CN106372273B - One kind faces hydrogen heavy wall cylindrical shell elastic limit loading prediction method - Google Patents
One kind faces hydrogen heavy wall cylindrical shell elastic limit loading prediction method Download PDFInfo
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- CN106372273B CN106372273B CN201610668815.6A CN201610668815A CN106372273B CN 106372273 B CN106372273 B CN 106372273B CN 201610668815 A CN201610668815 A CN 201610668815A CN 106372273 B CN106372273 B CN 106372273B
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- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
Abstract
The invention discloses one kind to face hydrogen heavy wall cylindrical shell elastic limit loading prediction method, the HELP of this method application hydrogen embrittlement is theoretical, according to the relation between the elastic response of cylindrical shell under hydrogen environment and atmospheric environment, the elastic limit load of hydrogen cylindrical shell is determined by solving Nonlinear System of Equations.It is excessively high that this method solves existing method application threshold, it is excessively complicated the defects of, while influence of the hydrogen to material mechanical performance is considered in prediction limits load, to engineering design with some reference value.
Description
Technical field
The present invention relates to the elastic responses for facing hydrogen bearing structure to predict field, the HELP theoretical predictions specifically based on hydrogen embrittlement
The elastic limit load of heavy wall cylindrical shell.
Background technology
Cylindrical shell is the key that pressure restraining element during hydrogen storage and defeated hydrogen in hydrogen system, determines heavy wall cylindrical shell in hydrogen environment
Under elastic limit load be the problem of design hydrogen container, hydrogenation reactor must take into consideration when hydrogen-contacting equipments.Existing prediction
The method of cylindrical shell ultimate load does not take into account influence of the hydrogen environment to cylindrical shell, simultaneously because hydrogen damage constitutive relation
Complexity, ultimate load and its complexity of the cylindrical shell under hydrogen environment are predicted using traditional method of addition, it is difficult in engineering
Upper popularization.Therefore propose that a kind of method that hydrogen cylindrical shell elastic limit load is faced in simple prediction has engineering significance.The present invention
Plasticity localization theoretical (HELP) is promoted to be applied to heavy wall cylindrical shell the hydrogen of hydrogen embrittlement, it is proposed that it is pre- that one kind faces hydrogen heavy wall cylindrical shell
Survey the simplification method of elastic limit load.
The content of the invention
In view of the above-mentioned deficiencies in the prior art, it is an object of the present invention to provide a kind of simplification faces hydrogen heavy wall cylindrical shell elasticity pole
Limit for tonnage lotus Forecasting Methodology, this method is according to the relation in atmospheric environment between the stress response of cylindrical shell in hydrogen environment, directly
Construction faces the governing equation of hydrogen cylindrical shell elastic limit loading problem.Hydrogen environment is considered in prediction limits load to cylindrical shell
The influence of performance.
The purpose of the present invention is what is be achieved through the following technical solutions：One kind faces hydrogen heavy wall cylindrical shell elastic limit load
Forecasting Methodology comprises the following steps：
Step 1：The initial value for making the ultimate load p of heavy wall cylindrical shell is p=0；
Step 2：Circumferential stress σ is calculated according to below equationθWith radial stress σr；
σr=-p
Wherein a is cylindrical shell inside radius, and b is cylindrical shell outer radius.
Step 3：Hydrogen concentration c is calculated according to below equation group；
Wherein, E be material elasticity modulus, ν be material Poisson's ratio, VHRepresent partial molar volume of the hydrogen in base material, VM
For the molal volume of base material, α is the hydrogen trap number of per unit lattice, the interstitial void binding site number of β per unit lattices, NL=
NA/VMFor the metallic atom quantity of per unit volume, NAFor Avgadro constant, NTRepresent the trap number of per unit volume.
R is ideal gas constant, and T is Kelvin's thermometric scale, c0For no-load when cylindrical shell in hydrogen concentration, WBIt is combined for the hydrogen trap of material
Energy.
Step 4：Calculate axial stress σz
Step 5：Calculate functional value g
Wherein σ0For the initial yield intensity of material, ξ is the parameter of characterization hydrogen damage degree.
Step 6：Judge g value sizes, if | g | >=εerr, then step 7 is performed to step 8, is otherwise terminated to calculate, is obtained facing hydrogen
Heavy wall cylindrical shell elastic limit load, wherein εerrFor convergence tolorence, ε can useerr=10-6；
Step 7：Design ultimate load p according to the following formula1
Wherein
Step 8：Make p=p1, return to step 2.
Further, the step 3 uses Newton Algorithm hydrogen concentration c, specifically includes following sub-step：
Step 301：Hydrogen concentration initial value c=c is set0；
Step 302：According to current hydrogen concentration c, parameters are calculated according to the following formula：
Step 303：Calculate following functional value g：
Step 304：Judge g value sizes, if | g | >=εerr, then step 305 is performed to step 306, is otherwise terminated to calculate, be obtained
To hydrogen concentration c, wherein εerrFor convergence tolorence, ε can useerr=10-6；
Step 305：Hydrogen concentration c is calculated according to the following formula1
Wherein
Step 306：Make c=c1, return to step 302.
The present invention has the following advantages：Hydrogen heavy wall cylindrical shell is faced using the method directly prediction for solving Nonlinear System of Equations
Elastic limit load need not write the finite element program of the constitutive model of hydrogen damage material.Consider in prediction limits load
Damaging action of the hydrogen to material, the ultimate load that present invention prediction obtains are partial to safety compared to existing method.
Description of the drawings
Fig. 1 is the objective for implementation schematic diagram of the present invention；
Fig. 2 is the elastic limit load and initial hydrogen concentration c that present example is calculated0Relation.
Specific embodiment
Below using the example shown in Fig. 1 and table 1 as objective for implementation, the invention will be further described.
Example shown in FIG. 1 is the heavy wall cylindrical shell of both ends constraint, and inside radius and outer radius are respectively a and b,
Concentration is c under unstress state0Hydrogen be uniformly distributed in cylindrical shell.The present invention can predict the cylindrical shell in hydrogen environment
Elastic limit load.
The material parameter and geometric parameter that 1 example of table is used
| Parameter | Numerical value |
| Inside radius a | 0.5m |
| Outer radius b | 0.75m |
| Elastic modulus E | 115GPa |
| Poisson's ratio υ | 0.34 |
| The partial molar volume V of hydrogenH | 1.18×10-6m3/mole |
| The molal volume V of metalM | 10.825×10-6m3/mole |
| Yield strength σ0 | 400MPa |
| Trap density NT | 4.2855×1019 |
| Interstitial void number of sites β | 1.0 |
| Hydrogen trap number α | 1.0 |
| Temperature T | 300K |
| Hydrogen damage factor ξ | 0.1 |
| Mean bindind energy WB | 29.3KJ/mole |
The realization process of the method for the present invention is as follows：
Step 1：Give an initial hydrogen concentration c0, such as c0=0.1, the initial value for making the ultimate load p of heavy wall cylindrical shell is
P=0；
Step 2：It brings current ultimate load p into below equation and calculates circumferential stress σθWith radial stress σr；
σr=-p
Wherein cylindrical shell inside radius a, outer radius b press value in table 1；
Step 3：Hydrogen concentration c is calculated according to below equation group；
Wherein each parameter presses value in table 1, and step 3 specifically includes following sub-step：
Step 301：Hydrogen concentration initial value c=c is set0；
Step 302：Following formula is brought into according to current hydrogen concentration c and calculates parameters：
Step 303：The parameter that step 202 is obtained brings following functional value into, calculates functional value g：
Step 304：Judge g value sizes, if | g | >=εerr, then step 205 is performed to step 206, is otherwise terminated to calculate, be obtained
To hydrogen concentration c, wherein convergence tolorence takes εerr=10-6；
Step 305：Hydrogen concentration c is calculated according to the following formula1
Wherein
Required each parameter is calculated by step 302；
Step 306：Make c=c1, return to step 302.
Step 4：The circumferential stress σ that step 2 is obtainedθWith radial stress σrAnd the hydrogen concentration c that step 3 obtains is brought into down
Formula calculates axial stress σz：
Step 5：The circumferential stress σ that step 2 is obtainedθWith radial stress σr, hydrogen concentration c and step 4 that step 3 obtains
Obtain axial stress σzIt brings following formula into and calculates functional value g
The wherein initial yield intensity σ of material01 value of table is pressed with hydrogen damage factor ξ.
Step 6：Judge g value sizes, if | g | >=εerr, then step 7 is performed to step 8, is otherwise terminated to calculate, is obtained facing hydrogen
Heavy wall cylindrical shell elastic limit load p, wherein convergence tolorence take εerr=10-6；
Step 7：Design ultimate load p according to the following formula1
Wherein
Step 8：Make p=p1, return to step 2.
Using different initial hydrogen concentration c0(0≤c0≤ 1) repeating step 1 to step 8 can obtain facing hydrogen cylindrical shell elasticity
Relation between ultimate load and initial hydrogen concentration, as shown in Figure 2.
Claims (2)
1. one kind faces hydrogen heavy wall cylindrical shell elastic limit loading prediction method, which is characterized in that comprises the following steps：
Step 1：The initial value for making the ultimate load p of heavy wall cylindrical shell is p=0；
Step 2：Circumferential stress σ is calculated according to below equationθWith radial stress σr；
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Step 3：Hydrogen concentration c is calculated according to below equation group；
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<mn>0</mn>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>L</mi>
</msub>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mfrac>
<mfrac>
<mrow>
<msub>
<mi>K</mi>
<mi>L</mi>
</msub>
<msub>
<mi>V</mi>
<mi>H</mi>
</msub>
</mrow>
<mrow>
<mn>3</mn>
<mi>R</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mfrac>
<mrow>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
<msup>
<mi>a</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mi>b</mi>
<mn>2</mn>
</msup>
<mo>-</mo>
<msup>
<mi>a</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mo>&lsqb;</mo>
<mi>&beta;</mi>
<mo>+</mo>
<mi>&alpha;</mi>
<mfrac>
<msub>
<mi>N</mi>
<mi>T</mi>
</msub>
<msub>
<mi>N</mi>
<mi>L</mi>
</msub>
</mfrac>
<mfrac>
<msub>
<mi>K</mi>
<mi>T</mi>
</msub>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>&theta;</mi>
<mi>L</mi>
</msub>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>T</mi>
</msub>
<msub>
<mi>&theta;</mi>
<mi>L</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mfrac>
<mo>&rsqb;</mo>
<mfrac>
<mrow>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>L</mi>
</msub>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mfrac>
<mfrac>
<mrow>
<msub>
<mi>K</mi>
<mi>L</mi>
</msub>
<msub>
<mi>V</mi>
<mi>H</mi>
</msub>
</mrow>
<mrow>
<mn>3</mn>
<mi>R</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mfrac>
<mi>E</mi>
<mn>3</mn>
</mfrac>
<mfrac>
<msub>
<mi>V</mi>
<mi>H</mi>
</msub>
<msub>
<mi>V</mi>
<mi>M</mi>
</msub>
</mfrac>
</mrow>
</mfrac>
</mrow>
<mrow>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>k</mi>
<mi>k</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
<msup>
<mi>a</mi>
<mn>2</mn>
</msup>
<mi>p</mi>
</mrow>
<mrow>
<msup>
<mi>b</mi>
<mn>2</mn>
</msup>
<mo>-</mo>
<msup>
<mi>a</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<mi>E</mi>
<mn>3</mn>
</mfrac>
<mfrac>
<msub>
<mi>V</mi>
<mi>H</mi>
</msub>
<msub>
<mi>V</mi>
<mi>M</mi>
</msub>
</mfrac>
<mrow>
<mo>(</mo>
<mi>c</mi>
<mo>-</mo>
<msub>
<mi>c</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>K</mi>
<mi>L</mi>
</msub>
<mo>=</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>k</mi>
<mi>k</mi>
</mrow>
</msub>
<msub>
<mi>V</mi>
<mi>H</mi>
</msub>
</mrow>
<mrow>
<mn>3</mn>
<mi>R</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>K</mi>
<mi>T</mi>
</msub>
<mo>=</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>W</mi>
<mi>B</mi>
</msub>
<mrow>
<mi>R</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mo>=</mo>
<msub>
<mi>c</mi>
<mn>0</mn>
</msub>
<mo>/</mo>
<mi>&beta;</mi>
</mrow>
<mrow>
<msub>
<mi>&theta;</mi>
<mi>L</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>K</mi>
<mi>L</mi>
</msub>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
</mrow>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>L</mi>
</msub>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
</mrow>
</mfrac>
</mrow>
Step 8：Make p=p1, return to step 2.
2. one kind according to claim 1 faces hydrogen heavy wall cylindrical shell elastic limit loading prediction method, which is characterized in that institute
It states step 3 and uses Newton Algorithm hydrogen concentration c, specifically include following sub-step：
Step 301：Hydrogen concentration initial value c=c is set0；
Step 302：According to current hydrogen concentration c, parameters are calculated according to the following formula：
<mrow>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>k</mi>
<mi>k</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
<msup>
<mi>a</mi>
<mn>2</mn>
</msup>
<mi>p</mi>
</mrow>
<mrow>
<msup>
<mi>b</mi>
<mn>2</mn>
</msup>
<mo>-</mo>
<msup>
<mi>a</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<mi>E</mi>
<mn>3</mn>
</mfrac>
<mfrac>
<msub>
<mi>V</mi>
<mi>H</mi>
</msub>
<msub>
<mi>V</mi>
<mi>M</mi>
</msub>
</mfrac>
<mrow>
<mo>(</mo>
<mi>c</mi>
<mo>-</mo>
<msub>
<mi>c</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>K</mi>
<mi>L</mi>
</msub>
<mo>=</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>k</mi>
<mi>k</mi>
</mrow>
</msub>
<msub>
<mi>V</mi>
<mi>H</mi>
</msub>
</mrow>
<mrow>
<mn>3</mn>
<mi>R</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>K</mi>
<mi>T</mi>
</msub>
<mo>=</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>W</mi>
<mi>B</mi>
</msub>
<mrow>
<mi>R</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>&theta;</mi>
<mi>L</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>K</mi>
<mi>L</mi>
</msub>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
</mrow>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>L</mi>
</msub>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
</mrow>
</mfrac>
</mrow>
<mrow>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mo>=</mo>
<msub>
<mi>c</mi>
<mn>0</mn>
</msub>
<mo>/</mo>
<mi>&beta;</mi>
</mrow>
Step 303：Calculate following functional value g：
<mrow>
<mi>g</mi>
<mo>=</mo>
<mi>c</mi>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>&beta;K</mi>
<mi>L</mi>
</msub>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
</mrow>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>L</mi>
</msub>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>&alpha;N</mi>
<mi>T</mi>
</msub>
</mrow>
<msub>
<mi>N</mi>
<mi>L</mi>
</msub>
</mfrac>
<mfrac>
<mrow>
<msub>
<mi>K</mi>
<mi>T</mi>
</msub>
<msub>
<mi>&theta;</mi>
<mi>L</mi>
</msub>
</mrow>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>&theta;</mi>
<mi>L</mi>
</msub>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>T</mi>
</msub>
<msub>
<mi>&theta;</mi>
<mi>L</mi>
</msub>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
Step 304：Judge g value sizes, if | g | >=εerr, then step 305 is performed to step 306, is otherwise terminated to calculate, is obtained hydrogen
Concentration c, wherein εerrFor convergence tolorence, ε can useerr=10-6；
Step 305：Hydrogen concentration c is calculated according to the following formula1
<mrow>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mi>c</mi>
<mo>-</mo>
<mfrac>
<mi>g</mi>
<msup>
<mi>g</mi>
<mo>&prime;</mo>
</msup>
</mfrac>
</mrow>
Wherein
<mrow>
<msup>
<mi>g</mi>
<mo>&prime;</mo>
</msup>
<mo>=</mo>
<mn>1</mn>
<mo>+</mo>
<mo>&lsqb;</mo>
<mi>&beta;</mi>
<mo>+</mo>
<mi>&alpha;</mi>
<mfrac>
<msub>
<mi>N</mi>
<mi>T</mi>
</msub>
<msub>
<mi>N</mi>
<mi>L</mi>
</msub>
</mfrac>
<mfrac>
<msub>
<mi>K</mi>
<mi>T</mi>
</msub>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>&theta;</mi>
<mi>L</mi>
</msub>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>T</mi>
</msub>
<msub>
<mi>&theta;</mi>
<mi>L</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mfrac>
<mo>&rsqb;</mo>
<mfrac>
<mrow>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>L</mi>
</msub>
<msubsup>
<mi>&theta;</mi>
<mi>L</mi>
<mn>0</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mfrac>
<mfrac>
<mrow>
<msub>
<mi>K</mi>
<mi>L</mi>
</msub>
<msub>
<mi>V</mi>
<mi>H</mi>
</msub>
</mrow>
<mrow>
<mn>3</mn>
<mi>R</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mfrac>
<mi>E</mi>
<mn>3</mn>
</mfrac>
<mfrac>
<msub>
<mi>V</mi>
<mi>H</mi>
</msub>
<msub>
<mi>V</mi>
<mi>M</mi>
</msub>
</mfrac>
</mrow>
Step 306：Make c=c1, return to step 302.
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| JP2002342694A (en) * | 2001-05-17 | 2002-11-29 | Araco Corp | Method and device for structural analysis of elastic material |
| CN100569552C (en) * | 2008-07-11 | 2009-12-16 | 清华大学 | The concentration dilution device that is used for the hydrogen of fuel battery passenger car discharging |
| CN102141466A (en) * | 2010-12-21 | 2011-08-03 | 浙江大学 | Boundary simulation device and method for thin-walled cylindrical shell structure experiment |
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| CN100569552C (en) * | 2008-07-11 | 2009-12-16 | 清华大学 | The concentration dilution device that is used for the hydrogen of fuel battery passenger car discharging |
| CN103154703A (en) * | 2010-10-05 | 2013-06-12 | 株式会社普利司通 | Method for predicting elastic response performance of rubber product, method for design, and device for predicting elastic response performance |
| CN102141466A (en) * | 2010-12-21 | 2011-08-03 | 浙江大学 | Boundary simulation device and method for thin-walled cylindrical shell structure experiment |
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