the basic units forming the target metamaterial compression bar are used as the target periodic units.
In one embodiment, the performing finite element analysis on the target cycle unit according to the finite element analysis model to obtain a plurality of characteristic stiffness parameters specifically includes: and performing four finite element analyses on the target periodic unit, loading displacement loads in a specific form in the four finite element analyses, wherein the displacement loads comprise strain and curvature, acquiring strain energy and reaction force in a finite element analysis model according to the displacement loads, and acquiring the characteristic stiffness parameters according to the strain energy and the reaction force.
In one embodiment, the quartic finite element analysis comprises;
in the first finite element analysis, the first strain and the first curvature are set to ∈ {0,0, ∈ respectively3Acquiring first strain energy U, wherein k is {0,0,0}1And a first reaction torque according to the first strain energy and the formula U1＝C3ε3 2Acquiring a first characteristic stiffness parameter C3sObtaining a second characteristic stiffness parameter H according to the ratio of the first reaction torque to the first strainsIf the metamaterial is achiral, then HsIs 0;
in the second finite element analysis, the second strain and the second curvature are set to ∈ {0,0,0} and κ {0,0, τ } respectively, and the second strain energy U is acquired2According to the second strain energy and formula U2＝D3τ2Acquiring a third characteristic stiffness parameter D3s；
In the third finite element analysis, the third strain and the third curvature are respectively set to be ∈ ═ epsilon { (epsilon)10,0 and k ═ 0,0,0, and a third strain energy U is obtained3According to the third strain energy and formula U3＝C1s(1-Hs 2/C3sD3s)ε1 2Acquiring a fourth characteristic stiffness parameter C1sAnd acquiring a fifth characteristic stiffness parameter C according to the symmetry2s；
In the fourth finite element analysis, the fourth strain and the fourth curvature are set to e ═ 0,0,0, and k ═ k { κ { (0, 0, 0) } respectively10,0}, and obtaining fourth strain energy U4According to the fourth strain energy and equation U4＝D1s(1-Hs 2/C3sD3s)κ1 2Acquiring a sixth characteristic stiffness parameter D1sAnd obtaining a seventh characteristic stiffness parameter D according to the symmetry2s。
In one embodiment, the obtaining an overall stiffness matrix of the metamaterial compression bar according to the deformation coordination condition of the target metamaterial compression bar by combining the plurality of characteristic stiffness parameters specifically includes: if the target metamaterial compression bar is formed by repeatedly arranging m × n periodic units, and the size of each target periodic unit is a, constructing a mechanical model by combining the characteristic stiffness parameters, and obtaining integral stiffness matrixes C, B and D of the target metamaterial compression bar according to the mechanical model, wherein the integral stiffness matrixes C, B and D are as follows:
Figure BDA0002921309050000031
Figure BDA0002921309050000032
Figure BDA0002921309050000033
wherein, H is mnHs，C1＝C2＝mnC1s，C3＝mnC3s，
Figure BDA0002921309050000034
Figure BDA0002921309050000035
Figure BDA0002921309050000036
In one embodiment, the buckling control equation is:
Figure BDA0002921309050000037
Figure BDA0002921309050000038
simultaneous equations (1) and (2), the general solution is obtained as:
Figure BDA0002921309050000039
Figure BDA00029213090500000310
wherein, it is made
Figure BDA0002921309050000041
Figure BDA0002921309050000042
Then there are:
Figure BDA0002921309050000043
Figure BDA0002921309050000044
Figure BDA0002921309050000045
in one embodiment, the boundary condition includes:
for the cantilever beam of the target metamaterial compression bar, the boundary conditions are as follows:
θ1(0)＝θ2(0)＝θ′1(L)-ηPθ2(L)＝θ′2(L)+ηPθ1(L)＝0；
for the simply supported beam of the target metamaterial compression bar, the boundary conditions are as follows:
θ1′(0)-ηPθ2(0)＝θ′2(0)+ηPθ1(0)＝θ′1(L)-ηPθ2(L)＝θ′2(L)+ηPθ1(L)＝0。
in one embodiment, the comparing the design load with the critical buckling load to determine the stability of the target metamaterial compression bar specifically includes: if the design load is larger than the critical buckling load, the target metamaterial compression bar is not stable, and buckling can occur to cause buckling; and if the design load is less than or equal to the critical buckling load, the target metamaterial is stable, and buckling cannot occur.
Compared with the prior art, the invention has the advantages and beneficial effects that:
1. according to the invention, the critical instability load of the metamaterial compression bar can be rapidly calculated or verified through a repeatable periodic unit, the design time required by judging the structural stability of the metamaterial compression bar is shortened, and the structural design efficiency is greatly improved.
2. The stiffness matrix of the metamaterial is obtained through characterization of a plurality of characteristic stiffness parameters, and the metamaterial can be suitable for chiral metamaterials or non-chiral metamaterials, so that the application range is expanded.
Drawings
FIG. 1 is a schematic flow chart of a method for analyzing the stability of a mechanical metamaterial compression bar according to an embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings by way of specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In one embodiment, as shown in fig. 1, a method for analyzing the stability of a mechanical metamaterial compression bar is provided, which comprises the following steps:
and S101, obtaining a sample period unit of the sample metamaterial compression bar, and constructing a finite element analysis model according to the sample period unit.
Specifically, since the mechanical metamaterial compression bar structure is generally periodically arranged by the basic units, the basic units constituting the metamaterial compression bar can be used as the periodic units, and therefore, the periodic units can be obtained by analyzing the basic units of the metamaterial of the compression bar structure. Sample period units of a plurality of sample metamaterial compression bars can be obtained, and a finite element analysis model is constructed according to the sample period units.
And S102, acquiring a target period unit of the target metamaterial compression bar, and performing finite element analysis on the target period unit according to a finite element analysis model to acquire a plurality of characteristic stiffness parameters.
Specifically, a target period unit of the target metamaterial compression bar is obtained, and finite element analysis is carried out on the target period unit for multiple times according to the constructed finite element analysis model, so that a plurality of characteristic rigidity parameters are obtained.
In this embodiment, four times of finite element analysis needs to be performed on the target periodic unit according to the finite element analysis model to obtain seven characteristic stiffness parameters, so as to determine the stability of the target metamaterial compression bar structure according to the seven characteristic stiffness parameters. In the process of four times of finite element analysis, a specific form of displacement load is required to be loaded respectively, wherein the displacement load comprises strain and curvature, so that strain energy and reaction force are obtained, and characteristic rigidity parameters are obtained according to the strain energy and the reaction force.
And S103, obtaining an overall stiffness matrix of the target metamaterial compression bar by combining a plurality of characteristic stiffness parameters according to the deformation coordination condition of the target metamaterial compression bar.
The deformation coordination condition is a condition which can still keep the integrity and continuity of the target metamaterial compression bar after the continuous solid is deformed. The deformation coordination condition of the target metamaterial compression bar can be obtained according to the parameters when the metamaterial compression bar is designed.
Specifically, a mechanical model can be constructed according to deformation coordination conditions of a single target period unit in the overall deformation of the target metamaterial compression bar, and the mechanical model is obtained under the condition that the strain energy is equal. For example, when the strut is axially compressed to a certain strain, each periodic unit also needs to compress the corresponding strain, so the strain energy of the strut as a whole can be expressed as a multiple of the strain energy of a single target periodic unit. Wherein the bending and twisting principle of the pressure rod is similar to the compression principle of the pressure rod. Therefore, the integral rigidity matrix of the target metamaterial compression bar is obtained by combining a plurality of characteristic rigidity parameters according to the deformation coordination condition of a single target period unit.
And step S104, constructing a buckling control equation, substituting the set boundary condition of the compression bar and the integral rigidity matrix into the buckling control equation, and solving to obtain the critical instability load.
Specifically, a constructed buckling control equation is substituted according to boundary conditions of the target metamaterial compression bar and an integral rigidity matrix, the equation is solved, and the critical instability load of the target metamaterial compression bar is obtained.
And step S105, comparing the design load with the critical instability load, and judging the stability of the target metamaterial compression bar.
Specifically, since the design load is set during the design of the compression bar, the design load is compared with the critical instability load, so as to judge the stability of the target metamaterial compression bar. If the design load is larger than the critical instability load, the target metamaterial compression bar is not stable, and buckling can occur to cause instability; otherwise, the target metamaterial compression bar is stable, and buckling cannot be sent to cause instability.
In the embodiment, a sample period unit of the sample metamaterial compression bar is obtained, and a finite element analysis model is constructed according to the sample period unit; carrying out finite element analysis on a target periodic unit of the target metamaterial compression bar according to the finite element analysis model to obtain a plurality of characteristic rigidity parameters, obtaining an integral rigidity matrix of the target metamaterial compression bar according to a plurality of characteristic rigidity parameters and the deformation coordination condition of the compression bar structure, substituting the integral rigidity matrix and the boundary condition of the compression bar into a buckling control equation, solving and obtaining a critical destabilizing load, comparing the temporary destabilizing load with a design load, thereby judging the stability of the target metamaterial, representing the whole compression bar structure through repeatable periodic units, the critical destabilization load of the target metamaterial compression bar structure is calculated, so that the stability of the target metamaterial compression bar structure is judged, the time for calculating the critical destabilization load is shortened, the structural design efficiency is improved, the rigidity matrix is suitable for chiral or achiral materials, and the application range is expanded.
Wherein, step S102 specifically includes: the target metamaterial compression bar is formed by periodically arranging basic units, and the basic units forming the target metamaterial compression bar are used as the target periodic units.
Wherein, step S102 further includes: and carrying out quartic finite element analysis on the target periodic unit, loading a displacement load in a specific form in the quartic finite element analysis, wherein the displacement load comprises strain and curvature, acquiring strain energy and reaction force in a finite element analysis model according to the displacement load, and acquiring the characteristic stiffness parameter according to the strain energy and the reaction force.
Wherein the fourth finite element analysis comprises:
in the first finite element analysis, the first strain and the first curvature are set to ∈ {0,0, ∈ respectively3Acquiring first strain energy U, wherein k is {0,0,0}1And a first reaction torque according to the first strain energy and the formula U1＝C3ε3 2Acquiring a first characteristic stiffness parameter C3sObtaining a second characteristic stiffness parameter H according to the ratio of the first reaction torque to the first strainsIf the metamaterial is achiral, then HsIs 0;
in the second finite element analysis, the second strain and the second curvature are set to ∈ {0,0,0} and κ {0,0, τ } respectively, and the second strain energy U is acquired2According to the second strain energy and formula U2＝D3τ2Acquiring a third characteristic stiffness parameter D3s；
In the third finite element analysis, the third strain and the third curvature are respectively set to be ∈ ═ epsilon { (epsilon)10,0 and k ═ 0,0,0, and a third strain energy U is obtained3According to the third strain energy and formula U3＝C1s(1-Hs 2/C3sD3s)ε1 2Acquiring a fourth characteristic stiffness parameter C1sAnd acquiring a fifth characteristic stiffness parameter C according to the symmetry2s；
In the fourth finite element analysis, the fourth strain and the fourth curvature are set to e ═ 0,0,0, and k ═ k { κ { (0, 0, 0) } respectively10,0}, and obtaining fourth strain energy U4According to the fourth strain energy and formula U4＝D1s(1-Hs 2/C3sD3s)κ1 2Acquiring a sixth characteristic stiffness parameter D1sAnd obtaining a seventh characteristic stiffness parameter D according to the symmetry2s。
In particular, the fourth characteristic stiffness parameter C1sAnd a fifth characteristic stiffness parameter C2sHas symmetry therebetween, then has C1s＝C2s. Similarly, the sixth characteristic stiffness parameter D1sAnd a seventh characteristic stiffness parameter D2sBetween, there is D1s＝D2s。
Wherein, step S103 specifically includes: if the target metamaterial compression bar is formed by repeatedly arranging m × n periodic units, the size of each periodic unit is a, a mechanical model is constructed by combining a plurality of characteristic stiffness parameters, and the overall stiffness matrixes C, B and D of the metamaterial compression bar obtained according to the mechanical model are as follows:
Figure BDA0002921309050000081
Figure BDA0002921309050000082
Figure BDA0002921309050000083
wherein, H is mnHs，C1＝C2＝mnC1s，C3＝mnC3s，
Figure BDA0002921309050000084
Figure BDA0002921309050000085
Figure BDA0002921309050000086
Wherein, the buckling control equation in step S104 is:
Figure BDA0002921309050000087
Figure BDA0002921309050000088
simultaneous equations (1) and (2), the general solution is obtained as:
Figure BDA0002921309050000089
Figure BDA00029213090500000810
wherein, it is made
Figure BDA0002921309050000091
Figure BDA0002921309050000092
Then there are:
Figure BDA0002921309050000093
Figure BDA0002921309050000094
Figure BDA0002921309050000095
the boundary conditions in step S104 include:
for the cantilever beam of the target metamaterial compression bar, the boundary conditions are as follows:
θ1(0)＝θ2(0)＝θ′1(L)-ηPθ2(L)＝θ′2(L)+ηPθ1(L)＝0；
for the simply supported beam of the target metamaterial compression bar, the boundary conditions are as follows:
θ′1(0)-ηPθ2(0)＝θ′2(0)+ηPθ1(0)＝θ′1(L)-ηPθ2(L)＝θ′2(L)+ηPθ1(L)＝0。
wherein, step S105 specifically includes: if the design load is larger than the critical instability load, the target metamaterial compression bar is unstable, and buckling can occur to cause instability; if the design load is less than or equal to the critical buckling load, the target metamaterial compression bar is stable, and buckling cannot occur.
The foregoing is a more detailed description of the present invention that is presented in conjunction with specific embodiments, and the practice of the invention is not to be considered limited to those descriptions. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (8)

1.一种力学超材料压杆稳定性分析方法，其特征在于，包括以下步骤：1. a mechanical metamaterial compression rod stability analysis method, is characterized in that, comprises the following steps: 获取样本超材料压杆的样本周期单元，根据所述样本周期单元构建有限元分析模型；Obtain a sample periodic unit of the sample metamaterial pressure rod, and construct a finite element analysis model according to the sample periodic unit; 获取目标超材料压杆的目标周期单元，根据所述有限元分析模型对所述目标周期单元进行有限元分析，获取若干特征刚度参数；Obtaining the target periodic element of the target metamaterial pressure rod, and performing finite element analysis on the target periodic element according to the finite element analysis model to obtain several characteristic stiffness parameters; 根据所述目标超材料压杆的变形协调条件，结合所述若干特征刚度参数得到目标超材料压杆的整体刚度矩阵；According to the deformation coordination conditions of the target metamaterial press rod, and combining the several characteristic stiffness parameters, the overall stiffness matrix of the target metamaterial press rod is obtained; 建立屈曲控制方程，将设定的压杆边界条件和所述整体刚度矩阵带入所述屈曲控制方程，求解获取临界失稳载荷；A buckling control equation is established, and the set boundary conditions of the compression bar and the overall stiffness matrix are brought into the buckling control equation, and the critical buckling load is obtained by solving; 将设计负载与所述临界失稳载荷进行比较，判断所述目标超材料压杆的稳定性。The design load is compared with the critical buckling load to determine the stability of the target metamaterial compression rod. 2.根据权利要求1所述的一种力学超材料压杆稳定性分析方法，其特征在于，所述获取目标超材料压杆的目标周期单元，具体包括：2. a kind of mechanical metamaterial compression rod stability analysis method according to claim 1, is characterized in that, the described acquisition target period element of target metamaterial compression rod, specifically comprises: 所述目标超材料压杆由基本单元周期排布而成，将组成所述目标超材料压杆的基本单元作为所述目标周期单元。The target metamaterial pressing rod is formed by periodic arrangement of basic units, and the basic unit constituting the target metamaterial pressing rod is used as the target periodic unit. 3.根据权利要求1所述的一种力学超材料压杆稳定性分析方法，其特征在于，所述根据所述有限元分析模型对所述目标周期单元进行有限元分析，获取若干特征刚度参数，具体包括：3. The method for analyzing the stability of a mechanical metamaterial compression rod according to claim 1, wherein the finite element analysis is performed on the target periodic element according to the finite element analysis model, and several characteristic stiffness parameters are obtained. , including: 对所述目标周期单元进行四个有限元分析，在四个有限元分析中加载有特定形式的位移载荷，所述位移载荷包括应变和曲率，根据所述位移载荷在有限元分析模型中获取应变能和反作用力，根据所述应变能和反作用力得到所述特征刚度参数。Four finite element analyses are performed on the target periodic element, and a specific form of displacement load is loaded in the four finite element analyses, and the displacement load includes strain and curvature, and the strain is obtained in the finite element analysis model according to the displacement load energy and reaction force, and the characteristic stiffness parameter is obtained according to the strain energy and reaction force. 4.根据权利要求3所述的一种力学超材料压杆稳定性分析方法，其特征在于，所述四次有限元分析包括；4. a kind of mechanical metamaterial compression rod stability analysis method according to claim 3, is characterized in that, described fourth order finite element analysis comprises; 在第一次有限元分析中，第一应变和第一曲率分别设定为ε＝{0,0,ε3}和κ＝{0,0,0}，获取第一应变能U1和第一反作用扭矩，根据所述第一应变能和公式U1＝C3ε3 2/2获取第一特征刚度参数C3s，根据第一反作用扭矩和第一应变的比值得到第二特征刚度参数Hs，若超材料为非手性时，则Hs为0；In the first finite element analysis, the first strain and the first curvature are set as ε = {0,0,ε3} and κ={0,0,0}, respectively, and the first strain energy U1 and the first a reaction torque, the first characteristic stiffness parameter C 3s is obtained according to the first strain energy and the formula U 1 =C 3 ε 3 2 /2, and the second characteristic stiffness parameter H is obtained according to the ratio of the first reaction torque and the first strain s , if the metamaterial is achiral, then H s is 0; 在第二次有限元分析中，第二应变和第二曲率分别设定为ε＝{0,0,0}和κ＝{0,0,τ}，获取第二应变能U2，根据所述第二应变能和公式U2＝D3τ2/2获取第三特征刚度参数D3s；In the second finite element analysis, the second strain and the second curvature are set as ε={0,0,0} and κ={0,0,τ}, respectively, and the second strain energy U 2 is obtained, according to the Obtain the third characteristic stiffness parameter D 3s by using the second strain energy and the formula U 2 =D 3 τ 2 /2; 在第三次有限元分析中，第三应变和第三曲率分别设定为ε＝{ε1,0,0}和κ＝{0,0,0}，获取第三应变能U3，根据所述第三应变能和公式U3＝C1s(1-Hs 2/C3sD3s)ε1 2/2获取第四特征刚度参数C1s，并根据对称性获取第五特征刚度参数C2s；In the third finite element analysis, the third strain and the third curvature are set as ε={ε 1 ,0,0} and κ={0,0,0}, respectively, and the third strain energy U 3 is obtained, according to The third strain energy and the formula U 3 =C 1s (1-H s 2 /C 3s D 3s )ε 1 2 /2 obtain the fourth characteristic stiffness parameter C 1s , and obtain the fifth characteristic stiffness parameter C according to the symmetry 2s ; 在第四次有限元分析中，第四应变和第四曲率分别设定为ε＝{0，0，0}和κ＝{κ1,0，0}，获取第四应变能U4，根据第四应变能和等式U4＝D1s(1-Hs 2/C3sD3s)κ1 2/2获取第六特征刚度参数D1s，并根据对称性获取第七特征刚度参数D2s。In the fourth finite element analysis, the fourth strain and the fourth curvature are set as ε={0, 0, 0} and κ={κ 1 , 0, 0}, respectively, and the fourth strain energy U 4 is obtained according to The fourth strain energy and equation U 4 =D 1s (1-H s 2 /C 3s D 3s )κ 1 2 /2 obtain the sixth characteristic stiffness parameter D 1s , and obtain the seventh characteristic stiffness parameter D 2s according to the symmetry . 5.根据权利要求4所述的一种力学超材料压杆稳定性分析方法，其特征在于，所述根据所述目标超材料压杆的变形协调条件，结合所述若干特征刚度参数得到超材料压杆的整体刚度矩阵，具体包括：5. The method for analyzing the stability of a mechanical metamaterial compression rod according to claim 4, wherein the metamaterial is obtained by combining the several characteristic stiffness parameters according to the deformation coordination conditions of the target metamaterial compression rod. The overall stiffness matrix of the compression rod, including: 若所述目标超材料压杆由m*n个周期单元重复排列而成，每个目标周期单元的尺寸为a，则结合所述若干特征刚度参数构建力学模型，根据所述力学模型得出目标超材料压杆的整体刚度矩阵C、B和D为：If the target metamaterial strut is repeatedly arranged by m*n periodic units, and the size of each target periodic unit is a, then a mechanical model is constructed in combination with the several characteristic stiffness parameters, and the target is obtained according to the mechanical model. The overall stiffness matrices C, B and D of the metamaterial strut are:
Figure FDA0002921309040000021
Figure FDA0002921309040000021
Figure FDA0002921309040000022
Figure FDA0002921309040000022
Figure FDA0002921309040000023
Figure FDA0002921309040000023
 其中，H＝mnHs，C1＝C2＝mnC1s，C3＝mnC3s，Wherein, H=mnH s , C 1 =C 2 =mnC 1s , C 3 =mnC 3s ,
Figure FDA0002921309040000024
Figure FDA0002921309040000024
Figure FDA0002921309040000031
Figure FDA0002921309040000031
Figure FDA0002921309040000032
Figure FDA0002921309040000032
 6.根据权利要求5所述的一种力学超材料压杆稳定性分析方法，其特征在于，所述屈曲控制方程为：6. a kind of mechanical metamaterial compression rod stability analysis method according to claim 5, is characterized in that, described buckling control equation is:
Figure FDA0002921309040000033
Figure FDA0002921309040000033
Figure FDA0002921309040000034
Figure FDA0002921309040000034
 联立方程(1)和(2)，获取通解为：Simultaneous equations (1) and (2), the general solution is obtained as:
Figure FDA0002921309040000035
Figure FDA0002921309040000035
Figure FDA0002921309040000036
Figure FDA0002921309040000036
 其中，令
Figure FDA0002921309040000037
Among them, let
Figure FDA0002921309040000037
Figure FDA0002921309040000038
Figure FDA0002921309040000038
 则有：
Figure FDA0002921309040000039
Then there are:
Figure FDA0002921309040000039
Figure FDA00029213090400000310
Figure FDA00029213090400000310
Figure FDA0002921309040000041
Figure FDA0002921309040000041
 7.根据权利要求6所述的一种力学超材料压杆稳定性分析方法，其特征在于，所述边界条件包括有：7. A kind of mechanical metamaterial compression rod stability analysis method according to claim 6, is characterized in that, described boundary condition comprises: 对于所述目标超材料压杆的悬臂梁，边界条件为：For the cantilever beam of the target metamaterial pressure rod, the boundary conditions are: θ1(0)＝θ2(0)＝θ′1(L)-ηPθ2(L)＝θ′2(L)+ηPθ1(L)＝0；θ 1 (0)=θ 2 (0)=θ′ 1 (L)−ηPθ 2 (L)=θ′ 2 (L)+ηPθ 1 (L)=0; 对于所述目标超材料压杆的简支梁，边界条件为：For the simply supported beam of the target metamaterial compression rod, the boundary conditions are: θ′1(0)-ηPθ2(0)＝θ′2(0)+ηPθ1(0)＝θ′1(L)-ηPθ2(L)＝θ′2(L)+ηPθ1(L)＝0。θ′ 1 (0)-ηPθ 2 (0)=θ′ 2 (0)+ηPθ 1 (0)=θ′ 1 (L)-ηPθ 2 (L)=θ′ 2 (L)+ηPθ 1 (L )=0. 8.根据权利要求1所述的一种力学超材料压杆稳定性分析方法，其特征在于，所述将设计负载与所述临界失稳载荷进行比较，判断所述目标超材料压杆的稳定性，具体包括：8. The method for analyzing the stability of a mechanical metamaterial pressure rod according to claim 1, wherein the design load is compared with the critical buckling load, and the stability of the target metamaterial pressure rod is judged. sex, including: 若所述设计负载大于所述临界失稳载荷，则表示所述目标超材料压杆不稳定，会发生屈曲导致失稳；If the design load is greater than the critical buckling load, it means that the target metamaterial compression rod is unstable, and buckling will cause instability; 若所述设计负载小于或等于临界失稳载荷，则表示所述目标超材料稳定，不会发生屈曲。If the design load is less than or equal to the critical buckling load, it means that the target metamaterial is stable without buckling.
CN202110118958.0A 2021-01-28 2021-01-28 Stability analysis method for mechanical metamaterial compression bar Active CN112784460B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110118958.0A CN112784460B (en) 2021-01-28 2021-01-28 Stability analysis method for mechanical metamaterial compression bar

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110118958.0A CN112784460B (en) 2021-01-28 2021-01-28 Stability analysis method for mechanical metamaterial compression bar

Publications (2)

Publication Number Publication Date
CN112784460A true CN112784460A (en) 2021-05-11
CN112784460B CN112784460B (en) 2023-05-16

Family

ID=75759386

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110118958.0A Active CN112784460B (en) 2021-01-28 2021-01-28 Stability analysis method for mechanical metamaterial compression bar

Country Status (1)

Country Link
CN (1) CN112784460B (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115252246A (en) * 2022-09-28 2022-11-01 微创神通医疗科技（上海）有限公司 Intracranial vascular interventional device and preparation method thereof
CN115783112A (en) * 2022-12-07 2023-03-14 北京理工大学 Composite structure containing foamed aluminum chiral periodic component and design method thereof

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105845121A (en) * 2016-04-19 2016-08-10 黄礼范 Sound-insulating, ventilating and heat transfer enhancing acoustic metamaterial unit, composite structure and preparation method
CN108153981A (en) * 2017-12-26 2018-06-12 中航沈飞民用飞机有限责任公司 A kind of composite material fuselage Material Stiffened Panel Post-Buckling Analysis of Structures method based on finite element analysis
CN109657284A (en) * 2018-11-27 2019-04-19 华中科技大学 A kind of equal geometry Topology Optimization Method towards Meta Materials
CN110096808A (en) * 2019-04-30 2019-08-06 中国石油工程建设有限公司北京设计分公司 A kind of spherical shell vault Finite Element Simulation Analysis method with ribbing under multiple spot load
CN110287637A (en) * 2019-07-03 2019-09-27 西南交通大学 A Calculation Method of Elastic-Plastic Buckling Capacity
CN111259592A (en) * 2020-01-20 2020-06-09 湖南工业大学 A method for topology optimization of piezoelectric metamaterial sheets for vibration energy harvesting
CN111597661A (en) * 2020-06-18 2020-08-28 南昌航空大学 A kind of aluminum alloy thin-walled member coupling processing stability control method

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105845121A (en) * 2016-04-19 2016-08-10 黄礼范 Sound-insulating, ventilating and heat transfer enhancing acoustic metamaterial unit, composite structure and preparation method
CN108153981A (en) * 2017-12-26 2018-06-12 中航沈飞民用飞机有限责任公司 A kind of composite material fuselage Material Stiffened Panel Post-Buckling Analysis of Structures method based on finite element analysis
CN109657284A (en) * 2018-11-27 2019-04-19 华中科技大学 A kind of equal geometry Topology Optimization Method towards Meta Materials
CN110096808A (en) * 2019-04-30 2019-08-06 中国石油工程建设有限公司北京设计分公司 A kind of spherical shell vault Finite Element Simulation Analysis method with ribbing under multiple spot load
CN110287637A (en) * 2019-07-03 2019-09-27 西南交通大学 A Calculation Method of Elastic-Plastic Buckling Capacity
CN111259592A (en) * 2020-01-20 2020-06-09 湖南工业大学 A method for topology optimization of piezoelectric metamaterial sheets for vibration energy harvesting
CN111597661A (en) * 2020-06-18 2020-08-28 南昌航空大学 A kind of aluminum alloy thin-walled member coupling processing stability control method

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
GAOJIAN LIN等: ""Buckling of lattice columns made from three-dimensional chiral mechanical metamaterials"", 《INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES》 *
JIAN HUA等: ""Parameters analysis and optimization of a typical multistable mechanical metamaterial"", 《EXTREME MECHANICS LETTERS》 *
苏继龙等: ""蜂窝结构力学超材料弹性及抗冲击性能的研究进展"", 《材料工程》 *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115252246A (en) * 2022-09-28 2022-11-01 微创神通医疗科技（上海）有限公司 Intracranial vascular interventional device and preparation method thereof
CN115252246B (en) * 2022-09-28 2022-12-16 微创神通医疗科技（上海）有限公司 Intracranial vascular interventional device and preparation method thereof
CN115783112A (en) * 2022-12-07 2023-03-14 北京理工大学 Composite structure containing foamed aluminum chiral periodic component and design method thereof

Also Published As

Publication number Publication date
CN112784460B (en) 2023-05-16

Similar Documents

Publication Publication Date Title
CN107103138B (en) Variable-rigidity lightweight method for laser shot blasting
Han et al. Evolutionary design of nonuniform cellular structures with optimized Poisson's ratio distribution
CN112784460A (en) Method for analyzing stability of mechanical metamaterial compression bar
Nie et al. Form finding and design optimization of cable network structures with flexible frames
Zhang et al. Mechanical properties of negative Poisson's ratio metamaterial units and honeycomb structures with cosine-like re-entrant structure
CN113191040A (en) Single-material structure topology optimization method and system considering structure stability
Bansal Dynamic simulation of a connecting rod made of aluminium alloy using finite element analysis approach
CN111191378A (en) Nonlinear constitutive relation analysis method, system and device for structures with negative Poisson's ratio
CN104537259A (en) Transverse isotropy fiber material performance prediction method based on micro-mechanical model
CN110135084B (en) Agricultural machinery half shaft reliability analysis method under complex uncertainty condition
CN111062072A (en) A form-finding design method for cable-membrane structures based on particle swarm optimization algorithm
Siad et al. Comparison of explicit and implicit finite element simulations of void growth and coalescence in porous ductile materials
Hart et al. Applications of the projective-iteration versions of finite-element method in problems of damage for engineering structures
Karpov et al. Strength and stability of orthotropic shells
CN112417621A (en) Method for analyzing influence of defects in truss structure on rigidity of structure in any direction
Alzahrani et al. Part 1: analytical modeling of symmetric multi-nose tube hydroforming
CN112084683B (en) Plastic deformation analysis method of aluminum alloy material hardware fitting for power transmission line
Mustakim et al. On the design and mechanical properties of a novel tubular auxetic anti-tri-missing rib structure
Hsu et al. Mesh deformation based on fully stressed design: the method and 2‐D examples
Phuong et al. Postbuckling analysis of externally pressured parabola, sinusoidal and cylindrical FG-GRCL panels using HSDT
Wang et al. Form-finding of elastic gridshell based on spatial elastica model
Nayak et al. Analysis of statically indeterminate non-uniform bar problem in post elastic domain by an iterative variational method
Ghorbanpour Arani et al. Pasternak effect on the buckling of embedded single-walled carbon nanotubes using non-local cylindrical shell theory
CN117094066B (en) Method, device and storage medium for determining bearing capacity of tower in wind turbine generator
Motevalli et al. Stress-ratio-dependent material parameters for improved numerical simulations of textile membrane structures

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant