CN113722831A - Beam bending energy absorption analysis method for multi-cell thin wall of Z-direction rib plate fixedly supported at two ends - Google Patents

Beam bending energy absorption analysis method for multi-cell thin wall of Z-direction rib plate fixedly supported at two ends Download PDF

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CN113722831A
CN113722831A CN202111037185.XA CN202111037185A CN113722831A CN 113722831 A CN113722831 A CN 113722831A CN 202111037185 A CN202111037185 A CN 202111037185A CN 113722831 A CN113722831 A CN 113722831A
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张君媛
谢坚
郑丹枫
陆炳全
张天麒
余雪婷
车文传
邸春赫
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Abstract

The invention discloses a beam bending energy-absorbing analysis method for a multi-cell thin wall of a Z-direction rib plate fixedly supported at two ends, which comprises the following steps: step one, loading is carried out on the middle of a multi-cell thin-wall beam of a Z-direction rib plate fixedly supported at two ends by a hammer head, and when the section of the multi-cell thin-wall beam enters a complete plastic state under the combined action of bending moment and axial force, the yield criterion of two stages is obtained; simplifying the deformation and stress of the multi-cell thin-wall beam to obtain the relationship between the axial force at the plastic hinge and the displacement of the section centroid axis; and step three, obtaining the relation between the external force which can be borne by the thin-wall beam and the displacement of the section centroid axis according to the yield criterion, the balance equation and the relation between the axial force at the plastic hinge and the displacement. The method has the characteristics of improving the accuracy of calculating the bending energy absorption characteristic of the multi-cell thin-wall beam, shortening the development period and reducing the design cost.

Description

Beam bending energy absorption analysis method for multi-cell thin wall of Z-direction rib plate fixedly supported at two ends
Technical Field
The invention relates to the technical field of automobile passive safety research, in particular to a beam bending energy-absorbing analysis method for a multi-cell thin wall of a Z-direction rib plate fixedly supported at two ends.
Background
The thin-wall beam structure is widely applied to the fields of automobiles, ships, aviation, aerospace and the like as a common bearing and energy absorbing part. The thin-walled beam structure on the vehicle body is often subjected to the action of transverse load to generate bending deformation in the collision process, such as a B column in a side collision accident, a bumper beam in a front column collision working condition and the like, and the energy absorption effect of the thin-walled beam structure in the bending deformation is widely concerned by researchers.
At present, the main research method for the anti-collision design of the thin-wall beam is to combine experiments and finite element analysis, carry out simulation calculation and structure optimization design on the thin-wall beam structure by utilizing large-deformation nonlinear finite element software, and verify the result of the design optimization by utilizing the experiments.
With the increasing safety awareness and the increasing safety regulations, how to improve the crashworthiness of automobiles becomes an important research topic. The multi-cell thin-wall beam has a more excellent energy absorption effect than a rectangular thin-wall beam, and is used for typical thin-wall beam safety members such as a bumper beam and a B column in a vehicle body structure to improve the collision resistance of the vehicle body.
Currently, theoretical research on an energy absorption mechanism of a multi-cell thin-wall beam during bending deformation mainly focuses on an energy absorption effect of the multi-cell thin-wall beam under a pure bending working condition or a three-point bending working condition with two ends simply supported. Since both ends of a member such as a B-pillar or a bumper beam on a vehicle body are connected to other members on the vehicle body, the member is affected by an axial force during bending deformation. Under the working condition that the axial force and the bending moment jointly act on the two ends of the multi-cell thin-wall beam for fixedly supporting, the bending energy absorption behavior of the multi-cell thin-wall beam is more complex. Meanwhile, finite element calculation and experimental research show that under the working condition of fixed support at two ends, the multi-cell thin-wall beam with the rib plate along the Z direction can absorb more energy than the multi-cell thin-wall beam with the rib plate along the Y direction. Therefore, the energy absorption of the multi-cell thin-wall beam with the rib plate along the Z direction when the beam is transversely bent and deformed under the condition of being fixedly supported at two ends can be studied.
Disclosure of Invention
The invention aims to design and develop a beam bending energy-absorbing analysis method for a multi-cell thin wall of a ribbed plate in a Z-direction clamped at two ends, establish an energy-absorbing model when the multi-cell thin wall beam of the ribbed plate along the Z direction generates transverse bending deformation under the combined action of bending moment and axial force, and accurately predict the beam bending energy-absorbing characteristic of the multi-cell thin wall of the ribbed plate in the Z-direction clamped at two ends by combining various parameters of the thin wall beam.
The technical scheme provided by the invention is as follows:
a beam bending energy-absorbing analysis method for a multi-cell thin wall of a Z-direction rib plate fixedly supported at two ends comprises the following steps:
step one, loading is carried out by using a hammer head in the middle of a multi-cell thin-wall beam of a Z-direction rib plate fixedly supported at two ends, and when the section of the multi-cell thin-wall beam enters a complete plastic state under the combined action of bending moment and axial force, the yield criterion of the section of the multi-cell thin-wall beam is obtained:
when in use
Figure BDA0003247688930000021
And then, the yield criterion of the section of the multi-cell thin-wall beam meets the following conditions:
Figure BDA0003247688930000022
when in use
Figure BDA0003247688930000023
And then, the yield criterion of the section of the multi-cell thin-wall beam meets the following conditions:
Figure BDA0003247688930000024
wherein a represents a first coefficient, H represents a height of a cross section,
Figure BDA0003247688930000025
denotes the distance between the neutral axis of the cross section and the centroid axis of the cross section, t denotes the wall thickness of the multi-cell thin-walled beam, α1Expressing the second coefficient, M the bending moment in cross section, M0The plastic ultimate bending moment of the cross section is shown, N represents the axial force of the cross section, N0Plastic ultimate axial force, alpha, representing a cross section2Represents a third coefficient;
step two, simplifying the deformation and stress of the multi-cell thin-wall beam, and obtaining the relationship between the axial force at the plastic hinge and the displacement of the section centroid axis:
Figure BDA0003247688930000031
in the formula, w represents the displacement of the centroid axis of the section, B represents the width of the section, and n represents the number of rib plates in the Z direction in the thin-wall beam;
and step three, obtaining the relation between the external force bearable by the thin-wall beam and the displacement of the hammer head according to the yield criterion, the balance equation and the relation between the axial force at the plastic hinge and the displacement of the section centroid axis:
Figure BDA0003247688930000032
wherein P represents the force of the hammer head, L represents the length of the thin-walled beam, wpDenotes the hammer head displacement, and k denotes a fourth coefficient.
Preferably, the plastic limit bending moment of the cross section satisfies:
Figure BDA0003247688930000033
in the formula, σ0Indicating the flow stress of the thin wall beam.
Preferably, the plastic limit axial force of the cross section satisfies:
N0＝σ0t[2B+(2+n)(H-2t)]；
in the formula, N0The plastic limit axial force of the cross section is shown.
Preferably, the flow stress of the thin-walled beam satisfies:
Figure BDA0003247688930000034
in the formula, σyDenotes the yield stress, σ, of the thin-walled beamuIndicating the ultimate stress of the thin wall beam.
Preferably, the section bending moment satisfies:
Figure BDA0003247688930000041
preferably, the section axial force satisfies:
N＝(2+n)aHtσ0。
preferably, the generalized strain rate is obtained according to the yield criterion and the orthogonality rule:
when in use
Figure BDA0003247688930000042
And, the generalized strain rate satisfies:
Figure BDA0003247688930000043
when in use
Figure BDA0003247688930000044
And, the generalized strain rate satisfies:
Figure BDA0003247688930000045
in the formula (I), the compound is shown in the specification,
Figure BDA0003247688930000046
which is indicative of the strain rate of the film,
Figure BDA0003247688930000047
is the rate of change of curvature;
according to the speed field at the plastic hinge in the deformation process of the thin-wall beam, obtaining the relationship between the generalized strain rate and the displacement:
Figure BDA0003247688930000048
preferably, the balance equation is:
Figure BDA0003247688930000049
preferably, the relationship between the displacement of the section centroid axis and the hammer head displacement satisfies:
w＝kwp。
preferably, the relationship between the fourth coefficient and the number of the rib plates in the Z direction in the thin-walled beam satisfies:
Figure BDA00032476889300000410
the invention has the following beneficial effects:
(1) the invention discloses a beam bending energy-absorbing analysis method for a multi-cell thin wall of a Z-direction ribbed plate fixedly supported at two ends, which establishes an energy absorption model when the multi-cell thin wall beam of the ribbed plate along the Z direction is subjected to transverse bending deformation under the combined action of bending moment and axial force, and calculates the yield criterion of the cross section when the cross section enters a complete plastic state under the combined action of the bending moment and the axial force.
(2) The invention discloses a beam bending energy-absorbing analysis method for a multi-cell thin-wall ribbed plate with two fixedly supported Z-direction ribs at two ends, which is designed and developed by the invention, deduces a relational expression between external force bearable by the multi-cell thin-wall beam with the ribs along the Z direction and hammer displacement, obtains a mechanical relation between structural parameters (section size and number of the ribs along the Z direction) and bending performance of the multi-cell thin-wall beam with the ribs along the Z direction, and can accurately predict the bending energy-absorbing characteristic of the multi-cell thin-wall beam with the ribs along the Z direction.
(3) The invention designs and develops a beam bending energy-absorbing analysis method with Z-direction ribbed plates supported at two ends and multiple thin walls, and in the concept of vehicle body collision resistance, the bending performance of the multi-cell thin-wall beam with the ribbed plates along the Z direction under the supporting at two ends can be quickly calculated only according to the given cross section size of the thin-wall beam, the number of the ribbed plates along the Z direction and the material characteristics of the thin-wall beam.
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FIG. 1 is a schematic flow diagram of a beam bending energy absorption analysis method for a multi-cell thin wall of a two-end clamped Z-direction rib plate.
Fig. 2 is a structural schematic view of a multi-cell thin-wall beam with the rib plate along the Z direction.
FIG. 3 is a schematic view of the cross-sectional stress distribution of the multi-cell thin-walled beam with two end-clamped Z-direction rib plates in the first stage of the bending process.
FIG. 4 is a schematic view of the cross-sectional stress distribution of the multi-cell thin-walled beam with two end-clamped Z-direction rib plates in the second stage of the bending process.
FIG. 5 is a schematic view of the cross-sectional yield curve of the multi-cell thin-walled beam with two end-clamped Z-direction ribs according to the present invention.
FIG. 6 is a simplified diagram of the deformation and stress of the multi-cell thin-walled beam with two end-supported Z-direction rib plates.
FIG. 7 is a schematic view of a finite element model of a multi-cell thin-walled beam with two end-clamped Z-direction ribs according to the present invention.
FIG. 8 is a schematic diagram showing comparison between theoretical calculation of beam bending energy absorption analysis of multi-cell thin wall with Z-direction rib plates fixedly supported at two ends when the number of the Z-direction rib plates in the thin-wall beam is 1 and load displacement curve results of finite element simulation.
FIG. 9 is a schematic diagram showing the comparison between the theoretical calculation of beam bending energy absorption analysis of multi-cell thin wall with Z-direction rib plates fixedly supported at both ends when the number of the Z-direction rib plates in the thin-wall beam is 2 and the load displacement curve result of finite element simulation.
FIG. 10 is a schematic diagram showing the comparison between the theoretical calculation of beam bending energy absorption analysis of multi-cell thin wall with Z-direction rib plates fixedly supported at both ends when the number of the Z-direction rib plates in the thin-wall beam is 3 and the load displacement curve result of finite element simulation.
FIG. 11 is a schematic diagram showing comparison between theoretical calculation of beam bending energy absorption analysis of multi-cell thin wall with Z-direction rib plates fixedly supported at two ends when the number of the Z-direction rib plates in the thin-wall beam is 4 and load displacement curve results of finite element simulation.
Detailed Description
The present invention is described in further detail below in order to enable those skilled in the art to practice the invention with reference to the description.
As shown in figure 1, the beam bending energy-absorbing analysis method of the multi-cell thin wall of the Z-direction ribbed plate with two fixedly supported ends, provided by the invention, comprises the steps of simplifying a stress-strain curve of a material by utilizing an ideal rigid-plastic model, calculating the flow stress of the thin-wall beam, calculating the plastic limit axial force and the plastic limit bending moment of a multi-cell section according to structural parameters of the section, then dividing the yield criterion of the multi-cell section into two stages for solving according to the distance between the neutral axis of the multi-cell section and the centroid of the section, and on the basis, simplifying the deformation and stress of the thin-wall beam fixedly supported at two ends by central loading, respectively calculating a relational expression of generalized strain rate and displacement and a relational expression of plastic hinge membrane force and hammer head displacement, and finally calculating an expression relational expression between external force bearable by the thin-wall beam and hammer head displacement by combining the yield criterion, the geometric equation and the balance condition of the thin-wall beam. The method is implemented based on a natural fund project (the project approval number is 51775228, the name is the theoretical model research of the collision resistance of the multi-material complex-section thin-wall beam structure of the automobile body). The method specifically comprises the following steps:
as shown in fig. 2, the material of the multi-cell thin-walled beam with the Z-direction rib plates fixedly supported at two ends is mainly a metal material, and an ideal rigid-plastic model is used for simplifying a stress-strain curve of the material to calculate the flow stress of the thin-walled beam, wherein the specific expression formula is as follows:
Figure BDA0003247688930000061
in the formula: sigma0Representing the flow stress, σ, of a thin-walled beamyDenotes the yield stress, σ, of the thin-walled beamuIndicating the ultimate stress of the thin wall beam.
As shown in fig. 3 and 4, the plastic limit axial force of the multi-cell section is calculated by using the structural parameters of the multi-cell section in the section of the multi-cell thin-wall beam with the Z-direction rib plate fixedly supported at the two ends and combining the flow stress of the multi-cell thin-wall beam, and the expression formula is as follows:
N0＝σ0t[2B+(2+n)(H-2t)] (2)
in the formula: n is a radical of0The plastic limit axial force of the section is represented, t represents the wall thickness of the multi-cell thin-wall beam, B represents the width of the section, H represents the height of the section, and n represents the number of rib plates in the Z direction in the thin-wall beam;
similarly, the plastic limit bending moment of the cross section can be calculated, and the expression formula is as follows:
Figure BDA0003247688930000071
in the formula, M0Representing the plastic limit bending moment of the cross section.
When the cross-section is brought into a fully plastic state under the combined action of bending moments and axial forces, as shown in fig. 5, it is assumed that the distance between the neutral axis of the cross-section and the centroid axis of the cross-section is
Figure BDA0003247688930000072
Dividing the yield criterion of the section into two according to whether the neutral axis of the section enters the bottom edge of the sectionRespectively calculating an expression formula of a yield criterion;
the first stage is as follows: when the distance between the neutral axis of the cross-section and the cross-sectional mandrel is
Figure BDA0003247688930000073
The cross-sectional yield criterion when satisfied:
as shown in fig. 3, a first stage section stress distribution is shown, wherein the composite stress is the sum of the bending stress and the axial stress, and the magnitude of the section axial force is 0 when the magnitude of the section bending moment is the plastic limit bending moment of the section, and the yield criterion expression formula of the stage can be calculated as follows:
Figure BDA0003247688930000074
wherein a represents a first coefficient, α1Representing a second coefficient;
when the distance between the neutral axis position of the cross-section and the cross-sectional mandrel is
Figure BDA0003247688930000075
In the process, the expression formula of the section bending moment and the section axial force which can be borne by the section is as follows:
Figure BDA0003247688930000081
N＝(2+n)aHtσ0 (6)
from the equations (2), (3), (4), (5) and (6), the following dimensionless parameters can be derived, and the ratio of the section bending moment to the section plastic limit bending moment and the ratio of the section axial force to the section plastic limit axial force are expressed as follows:
Figure BDA0003247688930000082
Figure BDA0003247688930000083
in the formula: a represents a first coefficient, and
Figure BDA0003247688930000084
the second parameter α can be calculated by eliminating the first parameter a according to the equations (4), (7) and (8)1The expression formula is as follows:
Figure BDA0003247688930000085
the specific yield criterion expression at this stage can be obtained by substituting equation (9) into equation (4).
In the yield criterion, the generalized force and the generalized strain rate are orthogonal, and according to the orthogonality relation, the expression formula of the curvature change rate and the membrane strain rate, which are the generalized strain rates corresponding to the section bending moment and the section axial force, can be obtained as follows:
Figure BDA0003247688930000086
and a second stage: when the distance between the neutral axis of the cross-section and the centroid axis of the cross-section is
Figure BDA0003247688930000087
The cross-sectional yield criterion when satisfied:
as shown in fig. 4, for the section stress distribution in the second stage, when the section enters the plastic axial force state, and the magnitude of the section axial force is the plastic limit axial force of the section, the magnitude of the section bending moment is 0, and the yield criterion expression formula in this stage is as follows:
Figure BDA0003247688930000091
in the formula, alpha2Represents a third coefficient;
when aH is H-2t, the expression formula of the section bending moment and the section axial force is as follows:
Figure BDA0003247688930000092
Figure BDA0003247688930000093
from equations (11), (12) and (13), the third parameter α can be calculated2The expression formula is as follows:
Figure BDA0003247688930000094
similarly, from the orthogonal rule, the expression formula for the curvature change rate and the film strain rate can be calculated as follows:
Figure BDA0003247688930000095
in the bending working condition discussed in the invention, the hammerhead loading point is in the middle position of the thin-wall beam, and in the bending process of the thin-wall beam, plastic deformation mainly occurs at the supporting positions at the two ends of the thin-wall beam and the plastic hinge position in the middle, so that the deformation and stress conditions of the thin-wall beam can be simplified as shown in fig. 6.
According to the speed field at the plastic hinge in the deformation process of the thin-wall beam, the relationship between the generalized strain rate and the displacement can be obtained, and the expression formula is as follows:
Figure BDA0003247688930000096
wherein w represents the displacement of the section centroid axis;
according to the formulas, the relationship between the axial force at the plastic hinge and the displacement of the section centroid axis can be calculated, and the expression formula is as follows:
Figure BDA0003247688930000101
according to the stress condition of one end of the thin-wall beam, a balance equation can be listed, and an expression formula is as follows:
Figure BDA0003247688930000102
F≈N；
thus, the equilibrium equation is obtained as:
Figure BDA0003247688930000103
in the formula, P represents the acting force of the hammer head, and L represents the length of the thin-walled beam.
Considering that the thin-wall beam at the hammer loading position is locally sunken, the displacement (downward) of the section centroid axis is smaller than the hammer displacement (downward), and the relationship between the displacements is as follows:
w＝kwp (19)
in the formula, k represents a fourth coefficient.
Since the fourth coefficient is related to the number of rib plates in the thin-wall beam along the Z direction, the expression formula is as follows:
Figure BDA0003247688930000104
according to the yield criterion, the geometric equation and the balance condition of the thin-wall beam, the relationship between the external force bearable by the thin-wall beam and the hammer head displacement can be calculated, and the expression formula is as follows:
Figure BDA0003247688930000105
examples
In this embodiment, the material used for the multi-cell thin-wall beam with the selected rib plate along the Z direction is aluminum alloy with a designation of Al6063-T5, and the mechanical properties of the material are shown in table 1:
TABLE 1 Al6063-T5 Material mechanical Properties Table
Figure BDA0003247688930000111
The schematic cross-sectional views of the thin-wall beam are shown in fig. 3 and 4, wherein the structural parameters of the multi-cell cross section are as follows: the wall thickness t of the multi-cell thin-wall beam is 2mm, the width B of the cross section is 60mm, the height H of the cross section is 60mm, the length L of the thin-wall beam is 800mm, the diameter of the loading hammer head is 30mm, and the number n of rib plates in the thin-wall beam along the Z direction is 1.
1. According to equation (1), substituting σy＝145MPa，σuCalculating the flow stress sigma of the thin-wall beam under 201MPa0＝171MPa；
2. Substituting the flow stress sigma of the thin-walled beam according to the formulas (2) and (3)0171MPa, the wall thickness t of the multi-cell thin-wall beam is 2mm, the width B of the section is 60mm, the height H of the section is 60mm, the number N of the ribbed plates in the Z direction in the thin-wall beam is 1, and the plastic limit axial force N of the section is calculated098496N, plastic limit bending moment M of cross section0＝2035584N·mm；
3. The plastic limit axial force N of the cross section is substituted according to the expressions (4) (9) and (11) (14)098496N, plastic limit bending moment M of cross section0Respectively calculating the yield criterion of two stages of the multi-cell section as 2035584 N.mm;
4. obtaining a relational expression between the axial force at the plastic hinge and the displacement of the section-shaped mandrel according to the expression (17);
5. substituting the length L of the thin-wall beam into 800mm according to the formula (21), and calculating a relational expression between the external force which can be borne by the thin-wall beam and the displacement of the hammer head;
the same steps are adopted to theoretically calculate the load displacement curve of the thin-wall beam for three groups of multi-cellular thin-wall beams with the number n of the rib plates in the Z direction being 2, 3 and 4 respectively, and meanwhile, as shown in figure 7, commercial finite element software Ls-dyna is utilized to divide the thin-wall beam into 2 multiplied by 2mm by using a Belytschko-Tsay shell unit2Grid of dimensions, 5 integration points in thickness direction, and using a stiffness based hourglassAnd controlling, namely selecting an MAT _123 material model MAT _ MODIFIED _ PIECEWISE _ LINEAR _ PLASTICITY model to simulate the constitutive relation of the aluminum alloy Al6063-T5, and establishing a finite element model of the multi-cell thin-wall beam with the rib plates along the Z direction under the working condition of fixed support at two ends. As shown in fig. 8-11, for the load displacement curve obtained by finite element analysis and theoretical calculation, the maximum error between the theoretical prediction and the simulation model is 4.7% at the plastic deformation stage of the thin-wall beam, and the load displacement curves predicted by the theory are all kept highly consistent with the simulation. The effectiveness of the method for analyzing the bending energy-absorbing characteristic of the multi-cell thin-wall beam with the rib plate along the Z direction under the condition of fixed support at two ends is verified through finite element simulation analysis.
The invention designs and develops a beam bending energy-absorbing analysis method for a multi-cell thin wall with a Z-direction ribbed plate fixedly supported at two ends, establishes an energy absorption model when the multi-cell thin wall beam with the ribbed plate along the Z direction is subjected to transverse bending deformation under the combined action of bending moment and axial force, calculates the yield criterion of the cross section when the cross section enters a complete plastic state under the combined action of the bending moment and the axial force, deduces a relational expression between external force and hammer head displacement which can be borne by the multi-cell thin wall beam with the ribbed plate along the Z direction, obtains a mechanical relation between structural parameters (cross section size and number of ribbed plates along the Z direction) and bending performance of the multi-cell thin wall beam with the ribbed plate along the Z direction, and can quickly calculate the bending performance of the multi-cell thin wall beam with the ribbed plate along the Z direction under the two-end fixing support only according to the given cross section size of the thin wall beam, the number of the ribbed plates along the Z direction and the material characteristics of the thin wall beam in the concept of the collision resistance of a vehicle body, the bending energy absorption characteristic of the multi-cell thin-wall beam with the rib plate along the Z direction can be accurately predicted, compared with finite element simulation calculation and experiments, the forward design of the thin-wall beam structure can be realized, the simulation trial and error and the experiment frequency are greatly reduced, the development period is shortened, and the design and development cost is reduced.
While embodiments of the invention have been described above, it is not limited to the applications set forth in the description and the embodiments, which are fully applicable to various fields of endeavor for which the invention may be embodied with additional modifications as would be readily apparent to those skilled in the art, and the invention is therefore not limited to the details given herein and to the embodiments shown and described without departing from the generic concept as defined by the claims and their equivalents.

Claims (10)

1. A beam bending energy-absorbing analysis method for a multi-cell thin wall of a Z-direction rib plate fixedly supported at two ends is characterized by comprising the following steps:
step one, loading is carried out by using a hammer head in the middle of a multi-cell thin-wall beam of a Z-direction rib plate fixedly supported at two ends, and when the section of the multi-cell thin-wall beam enters a complete plastic state under the combined action of bending moment and axial force, the yield criterion of the section of the multi-cell thin-wall beam is obtained:
when in use
Figure FDA0003247688920000011
And then, the yield criterion of the section of the multi-cell thin-wall beam meets the following conditions:
Figure FDA0003247688920000012
when in use
Figure FDA0003247688920000013
And then, the yield criterion of the section of the multi-cell thin-wall beam meets the following conditions:
Figure FDA0003247688920000014
wherein a represents a first coefficient, H represents a height of a cross section,
Figure FDA0003247688920000015
denotes the distance between the neutral axis of the cross section and the centroid axis of the cross section, t denotes the wall thickness of the multi-cell thin-walled beam, α1Expressing the second coefficient, M the bending moment in cross section, M0The plastic ultimate bending moment of the cross section is shown, N represents the axial force of the cross section, N0Plastic ultimate axial force, alpha, representing a cross section2Represents a third coefficient;
step two, simplifying the deformation and stress of the multi-cell thin-wall beam, and obtaining the relationship between the axial force at the plastic hinge and the displacement of the section centroid axis:
Figure FDA0003247688920000016
in the formula, w represents the displacement of the centroid axis of the section, B represents the width of the section, and n represents the number of rib plates in the Z direction in the thin-wall beam;
and step three, obtaining the relation between the external force bearable by the thin-wall beam and the displacement of the hammer head according to the yield criterion, the balance equation and the relation between the axial force at the plastic hinge and the displacement of the section centroid axis:
Figure FDA0003247688920000021
wherein P represents the force of the hammer head, L represents the length of the thin-walled beam, wpDenotes the hammer head displacement, and k denotes a fourth coefficient.
2. The beam bending energy-absorbing analysis method of the multi-cell thin wall with the Z-direction rib plates fixedly supported at two ends as claimed in claim 1, wherein the plastic limit bending moment of the section meets the following requirements:
Figure FDA0003247688920000022
in the formula, σ0Indicating the flow stress of the thin wall beam.
3. The beam bending energy-absorbing analysis method of the multi-cell thin wall with the Z-direction rib plates fixedly supported at two ends as claimed in claim 2, wherein the plastic limit axial force of the section meets the following requirements:
N0＝σ0t[2B+(2+n)(H-2t)]；
in the formula, N0The plastic limit axial force of the cross section is shown.
4. The beam bending energy-absorbing analysis method of the multi-cell thin wall with the Z-direction rib plates fixedly supported at two ends as claimed in claim 3, wherein the flow stress of the thin-wall beam meets the following requirements:
Figure FDA0003247688920000023
in the formula, σyDenotes the yield stress, σ, of the thin-walled beamuIndicating the ultimate stress of the thin wall beam.
5. The beam bending energy-absorbing analysis method of the multi-cell thin wall with the Z-direction rib plates fixedly supported at two ends as claimed in claim 4, wherein the section bending moment satisfies the following conditions:
Figure FDA0003247688920000024
6. the beam bending energy-absorbing analysis method of the multi-cell thin wall with the Z-direction rib plates fixedly supported at two ends as claimed in claim 5, wherein the section axial force satisfies the following conditions:
N＝(2+n)aHtσ0。
7. the beam bending energy-absorbing analysis method of the multi-cell thin wall with the Z-direction rib plates fixedly supported at two ends as claimed in claim 6, characterized in that the generalized strain rate is obtained according to the yield criterion and the orthogonal rule:
when in use
Figure FDA0003247688920000031
And, the generalized strain rate satisfies:
Figure FDA0003247688920000032
when in use
Figure FDA0003247688920000033
And, the generalized strain rate satisfies:
Figure FDA0003247688920000034
in the formula (I), the compound is shown in the specification,
Figure FDA0003247688920000035
which is indicative of the strain rate of the film,
Figure FDA0003247688920000036
is the rate of change of curvature;
according to the speed field at the plastic hinge in the deformation process of the thin-wall beam, obtaining the relationship between the generalized strain rate and the displacement:
Figure FDA0003247688920000037
8. the beam bending energy-absorbing analysis method of multi-cell thin wall with Z-direction rib plates fixedly supported at two ends as claimed in claim 7, wherein the balance equation is as follows:
Figure FDA0003247688920000038
9. the beam bending energy-absorbing analysis method of the multi-cell thin wall with the Z-direction rib plates fixedly supported at two ends as claimed in claim 8, wherein the relationship between the displacement of the section centroid axis and the displacement of the hammer head satisfies:
w＝kwp。
10. the beam bending energy-absorbing analysis method of multi-cell thin wall with two end-clamped Z-direction rib plates as claimed in claim 9, wherein the relationship between the fourth coefficient and the number of the Z-direction rib plates in the thin wall beam satisfies:
Figure FDA0003247688920000039
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