CN105426622A - Bending characteristic analysis method for thin-walled beam with twelve-right-angle cross section - Google Patents
Bending characteristic analysis method for thin-walled beam with twelve-right-angle cross section Download PDFInfo
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- CN105426622A CN105426622A CN201510860307.3A CN201510860307A CN105426622A CN 105426622 A CN105426622 A CN 105426622A CN 201510860307 A CN201510860307 A CN 201510860307A CN 105426622 A CN105426622 A CN 105426622A
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Abstract
The invention discloses a bending characteristic analysis method for a thin-walled beam with a twelve-right-angle cross section, and aims to solve the problem that a finite element method or a test method cannot be used to analyze the bending resistance of the thin-walled beam due to lack of a geometric model of a detailed structure during a vehicle body crash resistance concept design stage. The method comprises the steps of 1) dividing a bending process of the thin-walled beam with the twelve-right-angle cross section into an initial damage stage and a plastic hinge forming stage; 2) calculating a bending characteristic of the thin-walled beam with the twelve-right-angle cross section during the initial damage stage: establishing a maximum bending moment expression of a thin-walled beam with a rectangular cross section, and establishing a maximum bending moment expression of the thin-walled beam with the twelve-right-angle cross section; 3) calculating a bending characteristic of the thin-walled beam with the twelve-right-angle cross section during the plastic hinge forming stage: calculating energy dissipation of a fixed plastic hinge, calculating energy dissipation of a rolling plastic hinge, calculating tension energy dissipation, calculating total energy dissipation, and establishing a bending moment expression of the thin-walled beam with the twelve-right-angle cross section; and 4) drawing a moment-rotation curve of the thin-walled beam with the twelve-right-angle cross section and establishing an analytic expression.
Description
Technical field
The present invention relates to the analytical approach in a kind of research on vehicle passive safety field, or rather, the present invention relates to a kind of 12 right-angle cross-section thin walled beam flexural property analytical approachs.
Background technology
Thin walled beam structure is main energy-absorbing and the load parts of body of a motor car, and the thin walled beam structure that current vehicle body uses mostly is square-section, and in order to reach higher minibus and lightweight requirements, many right-angle cross-section thin walled beam had been suggested in recent years.Owing to adding the right angle quantity in cross section, many right-angle cross-section thin walled beam has higher energy absorbing efficiency and obvious light weight effect relative to square-section thin walled beam.Wherein, the 12 right-angle cross-section thin walled beams of similar " dumbbell shape " have good symmetry, in vehicle body made of composite materials, have preliminary use, along with the development of forming technique, 12 right angle thin walled beams will have in automotive body structure to be applied more widely.
Bending is a kind of primary deformable mode of thin walled beam when being subject to external impact load, and the anti-bending strength of thin walled beam depends on cross sectional shape, size and Material selec-tion.Current thin walled beam Analysis on Flexural and the design test method(s) that adopts in conjunction with Finite Element Simulation Analysis more, and this method needs the mock-up of structure or 3D geometric model just can carry out.But at vehicle body minibus conceptual phase, owing to lacking detailed construction geometry model, and design proposal is changed frequent, the method that traditional finite element is combined with test is also inapplicable.Therefore, need a kind of thin walled beam flexural property analytical approach being adapted to conceptual phase, obtain the theoretical expression of thin walled beam bending moment and its sectional dimension, thickness etc., interpretation and application can be carried out to the anti-bending strength of 12 right-angle cross-section thin walled beams under the condition not having construction geometry model.
Retrieved by domestic and international pertinent literature, find no 12 similar right-angle cross-section thin walled beam flexural property analytical approachs.
Summary of the invention
Technical matters to be solved by this invention Finite Element Method or test method cannot be used to solve vehicle body minibus conceptual phase to carry out the problem of thin walled beam Analysis on Flexural owing to lacking the geometric model of detailed construction, provides a kind of 12 right-angle cross-section thin walled beam flexural property analytical approachs.
For solving the problems of the technologies described above, the present invention adopts following technical scheme to realize: the step of 12 described right-angle cross-section thin walled beam flexural property analytical approachs is as follows:
1) by 12 right-angle cross-section thin walled beam BENDING PROCESS segmentations;
The bending deformation process of 12 right-angle cross-section thin walled beams is divided into 12 right-angle cross-section thin walled beam diastrophic initial damaged stage and the diastrophic plastic hinge formation stages of 12 right-angle cross-section thin walled beams;
2) flexural property in 12 right-angle cross-section thin walled beams initial damaged stage is calculated:
(1) square-section thin walled beam maximum bending moment expression formula is set up;
(2) 12 right-angle cross-section thin walled beam maximum bending moment expression formulas are set up;
3) flexural property of 12 right-angle cross-section thin walled beam plastic hinge formation stages is calculated:
(1) fixing plastic hinge energy dissipation is calculated;
(2) rolling plastic hinge energy dissipation is calculated;
(3) calculate tensile energy to dissipate;
(4) calculate gross energy to dissipate:
(5) expression formula of 12 right-angle cross-section thin walled beam plastic hinge formation stages bending moments is set up:
In formula, W
yfor 12 right-angle cross-section thin walled beam plastic hinge formation stages y are to the gross energy dissipated time bending; W
sifor the energy that fixing yield line absorbs, W
rjfor the energy of rolling plastic hinge line absorption, W
tkfor the energy that Extrude Face absorbs, unit is J; M
y1(o) be 12 right-angle cross-section thin walled beam plastic hinge formation stages y to bending moment, Δ o is the fractional increments of corner o, and unit is rad;
4) draw 12 right-angle cross-section thin walled beam moment of flexure-rotation curves and set up the analytical expression of 12 right-angle cross-section thin walled beam bending moment-rotation curves:
In formula, M
y(o) be 12 right-angle cross-section thin walled beam y to bending moment, M
maxyfor y is to maximum bending moment, o
tfor the intersection point corner of maximum bending moment curve and plastic hinge formation stages bending moment curve, unit is rad.
The 12 right-angle cross-section thin walled beam diastrophic initial damaged stages described in technical scheme refer to: angle of bend is 5 °-10 °, and the major parameter characterizing this stage 12 right-angle cross-section thin walled beam flexural property is maximum bending moment;
Described 12 right-angle cross-section thin walled beam diastrophic plastic hinge formation stages refers to: in 12 right-angle cross-section thin walled beam diastrophic initial damaged stages along with angle of bend strengthens further, yield line starts to be formed, until angle of bend reaches 25 °-35 °, the major parameter characterizing the 12 right-angle cross-section thin walled beam flexural properties in this stage is bending moment curve.
Square-section thin walled beam maximum bending moment expression formula step of setting up described in technical scheme is:
1) square-section thin walled beam maximum bending moment expression formula is set up:
Method described in this patent adopts the concept on effective edge of a wing to have derived the expression formula of square-section thin walled beam maximal bending moment, and for square-section thin walled beam, the limit stress of compression flange is:
In formula: σ
crfor limit stress, unit is MPa; E is the elastic modulus of material, and unit is MPa; A is square-section thin walled beam cross-sectional width, and unit is mm; B is square-section thin walled beam depth of section, and unit is mm; H is square-section thin walled beam thickness, and unit is mm;
According to limit stress σ
crwith material yield strength σ
yrelation, square-section thin walled beam maximum bending moment expression formula is:
Work as σ
cr< σ
y:
Work as σ
cr>=2 σ
y:
M
max＝M
p＝σ
yh[a(b-h)+0.5(b-2h)
2](2b)
Work as σ
y≤ σ
cr< 2 σ
y:
In formula: M
maxfor the maximum bending moment of square-section thin walled beam, unit is Nm; M
pfor intermediate variable, unit is Nm; σ
yfor the yield strength of material, unit is MPa;
2) 12 right-angle cross-section thin walled beam maximum bending moment expression formulas are set up:
12 right-angle cross-section thin walled beam y described in this method are b to width means
y, indent width means is b
a, z is divided into three sections to be followed successively by b to length
1, b
2, b
3, b
zfor thin walled beam z is to total length and b
z=b
1+ b
2+ b
3, thin walled beam thickness is h, and derive 12 right-angle cross-section thin walled beam maximum bending moment M
maxytime its cross section is equivalent to rectangle, and utilize rectangular thin-wall beam maximum bending moment expression formula (2a)-(2c), in formula, a gets b
y+ 2b
a, b gets b
1+ b
2+ b
3, obtaining 12 right-angle cross-section thin walled beam maximum bending moment expression formulas is:
Work as σ
cr< σ
y:
Work as σ
cr>=2 σ
y:
M
max＝M
p＝σ
yh[(b
y+2b
a)(b
1+b
2+b
3-h)+0.5(b
1+b
2+b
3-2h)
2](2b)′
Work as σ
y≤ σ
cr< 2 σ
y:
In formula: σ
crfor limit stress, unit is MPa; σ
yfor the yield strength of material, unit is MPa; H is thin walled beam thickness, and unit is mm; b
1, b
2, b
3be followed successively by 12 right-angle cross-section thin walled beam z to three segment length, unit is mm; b
ybe 12 right-angle cross-section thin walled beam y to width, b
afor indent width, unit is mm; M
pfor intermediate variable, unit is Nm; M
maxfor the maximum bending moment of square-section thin walled beam, unit is Nm.
Calculating described in technical scheme is fixed plastic hinge energy dissipation and is referred to: the basic geometric relationship of 12 right-angle cross-section thin walled beams is:
C
2C
4＝b
3C
2C
6＝HC
7C
6'+C
6C
6'＝b
3C
6C
2⊥C
2C
4
C
4C
7⊥C
6C
4C
6C
6'⊥C
6C
7(9)
B
6B
7＝B
2B
8'＝HB
7B
8'＝b
2B
2B
7＝B
2M+B
7M
B
2B
6⊥B
6B
7B
7M⊥MB
8'B
8B
8'⊥MB
8MB
8⊥MB
7(10)
A
2A
4＝b
1A
5A
5'+A
5'A
6＝b
1A
5A
5y'＝A
5A
5'+B
8B
8'
A
3A
5⊥A
5A
5y'A
5A
6⊥A
5A
5'(11)
In formula: b
1, b
2, b
3be followed successively by 12 right-angle cross-section thin walled beam z to three segment length, unit is mm; H is the half of the unstretched length of deformed region, and unit is mm;
The fixing plastic hinge that 12 right-angle cross-section thin walled beams are formed when occuring bending and deformation comprises:
(1) C
6c
6', C
6b
7, corner is 2 ρ; (2) C
3c
z, C
4c
y, corner is ρ; (3) C
1c
3and C
2c
4, corner is η; (4) C
3c
4, corner is ν; (5) C
1c
6and C
2c
6, corner is pi/2; Energy dissipation expression formula is respectively W
s1~ W
s5:
W
S1＝M
0·(C
6C
6'+b
a)·2ρ(12)
W
S2＝M
0b
yρ(13)
(6) A
6b
8', corner is 2 υ; (7) B
1a
3and B
2a
4, corner is (υ-ρ); (8) B
1b
7and B
2b
7, corner is
(9) B
7b
8', corner is (π-2 ω).Energy dissipation expression formula is respectively W
s6~ W
s9:
W
S7＝2M
0·b
a·(υ-ρ)(18)
(10) A
1a
zand A
2a
y, corner is (α-ρ); (11) A
5a
5' and A
5a
m, corner is 2 α; (12) A
1a
3and A
2a
4, corner is γ; (13) A
6a
5', corner is (π-2 θ); (14) A
3a
6and A
4a
6, corner is κ; (15) A
1a
5and A
2a
5, corner is pi/2.Energy dissipation expression formula is respectively W
s10~ W
s15.
W
S11＝M
0(b
y/2+A
5A
5y')·2α(22)
W
S15＝M
0·H·π(26)
In formula: W
sifor the energy of rolling plastic hinge line absorption, unit is J; M
0for unit length plastic limit bending moment, unit is N; Every lateral bend angle is ρ, and total angle of bend is o, and o=2 ρ, unit is rad; b
ybe 12 right-angle cross-section thin walled beam y to width, b
afor indent width, unit is mm.
Calculating rolling plastic hinge energy dissipation described in technical scheme refers to: the rolling plastic hinge that 12 right-angle cross-section thin walled beams are formed when occuring bending and deformation comprises: 1) C
1c
6', C
2c
6'; 2) C
3c
6' and C
4c
6'; 3) A
1a
5', A
2a
5'; Energy dissipation expression formula is respectively W
r1~ W
r3:
In formula: W
rjfor the energy of rolling plastic hinge line absorption, unit is J; M
0for unit length plastic limit bending moment, unit is N; H is the half of the unstretched length of deformed region, and unit is mm; 1/r is mean curvature, and unit is 1/mm; R is rolling radius, and unit is mm.
Calculating tensile energy described in technical scheme dissipates and refers to:
Face C
1c
2c
4c
3area knots modification Δ S
1and stretching energy absorption W
t1be respectively:
ΔS
1＝C
4C
7·C
7C
6'+H·C
6C
6'+b
3·C
2C
6'-2Hb
3(30)
W
T1＝N·ΔS
1(31)
Base area knots modification Δ S
2and stretching energy absorption W
t2be respectively:
ΔS
2＝b
y(C
4C
7-H)(32)
W
T2＝N·ΔS
2(33)
Face A
3b
1b
2a
4area knots modification Δ S
3and stretching energy absorption W
t3be respectively:
ΔS
3＝2·(0.5b
a·cosω·b
a·sinω)＝b
a 2·cosω·sinω(34)
W
T3＝N·ΔS
3(35)
In formula: W
tkfor the energy of rolling plastic hinge line absorption, unit is J; b
3be followed successively by 12 right-angle cross-section thin walled beam z to the 3rd segment length, unit is mm; H is the half of the unstretched length of deformed region, and unit is mm; b
ybe 12 right-angle cross-section thin walled beam y to width, b
afor indent width, unit is mm; N is surrender membrane forces, and unit is MPamm; Δ S
kfor the area knots modification in this face, unit is mm
2.
Compared with prior art the invention has the beneficial effects as follows:
1) 12 right-angle cross-section thin walled beam flexural property analytical approachs of the present invention have been derived the analytical expression of 12 right-angle cross-section thin walled beam Moment Rotations, obtain the mechanical relationship between 12 right-angle cross-section thin walled beam structure parameters (sectional dimension, material) and anti-bending strength (maximum bending moment, bending moment), can the flexural property of Accurate Prediction 12 right-angle cross-section thin walled beam.
2) 12 right-angle cross-section thin walled beam flexural property analytical approachs of the present invention are utilized only just can to calculate the bending property of 12 right-angle cross-section thin walled beams fast according to the thin walled beam sectional dimension provided and material behavior at vehicle body minibus conceptual phase, overcome traditional design method and need to set up the shortcoming that detailed limit element artificial module just can carry out analyzing, the method reduce Computer Simulation and test number (TN), reduce cost of development, shorten the design cycle.
Accompanying drawing explanation
Below in conjunction with accompanying drawing, the present invention is further illustrated:
Fig. 1 is the FB(flow block) of 12 right-angle cross-section thin walled beam flexural property analytical approachs of the present invention;
Fig. 2-a is the axonometric projection graph of 12 right-angle cross-section thin walled beam structures of the present invention;
Fig. 2-b is the left view of 12 right-angle cross-section thin walled beam cross-sectional structure sizes of the present invention;
Fig. 3 is the radial sectional schematic diagram of the flexural deformation mechanism that 12 right-angle cross-section thin walled beams of the present invention simplify;
Fig. 4-a is the characteristic point position schematic diagram of 12 right-angle cross-section thin walled beam flexural deformation structure left side cross-sectional of the present invention.
Fig. 4-b is the characteristic point position schematic diagram of 12 right-angle cross-section thin walled beam flexural deformation structure midsections of the present invention.
Fig. 4-c is the characteristic point position schematic diagram in cross section on the right side of 12 right-angle cross-section thin walled beam flexural deformation structures of the present invention.
Fig. 5 is 12 right-angle cross-section thin walled beam moment-rotation relation method for drafting schematic diagram of the present invention.
Fig. 6 is 12 right-angle cross-section thin walled beam moment-rotation relation method for drafting schematic diagram in embodiment 1 of the present invention.
Fig. 7 is 12 right-angle cross-section thin walled beam simple bending limit element artificial module schematic diagram of the present invention, in figure, beam one end is retrained, the other end to be connected with BEAM unit at a distance by being rigidly connected, and by applying displacement to BEAM cell node, making thin walled beam produce pure bending and being out of shape.
Fig. 8 is 12 right-angle cross-section thin walled beam moment-rotation relation contrasts in the embodiment of the present invention 1.
Fig. 9 is 12 right-angle cross-section thin walled beam moment-rotation relation contrasts in the embodiment of the present invention 2.
Figure 10 is 12 right-angle cross-section thin walled beam moment-rotation relation contrasts in embodiment 3 of the present invention.
Embodiment
Below in conjunction with accompanying drawing, the present invention is explained in detail:
Below in conjunction with accompanying drawing, the present invention is described in detail:
First the bending deformation process of 12 right-angle cross-section thin walled beams is divided into two stages by 12 right-angle cross-section thin walled beam flexural property analytical approachs of the present invention, i.e. initial damaged stage and plastic hinge formation stages; Then calculate the flexural property in 12 right-angle cross-section thin walled beams initial damaged stage, obtain the maximum bending moment expression formula of 12 right-angle cross-section thin walled beams; Then calculate the flexural property of 12 right-angle cross-section thin walled beam plastic hinge formation stages, obtain 12 right-angle cross-section thin walled beam flexional dissipation expression formula and bending moment curves; Finally draw 12 right-angle cross-section thin walled beam moment-rotation relation according to the result of second, third step.
The step of 12 described right-angle cross-section thin walled beam flexural property analytical approachs is as follows:
1. by 12 right-angle cross-section thin walled beam BENDING PROCESS segmentations
The bending deformation process of 12 right-angle cross-section thin walled beams is divided into two stages by the present invention, i.e. 12 right-angle cross-section thin walled beam diastrophic initial damaged stage and the diastrophic plastic hinge formation stages of 12 right-angle cross-section thin walled beams.
1) in the 12 right-angle cross-section thin walled beam diastrophic initial damaged stages described in, angle of bend is less, is generally 5 °-10 °, and the major parameter characterizing this stage 12 right-angle cross-section thin walled beam flexural property is maximum bending moment.
2) in 12 right-angle cross-section thin walled beam diastrophic initial damaged stages along with angle of bend strengthens further, yield line starts to be formed, until angle of bend reaches 25 °-35 °, this stage contains angle of bend scope automobile being commonly used thin walled beam, be called plastic hinge formation stages, the major parameter characterizing the 12 right-angle cross-section thin walled beam flexural properties in this stage is bending moment curve.
2. calculate the flexural property in 12 right-angle cross-section thin walled beams initial damaged stage
The major parameter characterizing the diastrophic initial damaged stage flexural property of 12 right-angle cross-section thin walled beam is maximum bending moment.The present invention derives 12 right-angle cross-section thin walled beam maximum bending moment expression formulas on the basis of square-section thin walled beam maximum bending moment expression formula.
1) square-section thin walled beam maximum bending moment expression formula is set up:
Method described in this patent adopts the concept on effective edge of a wing to have derived the expression formula of square-section thin walled beam maximal bending moment.For square-section thin walled beam, the limit stress of its compression flange is:
In formula: σ
crfor limit stress, unit is MPa; E is the elastic modulus of material, and unit is MPa; A is square-section thin walled beam cross-sectional width, and unit is mm; B is square-section thin walled beam depth of section, and unit is mm; H is square-section thin walled beam thickness, and unit is mm.
According to limit stress σ
crwith material yield strength σ
yrelation, square-section thin walled beam maximum bending moment expression formula is:
Work as σ
cr< σ
y:
Work as σ
cr>=2 σ
y:
M
max＝M
p＝σ
yh[a(b-h)+0.5(b-2h)
2](2b)
Work as σ
y≤ σ
cr< 2 σ
y:
In formula: M
maxfor the maximum bending moment of square-section thin walled beam, unit is Nm; M
pfor intermediate variable, unit is Nm; σ
yfor the yield strength of material, unit is MPa.
2) 12 right-angle cross-section thin walled beam maximum bending moment expression formulas are set up:
Consult Fig. 2,12 right-angle cross-section thin walled beam y of the present invention are b to width means
y, indent width means is b
a, z is divided into three sections to be followed successively by b to length
1, b
2, b
3, b
zfor thin walled beam z is to total length and b
z=b
1+ b
2+ b
3, thin walled beam thickness is h.Derive 12 right-angle cross-section thin walled beam maximum bending moment M
maxytime its cross section is equivalent to rectangle, and utilize rectangular thin-wall beam maximum bending moment expression formula (2a)-(2c), in formula, a gets b
y+ 2b
a, b gets b
1+ b
2+ b
3, obtaining 12 right-angle cross-section thin walled beam maximum bending moment expression formulas is:
Work as σ
cr< σ
y:
Work as σ
cr>=2 σ
y:
M
max＝M
p＝σ
yh[(b
y+2b
a)(b
1+b
2+b
3-h)+0.5(b
1+b
2+b
3-2h)
2](2b)′
Work as σ
y≤ σ
cr< 2 σ
y:
In formula: σ
crfor limit stress, unit is MPa; σ
yfor the yield strength of material, unit is MPa; H is thin walled beam thickness, and unit is mm; b
1, b
2, b
3be followed successively by 12 right-angle cross-section thin walled beam z to three segment length, unit is mm; b
ybe 12 right-angle cross-section thin walled beam y to width, b
afor indent width, unit is mm; M
pfor intermediate variable, unit is Nm; M
maxfor the maximum bending moment of square-section thin walled beam, unit is Nm;
3. calculate the flexural property of 12 right-angle cross-section thin walled beam plastic hinge formation stages
The major parameter characterizing 12 right-angle cross-section thin walled beam plastic hinge formation stages characteristics is bending moment expression formula.Energy dissipation approach, by the flexural deformation mechanism of structure 12 right-angle cross-section thin walled beam, is classified by the present invention, and then Derivation of The Energy dissipation expression formula, obtains the bending moment expression formula of 12 right-angle cross-section thin walled beams finally by the mode of getting fractional increments.
Consult Fig. 3, the 12 right-angle cross-section thin walled beams that the present invention sets up are around the radial sectional schematic diagram of y-axis flexural deformation mechanism, and in figure, distressed structure is symmetrical about z-axis, the unstretched length of deformed region is 2H, every lateral bend angle is ρ, and total angle of bend is o, and o=2 ρ.
When 12 right-angle cross-section thin walled beams occur bending and deformation, dissipation of energy approach comprises three kinds, is the energy-absorbing around fixing yield line energy-absorbing, hinge of rolling line and Liang Bi stretching energy-absorbing respectively.Every root fixes the energy W that yield line absorbs
siequal unit plastic limit bending moment M
0be multiplied by the hinge line length l of plastic hinge
iwith the rotational angle ω around hinge line
i; The energy W of every root rolling plastic hinge line absorption
rjequal M
0be multiplied by the area S that hinge line is inswept
jwith mean curvature 1/r; The energy W that each Extrude Face absorbs
tkequal to surrender the area knots modification Δ S that membrane forces N is multiplied by this face
k.
W
Si＝M
0·l
i·ω
i(3)
W
Tk＝N·ΔS
k(7)
N＝σ
0·h(8)
In formula: W
sifor every root fixes the energy of yield line absorption, unit is J; l
ifor this hinge line length, unit is mm; ω
ifor the rotational angle around this hinge line, unit is rad; M
0for unit length plastic limit bending moment, unit is N; σ
0for material equivalent flow dynamic stress, unit is MPa; W
rjfor the energy of every root rolling plastic hinge line absorption, unit is J; S
jfor the area that this hinge line is inswept, unit is mm
2; 1/r is mean curvature, and unit is 1/mm; R is rolling radius, and unit is mm; The half of the unstretched length of H deformed region, unit is mm; W
tkfor the energy that each Extrude Face absorbs, unit is J; Δ S
kfor the area knots modification in this face, unit is mm
2; N is surrender membrane forces, and unit is MPamm.
Because 12 right-angle cross-section thin walled beam distressed structures are about x-z plane symmetry, the present invention is for the half structure marked in Fig. 3, Fig. 4, to derive 12 right-angle cross-section thin walled beam flexional dissipation expression formulas, and add symmetrical side structure energy dissipation when calculating total energy absorption.
1) fixing plastic hinge energy dissipation is calculated
Consult Fig. 3 and Fig. 4, the present invention set up 12 right-angle cross-section thin walled beams simplify the radial sectional schematic diagram of flexural deformation mechanism and the key position schematic diagram of distressed structure in, basic geometric relationship is:
C
2C
4＝b
3C
2C
6＝HC
7C
6'+C
6C
6'＝b
3C
6C
2⊥C
2C
4
C
4C
7⊥C
6C
4C
6C
6'⊥C
6C
7(9)
B
6B
7＝B
2B
8'＝HB
7B
8'＝b
2B
2B
7＝B
2M+B
7M
B
2B
6⊥B
6B
7B
7M⊥MB
8'B
8B
8'⊥MB
8MB
8⊥MB
7(10)
A
2A
4＝b
1A
5A
5'+A
5'A
6＝b
1A
5A
5y'＝A
5A
5'+B
8B
8'
A
3A
5⊥A
5A
5y'A
5A
6⊥A
5A
5'(11)
In formula: b
1, b
2, b
3be followed successively by 12 right-angle cross-section thin walled beam z to three segment length, unit is mm; H is the half of the unstretched length of deformed region, and unit is mm;
Other line segment and angle can be tried to achieve according to above-mentioned geometric relationship.
The fixing plastic hinge that 12 right-angle cross-section thin walled beams are formed when occuring bending and deformation comprises:
(1) C
6c
6', C
6b
7, corner is 2 ρ; (2) C
3c
z, C
4c
y, corner is ρ; (3) C
1c
3and C
2c
4, corner is η; (4) C
3c
4, corner is ν; (5) C
1c
6and C
2c
6, corner is pi/2.Energy dissipation expression formula is respectively W
s1~ W
s5:
W
S1＝M
0·(C
6C
6'+b
a)·2ρ(12)
W
S2＝M
0b
yρ(13)
(6) A
6b
8', corner is 2 υ; (7) B
1a
3and B
2a
4, corner is (υ-ρ); (8) B
1b
7and B
2b
7, corner is
(9) B
7b
8', corner is (π-2 ω).Energy dissipation expression formula is respectively W
s6~ W
s9:
W
S7＝2M
0·b
a·(υ-ρ)(18)
(10) A
1a
zand A
2a
y, corner is (α-ρ); (11) A
5a
5' and A
5a
m, corner is 2 α; (12) A
1a
3and A
2a
4, corner is γ; (13) A
6a
5', corner is (π-2 θ); (14) A
3a
6and A
4a
6, corner is κ; (15) A
1a
5and A
2a
5, corner is pi/2.Energy dissipation expression formula is respectively W
s10~ W
s15.
W
S11＝M
0(b
y/2+A
5A
5y')·2α(22)
W
S15＝M
0·H·π(26)
In formula: W
sifor the energy of rolling plastic hinge line absorption, unit is J; M
0for unit length plastic limit bending moment, unit is N; Every lateral bend angle is ρ, and total angle of bend is o, and o=2 ρ, unit is rad; b
ybe 12 right-angle cross-section thin walled beam y to width, b
afor indent width, unit is mm.
2) rolling plastic hinge energy dissipation is calculated
The rolling plastic hinge that 12 right-angle cross-section thin walled beams are formed when occuring bending and deformation comprises: 1) C
1c
6', C
2c
6'; 2) C
3c
6' and C
4c
6'; 3) A
1a
5', A
2a
5'.Energy dissipation expression formula is respectively W
r1~ W
r3:
In formula: W
rjfor the energy of rolling plastic hinge line absorption, unit is J; M
0for unit length plastic limit bending moment, unit is N; H is the half of the unstretched length of deformed region, and unit is mm; 1/r is mean curvature, and unit is 1/mm; R is rolling radius, and unit is mm;
3) calculate tensile energy to dissipate
Face C
1c
2c
4c
3area knots modification Δ S
1and stretching energy absorption W
t1be respectively:
ΔS
1＝C
4C
7·C
7C
6'+H·C
6C
6'+b
3·C
2C
6'-2Hb
3(30)
W
T1＝N·ΔS
1(31)
Base area knots modification Δ S
2and stretching energy absorption W
t2be respectively:
ΔS
2＝b
y(C
4C
7-H)(32)
W
T2＝N·ΔS
2(33)
Face A
3b
1b
2a
4area knots modification Δ S
3and stretching energy absorption W
t3be respectively:
ΔS
3＝2·(0.5b
a·cosω·b
a·sinω)＝b
a 2·cosω·sinω(34)
W
T3＝N·ΔS
3(35)
Line segment length in formula (12)-(35) and angle can be tried to achieve according to the basic geometric relationship in formula (9)-(11).
4) calculate gross energy to dissipate
Consider symmetrical side structure, 12 right-angle cross-section thin walled beam y are to the gross energy W dissipated time bending
yfor fixing plastic hinge energy-absorbing, rolling plastic hinge energy-absorbing and stretching energy-absorbing sum, that is:
5) expression formula of 12 right-angle cross-section thin walled beam plastic hinge formation stages bending moments is set up:
According to energy minimum principle, the half H for unstretched length obtaining deformed region is:
By getting fractional increments, the moment M that corner o is corresponding can be tried to achieve
y1(o) be:
In formula, W
yfor 12 right-angle cross-section thin walled beam plastic hinge formation stages y are to the gross energy dissipated time bending; W
sifor the energy that fixing yield line absorbs, W
rjfor the energy of rolling plastic hinge line absorption, W
tkfor the energy that Extrude Face absorbs, unit is J; M
y1(o) be 12 right-angle cross-section thin walled beam plastic hinge formation stages y to bending moment, Δ o is the fractional increments of corner o, and unit is rad.
4. draw 12 right-angle cross-section thin walled beam moment-rotation relation
The bending moment obtained in the step 3 of embodiment described in this patent is only applicable to plastic hinge formation stages, and is not suitable for the initial damaged stage.In order to obtain the complete moment-rotation relation of 12 right-angle cross-section thin walled beams, consult Fig. 5, by the maximal bending moment M obtained in step 2
maxydo the bending moment curve intersection that horizontal line and step 2 Chinese style (38) obtain, the corner of point of intersection is designated as o
t, merging maximum bending moment and bending moment curve finally obtain 12 right-angle cross-section y to bending moment-rotation relation, and its expression formula is:
In formula, M
y(o) be 12 right-angle cross-section thin walled beam y to bending moment, M
maxyfor y is to maximum bending moment, o
tfor the intersection point corner of maximum bending moment curve and plastic hinge formation stages bending moment curve, unit is rad.
In sum, the 12 right-angle cross-section thin walled beam flexural property analytical approachs that just can be proposed according to the present invention by the physical dimension of given 12 right-angle cross-section thin walled beams and material properties try to achieve the maximum bending moment expression formula of structure and bending moment reaches formula, and then obtain the moment-rotation relation of 12 right-angle cross-section thin walled beams in BENDING PROCESS.
How the present invention utilizes 12 right-angle cross-section thin walled beam flexural property analytical approachs proposed by the invention in conjunction with three embodiment introductions.
Embodiment 1:
12 right-angle cross-section thin walled beam sectional dimensions are: b
y=80mm, b
a=20mm, b
1=b
2=b
3=30mm, b
z=b
1+ b
2+ b
3=90mm, thickness h=1.2mm, the material used is mild carbon steel, yield limit σ
y=162MPa, the step of 12 right-angle cross-section thin walled beam flexural property analytical approachs is as follows:
1. 12 right-angle cross-section thin walled beam BENDING PROCESS segmentations
The bending deformation process of 12 right-angle cross-section thin walled beams is divided into two stages, is initial damaged stage and plastic hinge formation stages respectively.The flexural property of these two stage 12 right-angle cross-section thin walled beams is characterized respectively with maximum bending moment and bending moment curve.
2. calculate the flexural property in 12 right-angle cross-section thin walled beams initial damaged stage
The cross section of 12 right-angle cross-section thin walled beams is equivalent to rectangle, a=b
y+ 2b
a=120mm, b=b
1+ b
2+ b
3=90mm.Formula (1) is utilized to try to achieve limit stress σ
cr=103MPa, due to σ
cr< σ
y, therefore use formula (2a) to calculate the maximum bending moment of 12 right-angle cross-section thin walled beams, try to achieve M
maxy=2156Nm.
3. calculate the flexural property of 12 right-angle cross-section thin walled beam plastic hinge formation stages
Unit length plastic limit bending moment M is tried to achieve according to formula (4)
0=49N, tries to achieve surrender membrane forces N=194MPamm according to formula (8).
The bending moment curve of 12 right-angle cross-section thin walled beams is calculated by iterative manner.Get angle of bend fractional increments Δ o=0.001rad, hinge line length, the anglec of rotation of each fixing plastic hinge in each iterative step is tried to achieve according to the basic geometric relationship in formula (9)-(11), each rolling radius of rolling plastic hinge and the area knots modification of each Extrude Face, and then try to achieve the energy dissipation of each fixing plastic hinge, each energy dissipation of rolling plastic hinge and the tensile energy of each Extrude Face dissipate.Consider symmetrical side structure, utilize formula (36) to try to achieve in each iterative step 12 right-angle cross-section thin walled beam y to the gross energy dissipated time bending.
Utilizing formula (37), by getting fractional increments Δ o=0.001rad, obtaining the M curve M that corner o is corresponding
y1(o).
4. draw 12 right-angle cross-section thin walled beam moment-rotation relation
Consult Fig. 6, in order to obtain the complete moment-rotation relation of 12 right-angle cross-section thin walled beams, by the maximal bending moment M obtained in step 1
maxydo the bending moment curve intersection that horizontal line and step 2 Chinese style (37) obtain, the corner o of point of intersection
t=0.038rad, merges maximum bending moment and bending moment curve finally obtains 12 right-angle cross-section y to bending moment-rotation relation.
Consult table 1, the present invention also utilizes step 1 above ~ 4 to calculate the flexural property of 12 right-angle cross-section thin walled beams of other two kinds of different cross section sizes and material behavior.
12 right-angle cross-section thin walled beams of table 1 three kinds of different cross section sizes and material behavior
Consult Fig. 7, set up three corresponding 12 right-angle cross-section thin walled beam simple bending limit element artificial module of embodiment respectively, and calculating is solved to finite element model, obtain the FEM Numerical Simulation of 12 right-angle cross-section thin walled beam moment-rotation relation of three embodiments.Consult Fig. 8 to Figure 10,12 right-angle cross-section thin walled beam moment-rotation relation theory calculate of three embodiments and FEM Numerical Simulation contrast, and moment-rotation relation and the FEM Numerical Simulation of the 12 right-angle cross-section thin walled beams utilizing 12 right-angle cross-section thin walled beam flexural property analytical approachs of the present invention to obtain have very high consistance.
In sum, the 12 right-angle cross-section thin walled beam flexural property reduced chemical reaction kinetics model that the present invention proposes can describe the flexural property (moment-rotation relation) of 12 right-angle cross-section thin walled beams, the method can be utilized at vehicle body minibus conceptual phase, when there not being thin walled beam structure model, only according to 12 right-angle cross-section thin walled beam dimensional parameters and material behaviors, analyses and prediction are carried out to the transverse property of 12 right-angle cross-section thin walled beams, shorten the construction cycle, reduce cost of development.
Claims (6)
1. 12 right-angle cross-section thin walled beam flexural property analytical approachs, is characterized in that, the step of 12 described right-angle cross-section thin walled beam flexural property analytical approachs is as follows:
1) by 12 right-angle cross-section thin walled beam BENDING PROCESS segmentations;
The bending deformation process of 12 right-angle cross-section thin walled beams is divided into 12 right-angle cross-section thin walled beam diastrophic initial damaged stage and the diastrophic plastic hinge formation stages of 12 right-angle cross-section thin walled beams;
2) flexural property in 12 right-angle cross-section thin walled beams initial damaged stage is calculated:
(1) square-section thin walled beam maximum bending moment expression formula is set up;
(2) 12 right-angle cross-section thin walled beam maximum bending moment expression formulas are set up;
3) flexural property of 12 right-angle cross-section thin walled beam plastic hinge formation stages is calculated:
(1) fixing plastic hinge energy dissipation is calculated;
(2) rolling plastic hinge energy dissipation is calculated;
(3) calculate tensile energy to dissipate;
(4) calculate gross energy to dissipate:
(5) expression formula of 12 right-angle cross-section thin walled beam plastic hinge formation stages bending moments is set up:
In formula: W
yfor 12 right-angle cross-section thin walled beam plastic hinge formation stages y are to the gross energy dissipated time bending; W
sifor the energy that fixing yield line absorbs, W
rjfor the energy of rolling plastic hinge line absorption, W
tkfor the energy that Extrude Face absorbs, unit is J; M
y1(o) be 12 right-angle cross-section thin walled beam plastic hinge formation stages y to bending moment, Δ o is the fractional increments of corner o, and unit is rad;
4) draw 12 right-angle cross-section thin walled beam moment of flexure-rotation curves and set up the analytical expression of 12 right-angle cross-section thin walled beam bending moment-rotation curves:
In formula: M
y(o) be 12 right-angle cross-section thin walled beam y to bending moment, M
maxyfor y is to maximum bending moment, o
tfor the intersection point corner of maximum bending moment curve and plastic hinge formation stages bending moment curve, unit is rad.
2. according to 12 right-angle cross-section thin walled beam flexural property analytical approachs according to claim 1, it is characterized in that, the 12 described right-angle cross-section thin walled beam diastrophic initial damaged stages refer to: angle of bend is 5 °-10 °, and the major parameter characterizing this stage 12 right-angle cross-section thin walled beam flexural property is maximum bending moment;
Described 12 right-angle cross-section thin walled beam diastrophic plastic hinge formation stages refers to: in 12 right-angle cross-section thin walled beam diastrophic initial damaged stages along with angle of bend strengthens further, yield line starts to be formed, until angle of bend reaches 25 °-35 °, the major parameter characterizing the 12 right-angle cross-section thin walled beam flexural properties in this stage is bending moment curve.
3. according to 12 right-angle cross-section thin walled beam flexural property analytical approachs according to claim 1, it is characterized in that, described square-section thin walled beam maximum bending moment expression formula step of setting up is:
1) square-section thin walled beam maximum bending moment expression formula is set up:
Adopt the concept on effective edge of a wing to have derived the expression formula of square-section thin walled beam maximal bending moment, for square-section thin walled beam, the limit stress of compression flange is:
In formula: σ
crfor limit stress, unit is MPa; E is the elastic modulus of material, and unit is MPa; A is square-section thin walled beam cross-sectional width, and unit is mm; B is square-section thin walled beam depth of section, and unit is mm; H is square-section thin walled beam thickness, and unit is mm;
According to limit stress σ
crwith material yield strength σ
yrelation, square-section thin walled beam maximum bending moment expression formula is:
Work as σ
cr< σ
y:
Work as σ
cr>=2 σ
y:
M
max＝M
p＝σ
yh[a(b-h)+0.5(b-2h)
2](2b)
Work as σ
y≤ σ
cr< 2 σ
y:
In formula: M
maxfor the maximum bending moment of square-section thin walled beam, unit is Nm; M
pfor intermediate variable, unit is Nm; σ
yfor the yield strength of material, unit is MPa;
2) 12 right-angle cross-section thin walled beam maximum bending moment expression formulas are set up:
12 right-angle cross-section thin walled beam y described in this method are b to width means
y, indent width means is b
a, z is divided into three sections to be followed successively by b to length
1, b
2, b
3, b
zfor thin walled beam z is to total length and b
z=b
1+ b
2+ b
3, thin walled beam thickness is h, and derive 12 right-angle cross-section thin walled beam maximum bending moment M
maxytime its cross section is equivalent to rectangle, and utilize rectangular thin-wall beam maximum bending moment expression formula (2a)-(2c), in formula, a gets b
y+ 2b
a, b gets b
1+ b
2+ b
3, obtaining 12 right-angle cross-section thin walled beam maximum bending moment expression formulas is:
Work as σ
cr< σ
y:
Work as σ
cr>=2 σ
y:
M
max＝M
p＝σ
yh[(b
y+2b
a)(b
1+b
2+b
3-h)+0.5(b
1+b
2+b
3-2h)
2](2b)′
Work as σ
y≤ σ
cr< 2 σ
y:
In formula: σ
crfor limit stress, unit is MPa; σ
yfor the yield strength of material, unit is MPa; H is thin walled beam thickness, and unit is mm; b
1, b
2,b
3be followed successively by 12 right-angle cross-section thin walled beam z to three segment length, unit is mm; b
ybe 12 right-angle cross-section thin walled beam y to width, b
afor indent width, unit is mm; M
pfor intermediate variable, unit is Nm; M
maxfor the maximum bending moment of square-section thin walled beam, unit is Nm.
4., according to 12 right-angle cross-section thin walled beam flexural property analytical approachs according to claim 1, it is characterized in that, described calculating is fixed plastic hinge energy dissipation and is referred to:
The basic geometric relationship of 12 right-angle cross-section thin walled beams is:
C
2C
4＝b
3C
2C
6＝HC
7C
6'+C
6C
6'＝b
3C
6C
2⊥C
2C
4
C
4C
7⊥C
6C
4C
6C
6'⊥C
6C
7(9)
B
6B
7＝B
2B
8'＝HB
7B
8'＝b
2B
2B
7＝B
2M+B
7M
B
2B
6⊥B
6B
7B
7M⊥MB
8'B
8B
8'⊥MB
8MB
8⊥MB
7(10)
A
2A
4＝b
1A
5A
5'+A
5'A
6＝b
1A
5A
5y'＝A
5A
5'+B
8B
8'
A
3A
5⊥A
5A
5y'A
5A
6⊥A
5A
5'(11)
In formula: b
1, b
2,b
3be followed successively by 12 right-angle cross-section thin walled beam z to three segment length, unit is mm; H is the half of the unstretched length of deformed region, and unit is mm;
The fixing plastic hinge that 12 right-angle cross-section thin walled beams are formed when occuring bending and deformation comprises:
(1) C
6c
6', C
6b
7, corner is 2 ρ; (2) C
3c
z, C
4c
y, corner is ρ; (3) C
1c
3and C
2c
4, corner is η; (4) C
3c
4, corner is ν; (5) C
1c
6and C
2c
6, corner is pi/2; Energy dissipation expression formula is respectively W
s1~ W
s5:
W
S1＝M
0·(C
6C
6'+b
a)·2ρ(12)
W
S2＝M
0b
yρ(13)
(6) A
6b
8', corner is 2 υ; (7) B
1a
3and B
2a
4, corner is (υ-ρ); (8) B
1b
7and B
2b
7, corner is
(9) B
7b
8', corner is (π-2 ω).Energy dissipation expression formula is respectively W
s6~ W
s9:
W
S7＝2M
0·b
a·(υ-ρ)(18)
(10) A
1a
zand A
2a
y, corner is (α-ρ); (11) A
5a
5' and A
5a
m, corner is 2 α; (12) A
1a
3and A
2a
4, corner is γ; (13) A
6a
5', corner is (π-2 θ); (14) A
3a
6and A
4a
6, corner is κ; (15) A
1a
5and A
2a
5, corner is pi/2.Energy dissipation expression formula is respectively W
s10~ W
s15;
W
S11＝M
0(b
y/2+A
5A
5y')·2α(22)
W
S15＝M
0·H·π(26)
In formula: W
sifor the energy of rolling plastic hinge line absorption, unit is J; M
0for unit length plastic limit bending moment, unit is N; Every lateral bend angle is ρ, and total angle of bend is o, and o=2 ρ, unit is rad; b
ybe 12 right-angle cross-section thin walled beam y to width, b
afor indent width, unit is mm.
5. according to 12 right-angle cross-section thin walled beam flexural property analytical approachs according to claim 1, it is characterized in that, described calculating rolling plastic hinge energy dissipation refers to:
The rolling plastic hinge that 12 right-angle cross-section thin walled beams are formed when occuring bending and deformation comprises: 1) C
1c
6', C
2c
6'; 2) C
3c
6' and C
4c
6'; 3) A
1a
5', A
2a
5'; Energy dissipation expression formula is respectively W
r1~ W
r3:
In formula: W
rjfor the energy of rolling plastic hinge line absorption, unit is J; M
0for unit length plastic limit bending moment, unit is N; H is the half of the unstretched length of deformed region, and unit is mm; 1/r is mean curvature, and unit is 1/mm; R is rolling radius, and unit is mm.
6. according to 12 right-angle cross-section thin walled beam flexural property analytical approachs according to claim 1, it is characterized in that, described calculating tensile energy dissipates and refers to:
Face C
1c
2c
4c
3area knots modification Δ S
1and stretching energy absorption W
t1be respectively:
ΔS
1＝C
4C
7·C
7C
6'+H·C
6C
6'+b
3·C
2C
6'-2Hb
3(30)
W
T1＝N·ΔS
1(31)
Base area knots modification Δ S
2and stretching energy absorption W
t2be respectively:
ΔS
2＝b
y(C
4C
7-H)(32)
W
T2＝N·ΔS
2(33)
Face A
3b
1b
2a
4area knots modification Δ S
3and stretching energy absorption W
t3be respectively:
ΔS
3＝2·(0.5b
a·cosω·b
a·sinω)＝b
a 2·cosω·sinω(34)
W
T3＝N·ΔS
3(35)
In formula: W
tkfor the energy of rolling plastic hinge line absorption, unit is J; b
3be followed successively by 12 right-angle cross-section thin walled beam z to the 3rd segment length, unit is mm; H is the half of the unstretched length of deformed region, and unit is mm; b
ybe 12 right-angle cross-section thin walled beam y to width, b
afor indent width, unit is mm; N is surrender membrane forces, and unit is MPamm; Δ S
kfor the area knots modification in this face, unit is mm
2.
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| CN113722831A (en) * | 2021-09-06 | 2021-11-30 | 吉林大学 | Beam bending energy absorption analysis method for multi-cell thin wall of Z-direction rib plate fixedly supported at two ends |
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107256289A (en) * | 2017-05-18 | 2017-10-17 | 吉林大学 | The method for building up of car crass reduced parameter FEM model |
| CN109299558A (en) * | 2018-10-09 | 2019-02-01 | 吉林大学 | Mesh font thin walled beam three-point bending crush characteristics Analytical Solution method |
| CN109299558B (en) * | 2018-10-09 | 2023-04-07 | 吉林大学 | Three-point bending crushing characteristic analytical solving method for mesh-shaped thin-walled beam |
| CN109543229A (en) * | 2018-10-24 | 2019-03-29 | 吉林大学 | 12 right-angle cross-section thin walled beam crush characteristics analysis method of Varying-thickness |
| CN109543229B (en) * | 2018-10-24 | 2022-09-02 | 吉林大学 | Crushing characteristic analysis method for variable-thickness twelve-right-angle-section thin-walled beam |
| CN113722831A (en) * | 2021-09-06 | 2021-11-30 | 吉林大学 | Beam bending energy absorption analysis method for multi-cell thin wall of Z-direction rib plate fixedly supported at two ends |
| CN113722831B (en) * | 2021-09-06 | 2023-11-17 | 吉林大学 | Beam bending energy absorption analysis method for multi-cell thin wall of two-end fixedly supported Z-direction rib plate |
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