CN111191378B - Nonlinear constitutive relation analysis method, system and device of negative poisson ratio structure - Google Patents
Nonlinear constitutive relation analysis method, system and device of negative poisson ratio structure Download PDFInfo
- Publication number
- CN111191378B CN111191378B CN202010014731.7A CN202010014731A CN111191378B CN 111191378 B CN111191378 B CN 111191378B CN 202010014731 A CN202010014731 A CN 202010014731A CN 111191378 B CN111191378 B CN 111191378B
- Authority
- CN
- China
- Prior art keywords
- load
- cell
- correction factor
- inclined wall
- wall plate
- 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.)
- Active
Links
- 238000004458 analytical method Methods 0.000 title claims abstract description 48
- 238000012937 correction Methods 0.000 claims abstract description 79
- 238000000034 method Methods 0.000 claims abstract description 66
- 239000000463 material Substances 0.000 claims abstract description 44
- 210000004027 cell Anatomy 0.000 claims description 86
- 238000005452 bending Methods 0.000 claims description 37
- 230000005489 elastic deformation Effects 0.000 claims description 14
- 238000012545 processing Methods 0.000 claims description 4
- 210000003850 cellular structure Anatomy 0.000 claims description 3
- 238000013461 design Methods 0.000 abstract description 6
- 238000004519 manufacturing process Methods 0.000 abstract description 6
- 238000004364 calculation method Methods 0.000 abstract description 4
- 238000012938 design process Methods 0.000 abstract description 3
- 238000010998 test method Methods 0.000 abstract description 3
- 230000006870 function Effects 0.000 description 10
- 238000010586 diagram Methods 0.000 description 7
- 230000000694 effects Effects 0.000 description 6
- 230000009466 transformation Effects 0.000 description 4
- 230000009286 beneficial effect Effects 0.000 description 3
- 238000012986 modification Methods 0.000 description 3
- 230000004048 modification Effects 0.000 description 3
- 230000008569 process Effects 0.000 description 3
- 238000003860 storage Methods 0.000 description 3
- 238000006467 substitution reaction Methods 0.000 description 3
- PRPINYUDVPFIRX-UHFFFAOYSA-N 1-naphthaleneacetic acid Chemical compound C1=CC=C2C(CC(=O)O)=CC=CC2=C1 PRPINYUDVPFIRX-UHFFFAOYSA-N 0.000 description 2
- 238000003491 array Methods 0.000 description 2
- 230000006835 compression Effects 0.000 description 2
- 238000007906 compression Methods 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 230000000737 periodic effect Effects 0.000 description 2
- 238000004088 simulation Methods 0.000 description 2
- 210000003537 structural cell Anatomy 0.000 description 2
- 238000010521 absorption reaction Methods 0.000 description 1
- 210000002421 cell wall Anatomy 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 238000013401 experimental design Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 239000006260 foam Substances 0.000 description 1
- 238000009413 insulation Methods 0.000 description 1
- 230000010354 integration Effects 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 230000000704 physical effect Effects 0.000 description 1
- 238000003825 pressing Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
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
-
- 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)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Catalysts (AREA)
- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
Abstract
The application discloses a nonlinear constitutive relation analysis method, a nonlinear constitutive relation analysis system and a nonlinear constitutive relation analysis device for a negative poisson ratio structure. The method comprises the steps of obtaining cells of a concave honeycomb structure; performing deformation analysis on the cells; obtaining a correction factor according to the deformation analysis result; establishing a nonlinear constitutive relation of the concave honeycomb structure according to the correction factor; and designing and producing a corresponding structure according to the nonlinear constitutive relation. By using the method provided by the application, the design, production and manufacturing processes are more convenient in the scene with special junction requirements on materials or structures, the design period of the product is further shortened, and the method has better calculation precision and application range than the numerical method and test method in the prior art. The application can be widely applied to the technical field of material science.
Description
Technical Field
The application relates to the technical field of material science, in particular to a method, a system and a device for analyzing a nonlinear constitutive relation of a negative poisson ratio structure.
Background
Negative poisson ratio: means that when stretched, the material expands laterally within the elastic range; while the transverse direction of the material instead contracts when compressed.
A cell: in the smallest structural unit of a multicellular structure, such as a honeycomb structure, one unit surrounded by each small hole is called a cell.
Bending moment: one kind of internal moment on the section of the stress member.
The honeycomb structure is a good lightweight structure due to the characteristics of high specific strength, high specific rigidity, good heat and sound insulation performance, strong energy absorption and the like. The microstructure of the honeycomb is different, and the macroscopic mechanical and physical properties are also different. The equivalent material parameters of the honeycomb structure can be adjusted by changing the geometry and material parameters of the honeycomb structure, and particularly, the concave honeycomb structure shows extremely strong Negative Poisson's Ratio (NPR) effect. The negative poisson's ratio material has the characteristic of becoming narrower when stretched and wider when extruded, and along with the development of modern industrial technology, the negative poisson's ratio material has great potential in various engineering fields of aviation, aerospace, machinery, traffic and the like due to the special mechanical properties thereof. Negative poisson's ratio materials have emerged for over 100 years, but until 1987, lakes et al have invented the first artificial negative poisson's ratio foam, which has not attracted much attention. However, the use of negative poisson materials in structures is limited by the low stiffness. In recent years researchers have done a great deal of work on the stiffness of negative poisson's ratio materials and Zied et al have increased the in-plane stiffness of the concave honeycomb structure by implanting two different substructures. Lu and Fu et al also have the effect of increasing the stiffness in the structural plane by increasing the cell riser thickness of the concave honeycomb structure using the finite element technique.
Most of the above researches are based on experiments or numerical simulations, and the concave honeycomb structure is generally regarded as an anisotropic material with periodic characteristics, and in engineering design and analysis, complicated geometric forms and anisotropic mechanical properties make the experimental design and analysis of the honeycomb structure time-consuming, laborious and uneconomical. With the development of computing science, it has become realistic to perform structural modeling and mechanical simulation on a large complex structure by using a general finite element program, however, a refined model greatly increases the difficulty of model computing, so that the computing efficiency is significantly reduced. Meanwhile, the complex and diverse structures and boundary conditions also cause the application of the model to have certain limitations.
Disclosure of Invention
The application aims to at least solve one of the technical problems existing in the prior art to a certain extent, and therefore, the application aims to provide a nonlinear constitutive relation analysis method, a nonlinear constitutive relation analysis system and a nonlinear constitutive relation analysis device with better calculation precision and a negative poisson ratio structure with an application range.
An object of an embodiment of the present application is to provide a method for analyzing a nonlinear constitutive relation of a negative poisson ratio structure, including the steps of:
obtaining a cell of a concave honeycomb structure;
performing deformation analysis on the cells;
obtaining a correction factor according to the deformation analysis result;
establishing a nonlinear constitutive relation of the concave honeycomb structure according to the correction factor;
designing and producing a corresponding structure according to the nonlinear constitutive relation;
the correction factor includes: young's modulus correction factor and Poisson's ratio correction factor.
In addition, the method for analyzing the nonlinear constitutive relation of the negative poisson ratio structure according to the above embodiment of the present application may further have the following additional technical features:
further, the step of performing deformation analysis on the cell specifically includes: acquiring a bending moment and a limiting bending moment at the end points of the inclined wall plates of the cells; comparing the bending moment with the ultimate bending moment to determine the deformation stage of the cell; the deformation stage includes an elastic deformation stage and a plastic deformation stage.
Further, the young's modulus correction factors include young's modulus correction factors in a horizontal coordinate direction and young's modulus correction factors in a vertical coordinate direction; the poisson ratio correction factors comprise poisson ratio correction factors in the horizontal coordinate direction and poisson ratio correction factors in the vertical coordinate direction.
Further, the step of obtaining the correction factor according to the result of the deformation analysis specifically includes: establishing a control equation of a half inclined wall plate of the cell; converting the control equation into a dimensionless equation, and simplifying the dimensionless equation; obtaining the projection rate of the dimensionless load and the inclined wall plate according to the simplified dimensionless equation; and obtaining a correction factor according to the dimensionless load and the projection rate of the inclined wall plate.
Further, the step of obtaining the correction factor according to the dimensionless load and the projection rate of the inclined wall plate specifically includes the following steps: obtaining the geometric characteristics of the cells and the Young's modulus of the concave honeycomb structure material; and obtaining a correction factor by combining the geometric feature, the Young modulus of the material, the dimensionless load and the projection rate of the inclined wall plate.
Further, the projection ratio includes a projection ratio in a horizontal coordinate direction and a projection ratio in a vertical coordinate direction.
Further, the step of establishing a control equation of the half-slope panel of the cell includes at least one of the following steps: when the load is a pulling load, a first control equation is established for the elastic deformation of the half inclined wall plate; when the load is a tensile load, a second control equation is established for the plastic deformation of the half inclined wallboard; when the load is a compressive load, a third control equation is established for the elastic deformation of the half inclined wall plate; and when the load is a compressive load, establishing a fourth control equation aiming at the plastic deformation of the half inclined wall plate.
Further, the load includes a load that the cell receives in a horizontal coordinate direction and a load that the cell receives in a vertical coordinate direction.
In a second aspect, an embodiment of the present application provides an analysis system for a nonlinear constitutive relation of a negative poisson ratio structure, including:
a target acquisition unit configured to acquire a cell of a concave cellular structure;
the deformation analysis unit is used for performing deformation analysis on the cell;
the core processing unit is used for obtaining a correction factor according to the deformation analysis result and establishing a nonlinear constitutive relation of the negative poisson ratio structure according to the correction factor;
and the output unit is used for simulating and outputting the structure according to the nonlinear constitutive relation.
In a third aspect, an embodiment of the present application provides an apparatus for analyzing a nonlinear constitutive relation of a negative poisson ratio structure, including:
at least one processor;
at least one memory for storing at least one program;
the at least one program, when executed by the at least one processor, causes the at least one processor to implement a method of analyzing a nonlinear constitutive relationship of the negative poisson's ratio structure.
The application has the advantages and beneficial effects that: the technical scheme provided by the application firstly carries out deformation analysis on the representative cell of the honeycomb structure, and thus obtains the correction factor of the nonlinear constitutive relation, and further establishes the nonlinear constitutive relation so as to design and fit the honeycomb structure; compared with the numerical method and the test method in the prior art, the method has better calculation precision and application range; in the scene with great junction demands on materials or structures, the design, production and manufacturing processes are more convenient, and the design period of the product is further shortened.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following description is made with reference to the accompanying drawings of the embodiments of the present application or the related technical solutions in the prior art, and it should be understood that the drawings in the following description are only for convenience and clarity of describing some embodiments in the technical solutions of the present application, and other drawings may be obtained according to these drawings without the need of inventive labor for those skilled in the art.
FIG. 1 is a flow chart of an embodiment of a method for analyzing nonlinear constitutive relations of a negative Poisson's ratio structure according to the present application;
FIG. 2 is a schematic diagram of a concave honeycomb structure and a cell structure in an embodiment of a method for analyzing a nonlinear constitutive relation of a negative Poisson's ratio structure according to the present application;
FIG. 3 is an overall force diagram of a concave honeycomb structure under a tensile load in the y-direction in an embodiment of a method for analyzing a nonlinear constitutive relationship of a negative Poisson's ratio structure according to the present application;
FIG. 4 is a schematic diagram of deformation of inclined wall plates under tensile load in a concave honeycomb structure according to an embodiment of the method for analyzing nonlinear constitutive relation of a negative Poisson's ratio structure of the present application;
FIG. 5 is a graph of an analysis of elastic deformation under tensile load of inclined wall plates in a concave honeycomb structure according to an embodiment of the method for analyzing a nonlinear constitutive relation of a negative Poisson's ratio structure of the present application;
FIG. 6 is a graph of a plastic deformation analysis of a tensile load of inclined wall plates in a concave honeycomb structure according to an embodiment of the method for analyzing a nonlinear constitutive relation of a negative Poisson's ratio structure of the present application;
FIG. 7 is a graph of the overall force diagram of a concave honeycomb structure under compressive loading in the y-direction in accordance with an embodiment of the method of analyzing the nonlinear constitutive relationship of a negative Poisson's ratio structure of the present application;
FIG. 8 is a schematic diagram of deformation under compressive load of a diagonal wall panel in a concave honeycomb structure according to an embodiment of the method for analyzing a nonlinear constitutive relationship of a negative Poisson's ratio structure of the present application;
FIG. 9 is a graph of elastic deformation analysis of a compressive load of inclined wall plates in a concave honeycomb structure according to an embodiment of the method for analyzing a nonlinear constitutive relation of a negative Poisson's ratio structure of the present application;
FIG. 10 is a graph of a plastic deformation analysis of a compressive load of inclined wall plates in a concave honeycomb structure according to an embodiment of the method for analyzing a nonlinear constitutive relation of a negative Poisson's ratio structure of the present application;
FIG. 11 is a graph showing a comparison of results of Alman strain and dimensionless Euler stress in a theoretical model and a finite element model in a specific example of a method for analyzing a nonlinear constitutive relationship of a negative Poisson's ratio structure according to the present application;
FIG. 12 is a graph showing k at different angles phi in an embodiment of the method for analyzing nonlinear constitutive relation of negative Poisson's ratio structure according to the present application 1 Graph of beta versus beta;
FIG. 13 shows k under different angles phi of the nonlinear constitutive relation of the negative Poisson's ratio structure according to an embodiment of the application 2 Graph of beta versus beta;
FIG. 14 is a diagram showing an example of a method for analyzing nonlinear constitutive relation of negative Poisson's ratio structure according to the present applicationM under included angles phi of different sizes 1 Graph of beta versus beta;
FIG. 15 is a graph showing the relationship of nonlinear constitutive relations of a negative Poisson's ratio structure for m under different angles phi 2 Graph of beta versus beta;
FIG. 16 is a graph showing k at different slenderness ratios t/l in an embodiment of a method for analyzing nonlinear constitutive relation of negative Poisson's ratio structure of the present application 1 Graph of beta versus beta;
FIG. 17 is a graph showing k at different slenderness ratios t/l in an embodiment of a method for analyzing nonlinear constitutive relation of negative Poisson's ratio structure of the present application 2 Graph of beta versus beta;
FIG. 18 is a graph showing the relationship between nonlinear constitutive relations of a negative Poisson's ratio structure according to the present application, m, at different elongated ratios t/l 1 Graph of beta versus beta;
FIG. 19 is a graph showing the relationship between nonlinear constitutive relations of a negative Poisson's ratio structure according to the present application, m, at different elongated ratios t/l 2 Graph of beta versus beta;
FIG. 20 is a graph showing the yield strength σ of different honeycomb materials in an embodiment of a method for analyzing a nonlinear constitutive relation of a negative Poisson's ratio structure according to the present application s Lower k 1 Graph of beta versus beta;
FIG. 21 is a graph showing the yield strength σ of different honeycomb materials in an embodiment of a method for analyzing a nonlinear constitutive relation of a negative Poisson's ratio structure according to the present application s Lower k 2 Graph of beta versus beta;
FIG. 22 is a graph showing the yield strength σ of different honeycomb materials in an embodiment of a method for analyzing a nonlinear constitutive relation of a negative Poisson's ratio structure according to the present application s Lower, m 1 Graph of beta versus beta;
FIG. 23 is a graph showing the yield strength σ of different honeycomb materials in an embodiment of a method for analyzing a nonlinear constitutive relation of a negative Poisson's ratio structure according to the present application s Lower, m 2 Graph of beta.
Detailed Description
Embodiments of the present application are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the application. The step numbers in the following embodiments are set for convenience of illustration only, and the order between the steps is not limited in any way, and the execution order of the steps in the embodiments may be adaptively adjusted according to the understanding of those skilled in the art.
The method, the system and the device for analyzing the nonlinear constitutive relation of the negative poisson ratio structure according to the embodiment of the application are described in detail below with reference to the accompanying drawings, and the method for analyzing the nonlinear constitutive relation of the negative poisson ratio structure according to the embodiment of the application will be described first with reference to the accompanying drawings.
Referring to fig. 1, the method for analyzing the nonlinear constitutive relation of the negative poisson ratio structure according to the embodiment of the present application mainly includes the following steps:
s01: obtaining a cell of a concave honeycomb structure; referring to fig. 2, the present embodiment regards the inner honeycomb structure as an anisotropic material with periodic characteristics, and selects a representative cell of the honeycomb structure for further processing, thereby reflecting the constitutive relation of the same type of concave honeycomb structure (same shape).
S02: performing deformation analysis on the cells; specifically, it is mainly determined whether the inclined wall plate of the cell is in an elastic deformation stage or a plastic deformation stage;
s021: calculating the bending moment M at the end point of the inclined wall plate representing the cell B And the limit bending moment M which can be born U ：
In sigma s Is the honeycomb yield strength, t is the honeycomb panel thickness, and b is the honeycomb depth.
S022: judging bending moment M B And limit bending moment M U Is of a size of (2);
if bending moment M B Less than the limit bending moment M U No plastic corner beta occurs 0 The semi-inclined wall plate is in an elastic deformation stage; if bending moment M B Greater than the limit bending moment M U Then the plastic rotation angle beta appears 0 The semi-inclined wall plate is in a plastic deformation stage, and the bending moment M is generated when a control equation of the semi-inclined wall plate is constructed and the dimensionless load and displacement are calculated B Equal to the ultimate bending moment M U 。
S03: obtaining a correction factor according to the deformation analysis result; specifically, aiming at geometric characteristics (angle and relative density) of the inner honeycomb structure, young modulus of a material and actual deformation conditions (corresponding equivalent material parameters are obtained through deformation analysis representing load bearing of cells in different directions), a correction factor capable of reflecting nonlinear constitutive relations of the same type of inner concave honeycomb structure is obtained.
Wherein the correction factor comprises: young's modulus correction factor k when cell bears load in X-axis direction 1 And poisson's ratio correction factor m 1 Young's modulus correction factor k when load is applied in Y-axis direction 2 And poisson's ratio correction factor m 2 The method comprises the steps of carrying out a first treatment on the surface of the Wherein the nonlinear equivalent material parameters of the cell include: representing the equivalent Young's modulus E of the cell in the X-axis direction 1 And equivalent poisson ratio v 1 Equivalent Young's modulus E of cell in Y-axis direction 2 And equivalent poisson ratio v 2 The method comprises the steps of carrying out a first treatment on the surface of the The cell nonlinear equivalent material parameter, nonlinear constitutive relation correction factor, relative density R of structure and Young modulus E of material s The set of relational equations of (2) is:
wherein the relative density of the structure is calculated from formula (3):
wherein ρ is * Is the density, ρ, of the concave honeycomb material 0 Is the density of the cell wall, h is the length of the cell riser, t is the thickness of the wall of the honeycomb structure, and phi is the angle between the hypotenuse of the cell and the Y-axis direction. In particular, whenAnd h=l, the relative density R is:
from equation (3) and equation (2), we can get:
in the formula, zeta is a dimensionless load,and->The projection rate of the cell sloping plate in the X-axis direction and the projection rate of the cell sloping plate in the Y-axis direction when the cell sloping plate bears load in the X-axis direction are respectively +.>And->The projection rate of the cell sloping plate in the X-axis direction and the Y-axis direction when the cell sloping plate bears load in the Y-axis direction are respectively +.>Is the sum of the deformations of cell riser DB and riser AC in fig. 1 (tensile positive and compressive negative).
Wherein zeta is a dimensionless load,and->The projection rate of the cell sloping plate in the X-axis direction and the projection rate of the cell sloping plate in the Y-axis direction when the cell sloping plate bears load in the X-axis direction are respectively +.>And->The projection rates of the cell sloping plates in the X-axis direction and the Y-axis direction when bearing loads in the Y-axis direction can be respectively connected with the corners of the two ends and the middle point of the structural cell sloping plates through large deformation analysis, and the specific process is as follows:
s031: using symmetry, establishing a control equation of the corresponding semi-inclined wall plate according to the bending theory of the beam;
specifically, according to the bending theory of the beam, the control equation is as follows:
in the formula (6), P is an equivalent load applied to the representative cell; e (E) s I is the bending rigidity of the cross section of the honeycomb inclined wall plate; s is an arc coordinate (s is more than or equal to 0 and less than or equal to 1/2) along the axis direction of the beam, and gamma is a corner at the arc coordinate s.
S032: converting the control equation into a dimensionless equation, and simplifying the dimensionless equation by utilizing boundary conditions;
specifically, the control equation may be further converted into a dimensionless equation:
in the formula (7) of the present application,stable for the compression bar under the working condition of hinging and supporting at two endsThe critical load, S=s/l (S is more than or equal to 0 and less than or equal to 0.5) is the dimensionless arc length. Two sides of the dimensionless equation are multiplied by +.>And integrates the dimensionless arc coordinates S while utilizing the boundary condition M 0 After=0, it can be:
in the formula (8), β is the rotation angle of the point O in the inclined wall plate.
S033: for the simplified dimensionless equation, the dimensionless load zeta is represented by a first elliptic integral F (beta) (beta is the corner at the O point);
the projection rate of the inclined wall plate of the honeycomb structure along the X-axis direction is represented by a first elliptic integral F (beta);
the projection ratio of the inclined wall plate of the honeycomb structure in the Y-axis direction is represented by a first type ellipse integral F (β) and a second type ellipse integral E (β).
More precisely, according to the fact that the load applied to the inner honeycomb structure is a pulling load or a pressing load, the four combination conditions of the elastic deformation stage or the plastic deformation stage of the semi-inclined wall plate are respectively connected with the corners of the two ends and the middle point of the inclined plate of the structural cell through large deformation analysis, the following is selected to describe the condition of bearing the load of the honeycomb structure in the Y-axis direction, when the load is born in the X-axis direction, the solving process is similar to that of bearing the load in the Y-axis direction, and only the projection rates in the X-axis direction and the Y-axis direction are required to be calculatedAnd->Phi transform of +.>And the projection ratios in the X-axis direction and the Y-axis direction are interchanged, in thatThis is not repeated:
A. referring to fig. 3, 4 and 5, when the load is a tensile load, the established control equation of the half-slope wall panel is as follows:
in the formula (9), E s I is the bending rigidity of the cross section of the honeycomb inclined wall plate; i is the cross-sectional moment of inertia of the honeycomb panel; gamma is the rotation angle at the arc coordinate S.
Projection rate of dimensionless load zeta and inclined wall plate along X-axis directionAnd projection ratio in Y-axis direction +.>The method comprises the following steps:
wherein:
in formula (11), F (β) is a first type of elliptic integral; e (beta) is a second class of elliptic integral; η is according to the coordinate transformation formulaThe new variable generated; beta is the corner of the midpoint of the inclined wall plate; η (eta) 0 Is the η value when the arc coordinate s=0, i.e., the rotation angle γ=0 at the arc coordinate S.
B. Referring to fig. 6, when the load is a tensile load, the control equation for the half-slope panel is established for the plastic deformation phase of the half-slope panel as:
in the formula (12), E s I is the bending rigidity of the cross section of the honeycomb inclined wall plate; i is the cross-sectional moment of inertia of the honeycomb panel; gamma is the rotation angle at the arc coordinate S, beta 0 Is the plastic rotation angle beta existing in the plastic deformation stage 0 From bending moment M at the end of inclined wall plate B Determining the bending moment M as described in step S022 B Equal to the ultimate bending moment M U Further, the following formula is obtained:
in formula (13), β is the corner of the midpoint of the diagonal wall; the boundary conditions of its control equation are:
in the formula (14), M O Is the bending moment representing the midpoint of the cell diagonal plate. Projection rate of dimensionless load zeta and inclined wall plate along X-axis directionAnd projection ratio in Y-axis direction +.>The method comprises the following steps:
wherein:
in formula (16) F (β) is a first type of elliptic integral; e (beta) is a secondEllipse-like integration; η' is according to the coordinate transformation formulaThe new variable generated; η' 0 When the arc coordinate s=0, i.e. the rotation angle γ=β at the arc coordinate S 0 η' value at that time.
C. Referring to fig. 7, 8 and 9, when the load is a compressive load, the control equation for the half-diagonal panel is established for the elastic deformation phase of the half-diagonal panel as follows:
in the formula (17), E s I is the bending rigidity of the cross section of the honeycomb inclined wall plate; i is the cross-sectional moment of inertia of the honeycomb panel; gamma is the rotation angle at the arc coordinate S.
Projection rate of dimensionless load zeta and inclined wall plate along X-axis directionAnd projection ratio in Y-axis direction +.>The method comprises the following steps:
wherein:
in formula (19) F (β) is a first type of elliptic integral; e (beta) is a second class of elliptic integral; η is according to the coordinate transformation formulaThe new variable generated; beta is the corner of the midpoint of the inclined wall plate; η (eta) 0 Is the η value when the arc coordinate s=0, i.e., the rotation angle γ=0 at the arc coordinate S.
D. When the load is a compressive load, the established control equation of the half-inclined wall plate is as follows for the plastic deformation stage of the half-inclined wall plate:
in the formula (20), E s I is the bending rigidity of the cross section of the honeycomb inclined wall plate; i is the cross-sectional moment of inertia of the honeycomb panel; gamma is the rotation angle at the arc coordinate S, beta 0 Is the plastic rotation angle beta existing in the plastic deformation stage 0 From bending moment M at the end of inclined wall plate B Determining the bending moment M as described in step S022 B Equal to the ultimate bending moment M U Further, the following formula is obtained:
in the formula (21), beta is the corner of the midpoint of the inclined wall plate, the dimensionless load zeta and the projection rate of the inclined wall plate along the X-axis directionAnd projection ratio in Y-axis direction +.>The method comprises the following steps:
wherein;
in formula (23) F (β) is a first type of elliptic integral; e (beta) is a second class of elliptic integral; η' is according to the coordinate transformation formulaThe new variable generated; η' 0 When the arc coordinate s=0, i.e. the rotation angle γ=β at the arc coordinate S 0 η' value at that time.
In the four cases of A, B, C, D, the Euler stress under large deformation can be obtained:
wherein σ' x And sigma' y Representing the situation when the load is applied in the X-axis direction, sigma x And sigma' y The case when a load is applied in the Y-axis direction is shown. The alman strain under large deformation can be expressed as:
wherein:is the sum of the deformations of cell riser DB and riser AC (positive in tension, negative in compression), A s =tb is the cross-sectional area of the panel, P is the equivalent load applied to the representative cell, h is the length of the riser of the cell, E S For the Young's modulus of the cell material, ζ is the dimensionless load, t is the thickness of the wall plate of the honeycomb structure, l is the length of the hypotenuse of the honeycomb structure, A s =tb is the cross-sectional area of the honeycomb panel; meanwhile, the formula (2) may be further expressed as:
s04: establishing a nonlinear constitutive relation of the concave honeycomb structure according to the correction factor;
referring to FIG. 11, the Almannich strain and absence of the present application is shown in an embodimentThe results of dimensional euler stresses in theoretical models and finite element models are schematically shown. The almann strain curve in the theoretical model and the almann strain curve in the finite element model are substantially identical, indicating that the concave honeycomb structure in the present embodiment is well fitted with the relatively fine finite element concave honeycomb structure. Wherein the structure and material parameters are as follows: phi=60°, l=10 mm, h=10 mm, b=1 mm, t=1 mm, e s ＝12MPa，σ s ＝10MPa。
Referring to fig. 12, 13, 14 and 15, the effect of the concave honeycomb parameter phi on the honeycomb parameter in the embodiment of the application is shown, the positive strain indicates the tensile load of the honeycomb structure, and the negative strain indicates the compressive load of the honeycomb structure. Wherein the structure and material parameters are as follows: phi=30 °, 45 °, 60 °, 75 °, l=10 mm, h=10 mm, b=1 mm, t=1 mm, e s ＝12MPa，σ s =10mpa. From the results, it can be seen that:
1. the larger the cell angle phi is, the Young's modulus correction factor k in the X-axis direction and Y-axis direction when the honeycomb structure is subjected to tensile load 1 And k 2 The larger the Young's modulus correction factor k in the X-axis direction 1 As the cell deformation becomes larger, the young's modulus correction factor k in the Y-axis direction becomes larger 2 As the cell deformation becomes larger and smaller; the greater the cell angle phi, the greater the poisson's ratio correction factor m in the X-axis direction 1 The smaller the poisson's ratio correction factor m in the Y-axis direction 2 The larger the poisson's ratio correction factor m in the X-axis direction 1 As the cell deformation becomes larger and smaller, the poisson ratio correction factor m in the Y-axis direction 2 As the cell deformation becomes larger;
2. the larger the cell angle phi is, the Young's modulus correction factor k in the X-axis direction and Y-axis direction when the honeycomb structure is subjected to compressive load 1 And k 2 The larger the Young's modulus correction factor k in the X-axis direction 1 As the cell deformation becomes larger and smaller, the Young's modulus correction factor k in the Y-axis direction 2 As the cell deformation becomes larger; the greater the cell angle phi, the greater the poisson's ratio correction factor m in the X-axis direction 1 The smaller the poisson's ratio correction factor m in the Y-axis direction 2 The larger the size of the container,poisson's ratio correction factor m in X-axis direction 1 As the cell deformation becomes larger, the poisson ratio correction factor m in the Y-axis direction becomes larger 2 As the cell deformation becomes larger and smaller;
3. the change effect of the Young modulus correction factor and the Poisson ratio correction factor in the X-axis direction is obviously stronger than that of the Young modulus correction factor and the Poisson ratio correction factor in the Y-axis direction.
Referring to FIGS. 16, 17, 18 and 19, the effect of the ratio t/l of the elongation of the concave honeycomb structure on structural parameters in the embodiments of the application is schematically shown, the positive strain is indicative of the tensile load experienced by the honeycomb structure, and the negative strain is indicative of the compressive load experienced by the honeycomb structure. Wherein the structure and material parameters are as follows: phi=60°, t/l=0.05, 0.1, 0.2, 0.4, 0.6, l=10 mm, h=10 mm, b=1 mm, e s ＝12MPa，σ s =10mpa; from the results, it can be seen that:
1. the greater the elongation ratio t/l of the honeycomb material, the earlier the structure is plastically deformed;
2. the greater the elongation ratio t/l, the Young's modulus correction factor k in the X-axis direction and in the Y-axis direction 1 And k 2 The smaller the elongation ratio t/l is, the poisson's ratio correction factor m in the X-axis direction is 1 And poisson's ratio correction factor m in Y-axis direction 2 The influence is not great.
Referring to fig. 20, 21, 22 and 23, the honeycomb material yield strength σ in the embodiment of the application is shown s The effect on structural parameters is schematically illustrated, positive strain being indicative of the tensile load experienced by the honeycomb structure, and negative strain being indicative of the compressive load experienced by the honeycomb structure. Wherein the structure and material parameters are as follows: phi=60°, l=10 mm, h=10 mm, b=1 mm, e s ＝12MPa，σ s =3 MPa, 5MPa, 8MPa, 10MPa, 15MPa; from the results, it can be seen that:
1. honeycomb material yield strength sigma s The larger the structure, the later the plastic deformation occurs;
2. honeycomb material yield strength sigma s The larger the Young's modulus correction factor k in the X-axis direction and in the Y-axis direction 1 And k 2 The larger; material yield strength sigma s Poisson's ratio correction factor m in X-axis direction 1 And Y axisPoisson's ratio correction factor m in direction 2 The influence is not great.
S05: designing and producing a corresponding structure according to the nonlinear constitutive relation;
compared with the prior art, the embodiment of the method for analyzing the nonlinear constitutive relation of the negative poisson ratio structure has the following advantages:
1) According to the embodiment of the application, the correction factors capable of reflecting the nonlinear constitutive relation of the same type of concave honeycomb structure are obtained through deformation analysis and combination of structural geometric features (angles, relative densities) and material Young modulus, the nonlinear constitutive relation reflecting the same type of concave honeycomb structure is established, and the elastoplastic deformation of the material is fully considered in the analysis process, so that the method has better calculation precision and application range compared with a numerical method and a test method;
2) In the scene industry with great demands on materials or structures, the embodiment of the application can conveniently and rapidly design the proper honeycomb structure, so that the design, production and manufacturing processes are more convenient, and the design period of the product is further shortened.
Secondly, the embodiment of the application provides an analysis system of the nonlinear constitutive relation of the negative poisson ratio structure.
The system specifically comprises:
a target acquisition unit configured to acquire a cell of a concave cellular structure;
the deformation analysis unit is used for performing deformation analysis on the cell;
the core processing unit is used for obtaining a correction factor according to the deformation analysis result and establishing a nonlinear constitutive relation of the negative poisson ratio structure according to the correction factor;
and the output unit is used for simulating and outputting the structure according to the nonlinear constitutive relation.
It can be seen that the content in the above method embodiment is applicable to the system embodiment, and the functions specifically implemented by the system embodiment are the same as those of the method embodiment, and the beneficial effects achieved by the method embodiment are the same as those achieved by the method embodiment.
Meanwhile, the embodiment of the application provides an analysis device of a nonlinear constitutive relation of a negative poisson ratio structure, which comprises:
at least one processor;
at least one memory for storing at least one program;
the at least one program, when executed by the at least one processor, causes the at least one processor to implement a method of analyzing a nonlinear constitutive relationship of the negative poisson's ratio structure.
Similarly, the content in the above method embodiment is applicable to the embodiment of the present device, and the functions specifically implemented by the embodiment of the present device are the same as those of the embodiment of the above method, and the beneficial effects achieved by the embodiment of the above method are the same as those achieved by the embodiment of the above method.
In some alternative embodiments, the functions/acts noted in the block diagrams may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may in fact be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Furthermore, the embodiments presented and described in the flowcharts of the present application are provided by way of example in order to provide a more thorough understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed, and in which sub-operations described as part of a larger operation are performed independently.
Furthermore, while the application is described in the context of functional modules, it should be appreciated that, unless otherwise indicated, one or more of the described functions and/or features may be integrated in a single physical device and/or software module or one or more functions and/or features may be implemented in separate physical devices or software modules. It will also be appreciated that a detailed discussion of the actual implementation of each module is not necessary to an understanding of the present application. Rather, the actual implementation of the various functional modules in the apparatus disclosed herein will be apparent to those skilled in the art from consideration of their attributes, functions and internal relationships. Accordingly, one of ordinary skill in the art can implement the application as set forth in the claims without undue experimentation. It is also to be understood that the specific concepts disclosed are merely illustrative and are not intended to be limiting upon the scope of the application, which is to be defined in the appended claims and their full scope of equivalents.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
Logic and/or steps represented in the flowcharts or otherwise described herein, e.g., a ordered listing of executable instructions for implementing logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions.
It is to be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above-described embodiments, the various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, may be implemented using any one or combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.
In the foregoing description of the present specification, reference has been made to the terms "one embodiment/example", "another embodiment/example", "certain embodiments/examples", and the like, means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present application have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the application, the scope of which is defined by the claims and their equivalents.
While the preferred embodiment of the present application has been described in detail, the present application is not limited to the embodiments described above, and various equivalent modifications and substitutions can be made by those skilled in the art without departing from the spirit of the present application, and these equivalent modifications and substitutions are intended to be included in the scope of the present application as defined in the appended claims.
Claims (9)
1. The analysis method of the nonlinear constitutive relation of the negative poisson ratio structure is characterized by comprising the following steps:
obtaining a cell of a concave honeycomb structure;
performing deformation analysis on the cells;
obtaining a correction factor according to the deformation analysis result;
establishing a nonlinear constitutive relation of the concave honeycomb structure according to the correction factor;
designing and producing a corresponding structure according to the nonlinear constitutive relation;
the correction factor includes: young's modulus correction factor and Poisson's ratio correction factor;
the step of obtaining the correction factor according to the deformation analysis result specifically comprises the following steps:
establishing a control equation of a half inclined wall plate of the cell;
converting the control equation into a dimensionless equation, and simplifying the dimensionless equation;
obtaining the projection rate of the dimensionless load and the inclined wall plate according to the simplified dimensionless equation;
obtaining a correction factor according to the dimensionless load and the projection rate of the inclined wall plate;
wherein the step of establishing a control equation of the half-slope panel of the cell comprises the steps of:
when the load is a pulling load, a first control equation is established for the elastic deformation of the half inclined wall plate;
when the load is a tensile load, a second control equation is established for the plastic deformation of the half inclined wallboard;
when the load is a compressive load, a third control equation is established for the elastic deformation of the half inclined wall plate;
when the load is a compressive load, a fourth control equation is established for the plastic deformation of the semi-inclined wall plate;
the first control equation is:the second control equation is: />-P sin(Φ+β 0 +γ); the third control equation is: />The fourth control equation is:wherein E is s I is the bending rigidity of the cross section of the honeycomb inclined wall plate; i is the cross-sectional moment of inertia of the honeycomb panel; gamma is the rotation angle at the arc coordinate S, beta 0 Is the plastic rotation angle beta existing in the plastic deformation stage 0 From bending moment M at the end of inclined wall plate B Determining; p is the equivalent load applied to the representative cell and phi is the cell angle.
2. The method for analyzing the nonlinear constitutive relation of the negative poisson's ratio structure according to claim 1, wherein the step of performing the deformation analysis on the cell specifically comprises:
acquiring a bending moment and a limiting bending moment at the end points of the inclined wall plates of the cells;
comparing the bending moment with the ultimate bending moment to determine the deformation stage of the cell;
the deformation stage includes an elastic deformation stage and a plastic deformation stage.
3. The method for analyzing the nonlinear constitutive relation of the negative poisson's ratio structure according to claim 1, wherein the young's modulus correction factors include a young's modulus correction factor in a horizontal coordinate direction and a young's modulus correction factor in a vertical coordinate direction; the poisson ratio correction factors comprise poisson ratio correction factors in the horizontal coordinate direction and poisson ratio correction factors in the vertical coordinate direction.
4. The method for analyzing the nonlinear constitutive relation of the negative poisson's ratio structure according to claim 1, wherein: the step of obtaining the correction factor according to the projection rate of the dimensionless load and the inclined wall plate specifically comprises the following steps:
obtaining the geometric characteristics of the cells and the Young's modulus of the concave honeycomb structure material;
and obtaining a correction factor by combining the geometric feature, the Young modulus of the material, the dimensionless load and the projection rate of the inclined wall plate.
5. The method for analyzing the nonlinear constitutive relation of the negative poisson ratio structure according to claim 1 or 4, wherein: the projection ratio includes a projection ratio in a horizontal coordinate direction and a projection ratio in a vertical coordinate direction.
6. The method for analyzing the nonlinear constitutive relation of the negative poisson's ratio structure according to claim 1, wherein: the load includes a load borne by the cell in a horizontal coordinate direction and a load borne by the cell in a vertical coordinate direction.
7. The method for analyzing the nonlinear constitutive relation of the negative poisson's ratio structure according to claim 1, wherein: young's modulus correction factor k of cell when bearing load in horizontal coordinate direction 1 Poisson's ratio correction factor m 1 And a Young's modulus correction factor k when bearing a load in the vertical coordinate direction 2 Poisson's ratio correction factor m 2 The method comprises the following steps:
wherein zeta is a dimensionless load,and->The projection rate of the cell sloping plate in the X-axis direction and the projection rate of the cell sloping plate in the Y-axis direction when the cell sloping plate bears load in the X-axis direction are respectively +.>And->The projection rate of the cell sloping plate in the X-axis direction and the Y-axis direction when the cell sloping plate bears load in the Y-axis direction are respectively +.>H is the length of the cell riser and phi is the cell angle; l is the length of the hypotenuse of the honeycomb.
8. An analysis system for nonlinear constitutive relations of a negative poisson's ratio structure, comprising:
a target acquisition unit configured to acquire a cell of a concave cellular structure;
the deformation analysis unit is used for performing deformation analysis on the cell;
the core processing unit is used for obtaining a correction factor according to the deformation analysis result and establishing a nonlinear constitutive relation of the negative poisson ratio structure according to the correction factor;
the output unit is used for simulating and outputting the structure according to the nonlinear constitutive relation;
the step of obtaining the correction factor according to the deformation analysis result specifically comprises the following steps:
establishing a control equation of a half inclined wall plate of the cell;
converting the control equation into a dimensionless equation, and simplifying the dimensionless equation;
obtaining the projection rate of the dimensionless load and the inclined wall plate according to the simplified dimensionless equation;
obtaining a correction factor according to the dimensionless load and the projection rate of the inclined wall plate;
wherein the step of establishing a control equation of the half-slope panel of the cell comprises the steps of:
when the load is a pulling load, a first control equation is established for the elastic deformation of the half inclined wall plate;
when the load is a tensile load, a second control equation is established for the plastic deformation of the half inclined wallboard;
when the load is a compressive load, a third control equation is established for the elastic deformation of the half inclined wall plate;
when the load is a compressive load, a fourth control equation is established for the plastic deformation of the semi-inclined wall plate;
the first control equation is:the second control equation is: />
The third control equation is: />The fourth control equation is: />Wherein E is s I is the bending rigidity of the cross section of the honeycomb inclined wall plate; i is the cross-sectional moment of inertia of the honeycomb panel; gamma is the rotation angle at the arc coordinate S, beta 0 Is the plastic rotation angle beta existing in the plastic deformation stage 0 From bending moment M at the end of inclined wall plate B Determining; p is the equivalent load applied to the representative cell and phi is the cell angle.
9. An analysis device for nonlinear constitutive relation of negative poisson's ratio structure, comprising:
at least one processor;
at least one memory for storing at least one program;
the at least one program, when executed by the at least one processor, causes the at least one processor to implement the method of analyzing a negative poisson's ratio structure nonlinear constitutive relationship of any one of claims 1-7.
Priority Applications (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010014731.7A CN111191378B (en) | 2020-01-07 | 2020-01-07 | Nonlinear constitutive relation analysis method, system and device of negative poisson ratio structure |
| PCT/CN2020/120393 WO2021139287A1 (en) | 2020-01-07 | 2020-10-12 | Method, system and apparatus for analyzing nonlinear constitutive relationship of negative poisson's ratio structure |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010014731.7A CN111191378B (en) | 2020-01-07 | 2020-01-07 | Nonlinear constitutive relation analysis method, system and device of negative poisson ratio structure |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111191378A CN111191378A (en) | 2020-05-22 |
| CN111191378B true CN111191378B (en) | 2023-10-31 |
Family
ID=70710694
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010014731.7A Active CN111191378B (en) | 2020-01-07 | 2020-01-07 | Nonlinear constitutive relation analysis method, system and device of negative poisson ratio structure |
Country Status (2)
| Country | Link |
|---|---|
| CN (1) | CN111191378B (en) |
| WO (1) | WO2021139287A1 (en) |
Families Citing this family (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111191378B (en) * | 2020-01-07 | 2023-10-31 | 广州大学 | Nonlinear constitutive relation analysis method, system and device of negative poisson ratio structure |
| CN112768006B (en) * | 2020-12-24 | 2023-04-07 | 广州大学 | Method, medium, and apparatus for establishing a star-honeycomb constitutive relation |
| CN112685906A (en) * | 2021-01-05 | 2021-04-20 | 广州大学 | Method, system, device and medium for analyzing accordion cellular structure constitutive relation |
| EP4397885A1 (en) * | 2021-08-30 | 2024-07-10 | Nature Architects Inc. | Vibration isolation structure |
| JP7049024B1 (en) | 2021-08-30 | 2022-04-06 | ＮａｔｕｒｅＡｒｃｈｉｔｅｃｔｓ株式会社 | Anti-vibration structure |
| CN114888949B (en) * | 2022-03-04 | 2024-01-16 | 山东大学 | Bidirectional negative poisson ratio structure |
| CN114694775A (en) * | 2022-03-16 | 2022-07-01 | 广州大学 | Method for establishing non-linear structural relationship of honeycomb structure of accordion with zero Poisson ratio |
| CN115985419B (en) * | 2022-12-11 | 2024-06-11 | 西南交通大学 | Design method of sandwich beam honeycomb core layer structure with gradient Poisson ratio distribution characteristic |
| CN117601508B (en) * | 2024-01-18 | 2024-04-19 | 嘉兴雅港复合材料有限公司 | Flexible aramid fiber honeycomb core suitable for complex curved surface and manufacturing method thereof |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7308387B1 (en) * | 2003-09-23 | 2007-12-11 | Livermore Software Technology Corp. | Method and system for numerically simulating foam-like material in finite element analysis |
| CN102529583A (en) * | 2010-12-10 | 2012-07-04 | 马正东 | Ultralightweight runflat tires based upon negative poisson ratio (npr) auxetic structures |
| CN106570255A (en) * | 2016-10-27 | 2017-04-19 | 南京航空航天大学 | Optimization method of negative Poisson ratio energy absorption structure based on pedestrian protection |
| CN108595728A (en) * | 2018-01-05 | 2018-09-28 | 东华大学 | A kind of laying Equivalent finite element model construction method of cellular material |
| CN110008512A (en) * | 2019-03-04 | 2019-07-12 | 三峡大学 | A kind of negative poisson's ratio lattice structure Topology Optimization Method considering bearer properties |
Family Cites Families (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7165463B2 (en) * | 2003-10-14 | 2007-01-23 | Northwestern University | Determination of young's modulus and poisson's ratio of coatings from indentation data |
| US8609220B2 (en) * | 2010-04-08 | 2013-12-17 | Compagnie Generale Des Etablissements Michelin | Shear compliant hexagonal meso-structures having high shear strength and high shear strain |
| CN103559361B (en) * | 2013-11-13 | 2016-03-16 | 齐齐哈尔轨道交通装备有限责任公司 | A kind of optimization method of component strength and stress analysis method thereof |
| WO2019062346A1 (en) * | 2017-09-27 | 2019-04-04 | The Hong Kong University Of Science And Technology | Method and apparatus for modeling and designing multi-dimensional cellular structures for additive manufacturing |
| CN111191378B (en) * | 2020-01-07 | 2023-10-31 | 广州大学 | Nonlinear constitutive relation analysis method, system and device of negative poisson ratio structure |
-
2020
- 2020-01-07 CN CN202010014731.7A patent/CN111191378B/en active Active
- 2020-10-12 WO PCT/CN2020/120393 patent/WO2021139287A1/en active Application Filing
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7308387B1 (en) * | 2003-09-23 | 2007-12-11 | Livermore Software Technology Corp. | Method and system for numerically simulating foam-like material in finite element analysis |
| CN102529583A (en) * | 2010-12-10 | 2012-07-04 | 马正东 | Ultralightweight runflat tires based upon negative poisson ratio (npr) auxetic structures |
| CN106570255A (en) * | 2016-10-27 | 2017-04-19 | 南京航空航天大学 | Optimization method of negative Poisson ratio energy absorption structure based on pedestrian protection |
| CN108595728A (en) * | 2018-01-05 | 2018-09-28 | 东华大学 | A kind of laying Equivalent finite element model construction method of cellular material |
| CN110008512A (en) * | 2019-03-04 | 2019-07-12 | 三峡大学 | A kind of negative poisson's ratio lattice structure Topology Optimization Method considering bearer properties |
Non-Patent Citations (3)
| Title |
|---|
| 刘祚秋等.蜂窝材料的非线性等效弹性参数研究.《专题研讨会报告—近空间飞行器材料与结构的力学问题》.2009,第370页. * |
| 祝涛等.蜂窝芯层非线性等效弹性参数.《上海航天》.2008,(第4期),第15-18页. * |
| 鲁超等.负泊松比蜂窝芯非线性等效弹性模量研究.《中国机械工程》.2014,第25卷(第11期),第1540-1544页. * |
Also Published As
| Publication number | Publication date |
|---|---|
| WO2021139287A1 (en) | 2021-07-15 |
| CN111191378A (en) | 2020-05-22 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111191378B (en) | Nonlinear constitutive relation analysis method, system and device of negative poisson ratio structure | |
| Bai et al. | Improved mechanical properties and energy absorption of Ti6Al4V laser powder bed fusion lattice structures using curving lattice struts | |
| Yang et al. | A stable node-based smoothed finite element method for metal forming analysis | |
| CN108038318B (en) | Calculation algorithm for initial rigidity and plastic failure strength of variable cross-section metal lattice structure | |
| JP2016224912A (en) | Opening reinforcement method for axial pressure reinforcement rib cylindrical shell | |
| CN111881531B (en) | Elastic parameter calculation and dimensionless design method for four-side concave pyramid lattice structure | |
| CN110837690A (en) | Method, medium, and apparatus for establishing non-linear constitutive relation of cellular structure | |
| CN110516293B (en) | Finite element calculation method for ultimate bearing capacity under bending, shearing and twisting combined action of midship structure | |
| Keralavarma et al. | An approximate yield criterion for anisotropic porous media | |
| Chen et al. | Multiscale modelling of functionally graded porous beams: Buckling and vibration analyses | |
| Tang et al. | Lattice-skin structures design with orientation optimization | |
| CN114636360A (en) | Five-die impact stealth composite lattice annular structure and parameter optimization method thereof | |
| CN113326582B (en) | Variable density lattice structure based on stress distribution and design method thereof | |
| Yuan et al. | Form finding for 3d printed pedestrian bridges | |
| Park et al. | Multidisciplinary design optimization of a structurally nonlinear aircraft wing via parametric modeling | |
| Zhang et al. | A level set method for reliability-based topology optimization of compliant mechanisms | |
| CN111881629A (en) | Pneumatic heat-structure heat conduction coupling nonlinear reduced order model method | |
| Liu et al. | Design of Additively Manufactured Functionally Graded Cellular Structures | |
| CN110688784A (en) | Finite element analysis method for stress performance of high-strength double-angle-steel combined section component | |
| CN115859715A (en) | Method for calculating equivalent performance of periodic porous structure material | |
| CN113139313B (en) | Equivalent lightweight structure analysis method based on finite element theory | |
| Anagnostou et al. | Optimized tooling design algorithm for sheet metal forming over reconfigurable compliant tooling | |
| Elie-dit-Cosaque et al. | Analysis and design of hydroformed thin-walled tubes using enhanced one-step method | |
| Zhang et al. | Study on Multi-step Forming Paths for Double Curved Parts of 1561 Aluminium Alloy | |
| Hsu et al. | Mesh deformation based on fully stressed design: the method and 2‐D examples |
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 |