CN110516317B - Nested honeycomb-like sandwich structure - Google Patents

Nested honeycomb-like sandwich structure Download PDF

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CN110516317B
CN110516317B CN201910718654.0A CN201910718654A CN110516317B CN 110516317 B CN110516317 B CN 110516317B CN 201910718654 A CN201910718654 A CN 201910718654A CN 110516317 B CN110516317 B CN 110516317B
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sandwich
honeycomb
equivalent
nested
cell
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CN110516317A (en
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李响
王艳苗
彭琦
徐兴兴
李锐
张友锋
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China Three Gorges University CTGU
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    • YGENERAL 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
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02TCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

In order to strengthen the transverse bearing capacity of the traditional square, hexagonal and honeycomb-like structures, the invention provides a nested honeycomb-like sandwich structure. The minimum unit of the structure is to construct square protection walls on the outer layer of the octagonal cell structure to form a nested honeycomb-like structure. Under the condition of equal density, the structure not only enables the sandwich structure to be lighter in weight and attractive in shape, but also can enhance the lateral compressive resistance, prevent the longitudinal structure from collapsing and improve the stability.

Description

Nested honeycomb-like sandwich structure
Technical Field
The invention relates to a sandwich structure, in particular to a nested honeycomb sandwich structure.
Background
The honeycomb sandwich structure is widely applied to the fields of house construction, aerospace, automobiles, ships and the like due to the advantages of light weight, high strength, good stability and the like. To meet different requirements in different fields, the multifunctional honeycomb sandwich structure is a development trend of the current society.
Disclosure of Invention
The invention aims to solve the technical problem of providing a nested honeycomb-like sandwich structure, breaks through the configuration mode of the traditional square-hexagonal honeycomb-like sandwich structure, and provides a honeycomb-like sandwich structure formed by nesting square-octagons, mainly aiming at fully utilizing the characteristics of the square-octagons, reducing crushing deformation in practical application and enhancing structural stability.
In order to solve the problems, the invention adopts the technical scheme that: a nested honeycomb-like sandwich structure, the smallest unit of the cross section of the structure is to construct square protection walls on the outer layer of an octagonal cell structure.
The octagonal cell structure adopts an octagonal cell structure with equal wall thickness; the square protection wall adopts a quadrilateral structure with equal wall thickness on opposite sides.
A further development consists of a combination of square and octagon sides with diagonal as long as the sides.
The invention breaks through the configuration mode of the traditional square, hexagonal and honeycomb-like sandwich structure, and provides a honeycomb-like sandwich structure formed by nesting square and octagons, which is mainly used for fully utilizing the characteristics of the square and octagons, reducing the crushing deformation in practical application and enhancing the structural stability.
Drawings
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
FIGS. 1 (a), (b) and (c) are schematic cross-sectional views of the overall structural assembly of the present invention.
Fig. 2 (a) and (b) are mechanical equivalent models of the structure of the present invention.
Fig. 3 (a), (b) and (c) are schematic illustrations of structural decomposition of the present invention.
Fig. 4 (a) and (b) are schematic diagrams of unidirectional stretching stress structures in x and y directions of a minimum unit of the invention.
Fig. 5 (a) and (b) are schematic cell structures according to the present invention.
Fig. 6 (a) and (b) are schematic views of stress structures of the minimum unit of the present invention when subjected to a plane shear load.
Fig. 7 is a schematic diagram of a nested honeycomb sandwich panel.
Detailed Description
As in fig. 1, a nested honeycomb-like sandwich structure is formed by a combination of right-angled triangles and half-octagon side lengths as well as a combined side length to form a simple body of the cross section of the structure.
A further development consists of a combination of square and octagon sides with diagonal as long as the sides. The minimum unit is to construct square protection walls on the outer layer of the octagonal cell structure.
The following checks are made with respect to the above-described structure to further illustrate the advantages of the structure of the present invention.
From the two angles of the micro-structure and the macro-structure, the mechanical properties of the nested honeycomb-like sandwich structure are comprehensively considered, and a model with the same mechanical properties as the original sandwich structure is established, namely the nested sandwich structure mechanical equivalent model. An equivalent model of the present invention is shown in fig. 2. The equivalent model is more convenient for the research of microscopic and macroscopic properties of the nested honeycomb-like sandwich structure.
The elastic constant derivation of the nested honeycomb-like sandwich structure mechanical equivalent model is firstly carried out before the model is applied, the defect that the Gibson classical cell theoretical formula cannot be directly applied to engineering problems is overcome on the basis of the existing research theory, the telescopic deformation of cell wall plates of the honeycomb-like sandwich structure is considered, and the mechanical equivalent model of the nested honeycomb-like sandwich structure is analyzed and solved by using the classical beam bending theory, hooke's law and an energy method-based equivalent elastic constant calculation method. In the invention, a structural unit formed by nesting each square-octagon of the honeycomb sandwich layer is defined as a cell unit body, and is called a cell for short. Fig. 5 is a cell to which the present invention relates, i.e., a minimum unit of the present invention.
As shown in FIG. 3, a represents the side length (mm) of the octagon, l represents the height (mm) of the sandwich cell wall plate, t represents the thickness (mm) of the octagon cell, t1 and t2 represent the thickness (mm) of the different cell walls of the quadrilateral, H 1 Representing the initial length of the base body in the x-direction, m, H 2 The initial length of the base body along the y direction is represented, and m and θ represent the included angle (°) between the octagonal side length and the vertical direction.
The invention adopts Gibson to solve the thought of sandwich mechanical parameters to simplify the cell model into a unidirectional stress state (namely, stress which is considered independently from the x direction or the y direction, as shown in figure 4, mechanical equivalent model derivation is carried out on the x direction or the y direction of the nested honeycomb sandwich structure by using classical beam bending theory, hooke's law and an equivalent elastic constant calculation method based on an energy method respectively to derive the mechanical parameters of each state, namely, the nested honeycomb sandwich structure is equivalent to the equivalent elastic constant of a homogeneous solid body).
Deriving the mechanical parameters of the nested honeycomb sandwich structure, namely the equivalent elastic constant, according to the beam bending theory and Hooke's law:
deriving equivalent elastic constant in x-direction
According to the balance condition of the moment, the method comprises the following steps:
∑M A =0 (01)
H 1 =2a sinθ+t 2 (05)
H 2 =2acosθ+a+t 1 =(2cosθ+1)a+t 1 (06)
symbol description:
m-cell node bending moment, N.m;
P x -a sandwich cell node external force, N;
b-AC cell wall actual length, m;
A x -the cross-sectional area of the sandwich cell in the x-direction under the influence of an external force, m 2
l-height of sandwich cell panel, m;
H 1 -an initial length of the basic body in x-direction, m;
H 2 -an initial length of the basic body in the y-direction, m;
according to the bending theory of the material mechanical beam, the deflection of the wallboard AC is obtained as follows:
wherein the method comprises the steps ofFor moment of inertia, take in ω 1 The method can obtain:
at external force P x The stretching amounts of the cell wall plates AC and BC are respectively as follows:
wherein the method comprises the steps ofAnd->Is AC and BC under external force P x Line strain under action, +.>Andis the positive stress on the AC and BC cell walls.
According to Hooke's law, the equivalent strain epsilon of the nested honeycomb-like sandwich structure in the x direction cx The method comprises the following steps:
meanwhile, the equivalent strain epsilon of the nested honeycomb-like sandwich structure in the y direction can be obtained Cy The method comprises the following steps:
according to the definition of the Poisson's ratio, the equivalent Poisson's ratio V of the nested honeycomb-like sandwich structure in the x direction can be obtained cx The method comprises the following steps:
according to the definition of the elastic modulus, the equivalent elastic modulus E of the nested honeycomb-like sandwich structure in the x direction can be obtained cx The method comprises the following steps:
equivalent elastic constant derivation of nested honeycomb-like sandwich structure in y direction
According to the balance condition of the moment, the method comprises the following steps:
∑M A =0 (17)
H 1 =2asinθ+t 2 (21)
H 2 =2acosθ+a+t 1 =(2cosθ+1)a+t 1 (22)
symbol description:
m-cell node bending moment, N.m;
P y -a sandwich cell node external force, N;
b-AC cell wall actual length, m;
A y -cross-sectional area of the sandwich cell in y-direction under force, m 2
l-height of sandwich cell panel, m;
H 1 -an initial length of the basic body in x-direction, m;
H 2 -an initial length of the basic body in the y-direction, m;
according to the bending theory of the material mechanical beam, the deflection of the wallboard AC is known as follows:
wherein the method comprises the steps ofFor moment of inertia, take in ω 1 The method can obtain:
according to Hooke's law, under external force P y Under the action, the stretching amounts of the cell wall plates AC and BD are respectively as follows:
wherein the method comprises the steps ofAnd->Is AC and BD under external force P y Line strain under action, +.>Andpositive stress on cell wall AC and BD cross sections.
The equivalent strain epsilon of the nested honeycomb-like sandwich structure in the y direction can be obtained according to Hooke's law cy The method comprises the following steps:
and (3) unfolding:
obtaining the product
Equivalent strain ε in the x-direction can be obtained by the same method cx The method comprises the following steps:
according to the definition of the Poisson's ratio, the equivalent Poisson's ratio V of the nested honeycomb-like sandwich in the y direction can be known cy The method comprises the following steps:
according to the definition of the elastic modulus, the equivalent elastic modulus of the nested honeycomb-like sandwich in the y direction can be known
Deducing mechanical parameters of the nested honeycomb-like sandwich by adopting an equivalent elastic constant calculation method based on an energy method
Derivation of equivalent elastic constant in x-direction
From the moment balance, it is possible to:
P cx =A cx δ cx (35)
H 1 =2asinθ+t 2
H 2 =2acosθ+a+t 1 =(2cosθ+1)a+t 1 (36)
according to the energy method, the deformation energy of the equivalent is:
symbol meaning:
m-cell node bending moment, N.m;
l-height of sandwich cell panel, m;
A cx -the cross-sectional area of the sandwich cell in the x-direction under the influence of an external force, m 2
V-equivalent volume, m 3
E cx -equivalent elastic modulus of the nested honeycomb-like sandwich in x-direction;
H 1 -an initial length of the basic body in x-direction, m;
H 2 -an initial length of the basic body in the y-direction, m;
the actual deformation energy of the nested honeycomb-like sandwich in the x-direction consists of the deformation energy of the AC and BC cell walls:
AC cell walls have both bending strain and axial strain, where the bending strain energy is:
will beThe following is carried into the above formula:
the axial strain energy of the AC cell wall is:
BC cell wall is only subjected to axial force:
bending strain energy of W 1 The axial strain energy is W 2
Wherein the method comprises the steps of
Will beCarry over into the above-mentioned type of obtaining E cx
Equivalent elastic constant derivation of nested honeycomb-like sandwich structure in y direction
From the moment balance, it is possible to: sigma M A =0 (49)
The total deformation energy of the equivalent in the y direction is:
symbol meaning:
m-cell node bending moment, N.m;
l-height of sandwich cell panel, m;
A cy -cross-sectional area of the sandwich cell in y-direction under force, m 2
V-equivalent volume, m 3
E cy -equivalent elastic modulus of the nested honeycomb-like sandwich in y-direction;
H 1 -an initial length of the basic body in x-direction, m;
H 2 -an initial length of the basic body in the y-direction, m;
the actual deformation energy of the nested honeycomb-like sandwich cell in the y-direction consists of the deformation energy of the AC and BD cell walls:
the AC cell wall has both bending strain and axial strain, then the bending strain energy is:
will beThe following is carried into the above formula:
the AC axial strain energy is:
BD cell wall is only axially stressed and therefore only axially strained, the axial strain energy is:
the bending strain energy and the axial strain energy are respectively:
wherein the method comprises the steps of
The total deformation energy can be expressed as u=w 1 +W 2 (58)
From the following componentsCan be obtained
From the following componentsCarry over into the above-mentioned type of obtaining E cy
Third, equivalent shear modulus G of nested honeycomb-like sandwich material cxy Is derived from (a)
According to analysis, the stress state of the calculation model not only needs to meet the stress balance of the mechanical analysis unit of the nested honeycomb, but also needs to meet the balance of each node. In modeling, the following assumptions are introduced:
(1) Assuming A, B, D that the nodes have no relative displacement;
(2) Assume that each node turns through the same angle;
(3) Assuming that the BC rod has no effect on the shear deformation of the AC rod;
(4) Shear deformation is formed by rotation of the AC rod about point a and bending of the AC rod;
the whole structure is used for taking the distance from the point A to obtain M A =0 get
The method is characterized in that the method is obtained by the theorem of equivalent unit shear stress in an equivalent structure:
the distance Sigma M is taken from the A point by the wall plate of the AC rod stress analysis unit A =0
The two ends of the AD cell wall are regarded as simple branches of an AD point, and bending moment exists at the AD point, so that the stress condition of the AD rod obtains a anticlockwise rotation angle generated at the A point
The AB cell wall causes the A point to rotate anticlockwise by assuming that the nodes rotate by the same angle
Assuming that the shear deformation is formed by rotation of the AC pole about point A and bending of the AC pole
Mu can be obtained AC
Wherein the method comprises the steps of
From the formulaEquivalent shear modulus G can be obtained cxy
Fourth, equivalent density calculation of nested honeycomb-like sandwich structure
The volume enclosed by the base body is:
V 1 =6atl+t 2 H 2 l+t 1 H 1 l={6at+t 2 [(2cosθ+1)a+t 1 ]+t 1 [2asinθ+t 2 ]}l (76)
the mass of the basic body is as follows:
m 1 =ρ s V 1 =ρ s {6at+t 2 [(2cosθ+1)a+t 1 ]+t 1 [2asinθ+t 2 ]}l(77)
wherein ρ is s To density of the sandwich material, kg/m 3
The volume of the quadrangle surrounded by the basic body equivalent solid model is as follows:
the mass of the equivalent is:
ρ ce for equivalent density of sandwich material, kg/m 3
According to the principle of mass conservation before and after the equivalent: m is m 1 =m ce The following steps are obtained:
the two methods are combined to derive each equivalent elastic constant expression of the nested honeycomb-like sandwich structure suitable for engineering application, wherein the expression is as follows:
the meaning of each symbol is: e (E) cx And E is cy Is equivalent elastic modulus of honeycomb sandwich in x and y directions, MPa;E s The elastic modulus of the sandwich material is MPa; v (V) cx ,V cy Is the equivalent poisson ratio of the honeycomb sandwich in the x and y directions; g cxy Equivalent shear modulus of the honeycomb sandwich in xy plane, MPa; ρ s To density of the sandwich material, kg/m 3 ;ρ ce For equivalent density of sandwich material, kg/m 3
Considering the convenience of actual processing and manufacturing, taking 0=45°, the equivalent parameters are:
/>
the nested honeycomb sandwich structure has better bearing performance, enhances the lateral pressure resistance, prevents the longitudinal collapse of the structure and improves the stability of the structure.

Claims (1)

1. The nested honeycomb-like sandwich structure has the smallest unit of the cross section of the structure that square protective walls are constructed on the outer layer of the octagonal cell structure;
the octagonal cell structure adopts an octagonal cell structure with equal wall thickness; the square protection wall adopts a quadrilateral structure with equal wall thickness on opposite sides;
the extended structure is composed of a square with diagonal lines and a long combined side length which is the same as the length of the octagonal side length;
the checking calculation method of the nested honeycomb-like sandwich structure comprises the following steps:
firstly, deriving the elastic constant of a mechanical equivalent model of a nested honeycomb-like sandwich structure before applying the model, considering the expansion deformation of cell wall plates of the honeycomb-like sandwich structure, analyzing and solving the mechanical equivalent model of the nested honeycomb-like sandwich structure by using a classical beam bending theory, hooke's law and an equivalent elastic constant calculation method based on an energy method, and defining a structural unit formed by nesting each square-octagon of a honeycomb sandwich layer as a cell unit body, namely a cell for short;
a represents the side length of an octagon, the unit is mm, t represents the thickness of an octagon cell, the unit is mm, and t 1 The wall thickness of a cell in the y direction of a quadrilateral is expressed in mm and t 2 The thickness of a cell wall in the x direction of the quadrangle is expressed in mm, and theta is the included angle between the length of the octagon side which is not coincident with the length of the quadrangle and the length of the quadrangle vertical side, and the unit is degree;
step one, deducing mechanical parameters of the nested honeycomb sandwich structure, namely equivalent elastic constants, according to a beam bending theory and Hooke's law:
according to the definition of the Poisson's ratio, the equivalent Poisson's ratio V of the nested honeycomb-like sandwich structure in the x direction can be obtained cx The method comprises the following steps:
according to the definition of the elastic modulus, the equivalent elastic modulus E of the nested honeycomb-like sandwich structure in the x direction can be obtained cx The method comprises the following steps:
definition according to poisson's ratioThe equivalent Poisson ratio V of the nested honeycomb-like sandwich in the y direction can be known cy The method comprises the following steps:
according to the definition of the elastic modulus, the equivalent elastic modulus E of the nested honeycomb-like sandwich in the y direction can be known cy
Deducing mechanical parameters of the nested honeycomb-like sandwich by adopting an equivalent elastic constant calculation method based on an energy method:
according to the energy method, the equivalent elastic modulus E of the nested honeycomb-like sandwich structure in the x direction can be obtained cx The method comprises the following steps:
according to the energy method, the equivalent elastic modulus E of the nested honeycomb-like sandwich structure in the x direction can be obtained cy The method comprises the following steps:
step three, equivalent shear modulus G of nested honeycomb-like sandwich material cxy Is derived from:
shear modulus G cxy The method comprises the following steps:
step four, calculating equivalent density of the nested honeycomb-like sandwich structure:
the expression of each equivalent elastic constant of the nested honeycomb sandwich structure suitable for engineering application is derived by two methods:
the meaning of each symbol is: e (E) cx And E is cy The equivalent elastic modulus of the honeycomb sandwich in the x and y directions is expressed in MPa; e (E) s The elastic modulus of the sandwich material is expressed as MPa; v (V) cx And V cy Is the equivalent poisson ratio of the honeycomb sandwich in the x and y directions; g cxy Equivalent shear modulus of the honeycomb sandwich in xy plane, the unit is MPa; ρ s Is the density of the sandwich material, and the unit is kg/m 3 ;ρ ce Is the equivalent density of the sandwich material, singlyAt a position of kg/m 3
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