CN109657293B - Equivalent elastic modulus prediction method for orthogonal corrugated sandwich structure - Google Patents
Equivalent elastic modulus prediction method for orthogonal corrugated sandwich structure Download PDFInfo
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Abstract
The invention discloses an equivalent elastic modulus prediction method of an orthogonal corrugated sandwich structure, wherein the orthogonal corrugated sandwich structure consists of an upper panel, a lower panel and a core material, the sandwich structure adopts bidirectional corrugated orthogonal superposition, the equivalent elastic modulus prediction method of the orthogonal corrugated sandwich structure firstly divides the orthogonal corrugated sandwich structure into a plurality of representative cells with the same shape, then each cell is equivalent to a homogeneous material, and finally the equivalent elastic modulus of the representative cell is obtained. The method for predicting the equivalent elastic modulus of the cross-corrugated sandwich structure can well predict the equivalent elastic modulus of the structure, and has the advantages of high efficiency, accurate calculation, good designability and the like.
Description
Technical Field
The invention relates to a mechanical calculation method of an orthogonal corrugated sandwich structure, in particular to an equivalent elastic modulus prediction method of the orthogonal corrugated sandwich structure.
Background
The corrugated sandwich structure generally consists of three parts, wherein the outermost side is provided with an upper panel and a lower panel which mainly bear normal stress; the intermediate layer is a core material, which mainly carries shear stresses. The core material and the panel can be integrally formed or can be adhered together by welding, gluing and other connecting means. The corrugated sandwich structure fully utilizes the advantages of high specific strength and specific modulus of the composite structure, improves the section inertia moment by means of the core material, thereby achieving ideal structural mechanical property, has more and more extensive application fields, and relates to national defense, military, vehicles, ships, submarines, buildings, bridges and the like. The currently reported corrugated structure is generally in a one-way corrugated form in the plane, the mechanical property in the plane has certain directionality, the mechanical property in one direction is very weak, and the significance of providing a novel corrugated structure with higher strength in two directions is great.
The core material surface of the bidirectional orthogonal corrugated structure is in an orthogonal corrugated form, and has good mechanical property, but the orthogonal corrugated structure is complex, so that the equivalent elastic modulus of the structure is difficult to obtain.
Disclosure of Invention
In view of this, the invention provides a method for predicting the equivalent elastic modulus of an orthogonal corrugated sandwich structure, which can well predict the equivalent elastic modulus of the structure and has the advantages of high efficiency, accurate calculation, good designability and the like.
An equivalent elastic modulus prediction method of an orthogonal corrugated sandwich structure is disclosed, wherein the orthogonal corrugated sandwich structure consists of an upper panel, a lower panel and a core material, concave pits are distributed on the front surface and the back surface of the core material according to a row-column rule, the orthogonal cross section of each concave pit is trapezoidal, the concave pits on the front surface form wave troughs in the same row or column, and the adjacent concave pits on the back surface form wave crests, so that regular sine wave distribution is formed; the upper panel and the lower panel are respectively fixed on the upper surface and the lower surface of the core material; the prediction method comprises the following implementation steps:
the method comprises the following steps: dividing the orthogonal corrugated sandwich structure into a plurality of representative cells with the same shape;
step two: each cell is equivalent to a homogeneous material;
step three: the equivalent elastic modulus of a representative cell was obtained by hypothesis and analysis.
Further, the equivalent elastic modulus includes equivalent elastic moduli in three directions.
Further, the calculation formula of the equivalent elastic modulus in the three directions is as follows:
a coordinate system is established by taking the middle point of the bottom of the front side of the orthogonal corrugated structure as the origin, taking the vertical direction as the z axis and the vertical direction of the upper panel and the lower panel as the z axis, and respectively taking the completely same directions of the other two structures as the x axis and the y axis,
wherein E is z Is the equivalent modulus of elasticity in the vertical direction, E y And E x Respectively, equivalent elastic moduli in two other directions of the same structure, E 0 In order to manufacture the elastic modulus of the structural parent material, c is the length of the horizontal corrugation of the orthogonal corrugation structure, l is the length of the inclined corrugation of the orthogonal corrugation structure, theta is the included angle between the inclined corrugation of the orthogonal corrugation structure and the vertical surface, delta is the thickness of the orthogonal corrugation structure, t is the thickness of the upper panel, and w is the thickness of the lower panel.
Has the advantages that:
the invention provides a simple method for predicting the equivalent elastic modulus of an orthogonal corrugated sandwich structure in three directions, and the elastic modulus prediction method can be well used for predicting the performance of the orthogonal corrugated sandwich structure, solves the problems that the existing method can only be obtained through experiments and finite elements, is complex and tedious in process, needs a large amount of manpower, material resources and financial resources and is difficult to use in engineering, increases the designability of the novel structure and facilitates engineering application.
Drawings
FIG. 1 is an exploded view of an orthogonal corrugated sandwich structure according to the present invention
FIG. 2 is an oblique view of an orthogonal corrugated sandwich structure of the present invention
FIG. 3 is a schematic view of an orthogonal corrugated sandwich structure of the present invention with the lower panel removed
FIG. 4 is a flow chart of the steps of the present invention
FIG. 5 is a schematic view of an orthogonal corrugated sandwich cell according to the present invention
Wherein, 1-upper panel, 2-core material and 3-lower panel.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
As shown in the attached drawings 1-3, the orthogonal corrugated sandwich structure of the invention is composed of an upper panel 1, a lower panel 3 and a core material 2, wherein the front surface and the back surface of the core material 2 are respectively provided with pits distributed according to the row-column rule, the orthogonal cross section of each pit is trapezoidal, the pits on the front surface form wave troughs in the same row or column, and the adjacent pits on the back surface form wave crests, thereby forming regular sine wave distribution; the upper panel 1 and the lower panel 3 are respectively fixed on the upper surface and the lower surface of the core material 2;
the invention relates to an equivalent elastic modulus prediction method for an orthogonal corrugated sandwich structure, which comprises the following implementation steps as shown in figure 4:
the method comprises the following steps: dividing the orthogonal corrugated sandwich structure into a plurality of representative cells with the same shape, wherein the cell structure is shown in FIG. 5;
step two: each cell is equivalent to a homogeneous material;
step three: the equivalent elastic modulus of a representative cell is obtained by hypothesis and analysis, and includes equivalent elastic moduli in three directions.
The calculation formula of the equivalent elastic modulus in the three directions is as follows:
a coordinate system is established by taking the middle point of the bottom of the front side of the orthogonal corrugated structure as the origin, taking the vertical direction as the z axis and the vertical direction of the upper panel and the lower panel as the z axis, and respectively taking the completely same directions of the other two structures as the x axis and the y axis,
wherein E is z Is the equivalent modulus of elasticity in the vertical direction, E y And E x Respectively equivalent elastic moduli in two other directions of the same structure, E 0 In order to manufacture the elastic modulus of the structural parent material, c is the length of the horizontal corrugation of the orthogonal corrugation structure, l is the length of the inclined corrugation of the orthogonal corrugation structure, theta is the included angle between the inclined corrugation of the orthogonal corrugation structure and the vertical surface, delta is the thickness of the orthogonal corrugation structure, t is the thickness of the upper panel, and w is the thickness of the lower panel.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (1)
1. The method for predicting the equivalent elastic modulus of the orthogonal corrugated sandwich structure is characterized in that the front surface and the back surface of the core material are provided with pits distributed according to a row-column rule, the orthogonal cross section of each pit is trapezoidal, the pits on the front surface form wave troughs in the same row or column, and the adjacent pits on the back surface form wave crests, so that regular sine wave distribution is formed; the upper panel and the lower panel are respectively fixed on the upper surface and the lower surface of the core material; the prediction method comprises the following implementation steps:
the method comprises the following steps: dividing the orthogonal corrugated sandwich structure into a plurality of representative cells with the same shape;
step two: each cell is equivalent to a homogeneous material;
step three: obtaining the equivalent elastic modulus of a representative cell element through hypothesis and analysis;
the equivalent elastic modulus comprises equivalent elastic moduli in three directions;
the calculation formula of the equivalent elastic modulus in the three directions is as follows:
a coordinate system is established by taking the middle point of the bottom of the front side of the orthogonal corrugated structure as an origin, taking the vertical direction as the z axis along the direction vertical to the upper panel and the lower panel, and respectively taking the directions completely same as the other two structures as the x axis and the y axis,
wherein E is z Is the equivalent modulus of elasticity in the vertical direction, E y And E x Respectively equivalent elastic moduli in two other directions of the same structure, E 0 In order to manufacture the elastic modulus of the structural parent material, c is the length of the horizontal corrugation of the orthogonal corrugation structure, l is the length of the inclined corrugation of the orthogonal corrugation structure, theta is the included angle between the inclined corrugation of the orthogonal corrugation structure and the vertical surface, delta is the thickness of the orthogonal corrugation structure, t is the thickness of the upper panel, and w is the thickness of the lower panel.
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Citations (3)
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| CN104163297A (en) * | 2014-07-30 | 2014-11-26 | 王勤 | Container bottom plate of double-layer orthogonal corrugated sandwich structure |
| CN106650141A (en) * | 2016-12-29 | 2017-05-10 | 北京航空航天大学 | Uncertainty analysis method for predicting performance of periodic material |
| CN108345742A (en) * | 2018-02-08 | 2018-07-31 | 北京航空航天大学 | A kind of vibration equivalence modeling method suitable for ripple sandwich structure |
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2018
- 2018-11-29 CN CN201811444469.9A patent/CN109657293B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104163297A (en) * | 2014-07-30 | 2014-11-26 | 王勤 | Container bottom plate of double-layer orthogonal corrugated sandwich structure |
| CN106650141A (en) * | 2016-12-29 | 2017-05-10 | 北京航空航天大学 | Uncertainty analysis method for predicting performance of periodic material |
| CN108345742A (en) * | 2018-02-08 | 2018-07-31 | 北京航空航天大学 | A kind of vibration equivalence modeling method suitable for ripple sandwich structure |
Non-Patent Citations (3)
| Title |
|---|
| An equivalent model for trapezoidal corrugated cores based on homogenization method;H. Mohammadi 等;《H. Mohammadi》;20151231;全文 * |
| Three-dimensional elasticity solution for sandwich panels with corrugated cores by using energy method;M. Shaban 等;《M. Shaban》;20171231;全文 * |
| 复合材料波纹夹层圆柱壳设计及轴压性能;冯丽娜 等;《符合材料学报》;20160229;全文 * |
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