CN106295021B - A kind of Forecasting Methodology for facing the strain of hydrogen heavy wall cylindrical shell elastic stress - Google Patents
A kind of Forecasting Methodology for facing the strain of hydrogen heavy wall cylindrical shell elastic stress Download PDFInfo
- Publication number
- CN106295021B CN106295021B CN201610670679.4A CN201610670679A CN106295021B CN 106295021 B CN106295021 B CN 106295021B CN 201610670679 A CN201610670679 A CN 201610670679A CN 106295021 B CN106295021 B CN 106295021B
- Authority
- CN
- China
- Prior art keywords
- msub
- mrow
- mfrac
- msup
- msubsup
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/06—Power analysis or power optimisation
Abstract
The invention discloses a kind of Forecasting Methodology for facing the strain of hydrogen heavy wall cylindrical shell elastic stress, the HELP of this method application hydrogen embrittlement is theoretical, directly predicts that elastic stress of the cylindrical shell under hydrogen environment strains with elastic stress strain of the cylindrical shell under atmospheric environment.Compared to the method for existing prediction hydrogen environment lower structure ess-strain, the present invention has the advantages that principle is simple.Forecasting Methodology is strained compared to existing cylindrical shell elastic stress, the present invention takes into account influence of the hydrogen environment to cylindrical shell ess-strain, has some reference value to engineering design.
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 stress strain 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 response be the problem of design hydrogen container, hydrogenation reactor must take into consideration when hydrogen-contacting equipments.Due to this structure of hydrogen damage
The complexity of relation, the method for existing mechanical response of the prediction material under hydrogen environment to the competency profiling of researcher very
Height, while need a large amount of programing works, it is difficult to it is promoted in engineering.Also without occurring facing hydrogen cylindrical shell stress dedicated for prediction
The method of strain.Therefore propose that a kind of method that hydrogen cylindrical shell ess-strain 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 a kind of to use atmospheric environment cylinder bullet
Property ess-strain prediction face hydrogen cylindrical shell elastic stress strain method.
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 providing one kind faces the strain of hydrogen heavy wall cylindrical shell elastic stress
Forecasting Methodology, this method strain to predict the elasticity for facing hydrogen cylindrical shell based on the cylindrical shell elastic stress in classical atmospheric environment
Ess-strain.
The purpose of the present invention is what is be achieved through the following technical solutions：One kind faces the strain of hydrogen heavy wall cylindrical shell elastic stress
Forecasting Methodology, this method comprises the following steps：
Step 1：The circumferential stress σ of heavy wall cylindrical shell is calculated according to the following formulaθAnd radial stress σr：
Wherein a is cylindrical shell inside radius, and b is cylindrical shell outer radius, and p is inner pressuring load, and r is to need to ask for ess-strain
Position.
Step 2：Below equation group is solved, calculates hydrogen concentration c：
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 3：Calculate axial stress σz
Step 4：Calculate circumferential strain εθAnd radial strain εr
Further, the step 2 uses Newton Algorithm hydrogen concentration c, specifically includes following sub-step：
Step 201：Hydrogen concentration initial value c=c is set0；
Step 202：According to current hydrogen concentration c, parameters are calculated according to the following formula：
Step 203：Calculate following functional value g：
Step 204：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 εerrFor convergence tolorence, ε can useerr=10-6；
Step 205：Hydrogen concentration c is calculated according to the following formula1
Wherein
Step 206：Make c=c1, return to step 202.
The present invention has the following advantages：Using the method for solving Nonlinear System of Equations, according to the cylindrical shell being easy to get in air
The elastic stress strain of cylindrical shell under hydrogen environment is directly predicted in elastic stress strain in environment, need not write complicated hydrogen loss
Hinder the finite element program of material constitutive model, it is relatively low using threshold.
Description of the drawings
Fig. 1 is the objective for implementation schematic diagram of the present invention；
Fig. 2 is distribution of the stress that is calculated of present example on different radii；
Fig. 3 is distribution of the strain that is calculated of present example on different radii.
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 a both ends constraint, and inside radius and outer radius are respectively a and b, are held
By constant internal pressure load p, concentration is c under unstress state0Hydrogen be uniformly distributed in cylindrical shell.The present invention can predict
Stress and strain of the cylindrical shell under internal pressure p effects in hydrogen environment.
The material parameter and geometric parameter that 1 example of table is used
The realization process of the method for the present invention is as follows：
Step 1：Choose a radius r (a≤r≤b), such as take r=a, by the inside radius a in table 1, outer radius b and
Inner pressuring load p brings the circumferential stress σ that the following formula calculates heavy wall cylindrical shell intoθAnd radial stress σr：
Step 2：Below equation group is solved, calculates hydrogen concentration c：
Wherein each parameter is listed in Table 1 below, and step 2 specifically includes following sub-step：
Step 201：Hydrogen concentration initial value c=c is set0；
Step 202：Following formula is brought into according to current hydrogen concentration c and calculates parameters：
Step 203：The parameter that step 202 is obtained brings following functional value into, calculates functional value g：
Step 204：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 205：Hydrogen concentration c is calculated according to the following formula1
Wherein
Required each parameter is calculated by step 202；
Step 206：Make c=c1, return to step 202.
Step 3：It brings the hydrogen concentration c that step 2 obtains into following formulas and calculates axial stress σz
Step 4：The circumferential stress σ that step 1 and step 3 are obtainedθ, radial stress σrWith axial stress σzBring following formula meter into
Calculate circumferential strain εθAnd radial strain εr
The stress and strain that repeating step 1 to step 4 using different r values can be calculated in whole cross section is distributed,
As a result as shown in Figure 2 and Figure 3, in addition it can be seen that distribution of the hydrogen concentration in cylindrical shell is uniform.
Claims (2)
1. a kind of Forecasting Methodology for facing the strain of hydrogen heavy wall cylindrical shell elastic stress, which is characterized in that this method comprises the following steps：
Step 1：The circumferential stress σ of heavy wall cylindrical shell is calculated according to the following formulaθAnd radial stress σr：
<mrow>
<msub>
<mi>&sigma;</mi>
<mi>&theta;</mi>
</msub>
<mo>=</mo>
<mfrac>
<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>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<msup>
<mi>b</mi>
<mn>2</mn>
</msup>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>&sigma;</mi>
<mi>r</mi>
</msub>
<mo>=</mo>
<mfrac>
<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>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mfrac>
<msup>
<mi>b</mi>
<mn>2</mn>
</msup>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
WhereinFor cylindrical shell inside radius, b is cylindrical shell outer radius, and p is inner pressuring load, and r is to need to ask for the position of ess-strain
It puts；
Step 2：Below equation group is solved, calculates hydrogen concentration c：
<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>
<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>
<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>
Wherein, E be material elasticity modulus, ν be material Poisson's ratio, VHRepresent partial molar volume of the hydrogen in base material, VMFor mother
The molal volume of material, α be per unit lattice hydrogen trap number, the interstitial void binding site number of β per unit lattices, NL=NA/VM
For the metallic atom quantity of per unit volume, NAFor Avgadro constant, NTRepresent the trap number of per unit volume；R is reason
Think gas constant, T is Kelvin's thermometric scale, c0For no-load when cylindrical shell in hydrogen concentration, WBFor the hydrogen trap combination energy of material；
Step 3：Calculate axial stress σz
<mrow>
<msub>
<mi>&sigma;</mi>
<mi>z</mi>
</msub>
<mo>=</mo>
<mi>v</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&sigma;</mi>
<mi>&theta;</mi>
</msub>
<mo>+</mo>
<msub>
<mi>&sigma;</mi>
<mi>r</mi>
</msub>
<mo>)</mo>
</mrow>
<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>
Step 4：Calculate circumferential strain εθAnd radial strain εr
<mrow>
<msub>
<mi>&epsiv;</mi>
<mi>&theta;</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>E</mi>
</mfrac>
<msub>
<mi>&sigma;</mi>
<mi>&theta;</mi>
</msub>
<mo>-</mo>
<mfrac>
<mi>v</mi>
<mi>E</mi>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>&sigma;</mi>
<mi>r</mi>
</msub>
<mo>+</mo>
<msub>
<mi>&sigma;</mi>
<mi>z</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<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>&epsiv;</mi>
<mi>r</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>E</mi>
</mfrac>
<msub>
<mi>&sigma;</mi>
<mi>r</mi>
</msub>
<mo>-</mo>
<mfrac>
<mi>v</mi>
<mi>E</mi>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>&sigma;</mi>
<mi>&theta;</mi>
</msub>
<mo>+</mo>
<msub>
<mi>&sigma;</mi>
<mi>z</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<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>
<mo>.</mo>
</mrow>
2. a kind of Forecasting Methodology for facing the strain of hydrogen heavy wall cylindrical shell elastic stress according to claim 1, which is characterized in that
The step 2 uses Newton Algorithm hydrogen concentration c, specifically includes following sub-step：
Step 201：Hydrogen concentration initial value c=c is set0；
Step 202：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 203：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 204：Judge g value sizes, if | g | >=εerr, then step 205 is performed to step 206, is otherwise terminated to calculate, is obtained hydrogen
Concentration c, wherein εerrFor convergence tolorence, ε can useerr=10-6；
Step 205：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 206：Make c=c1, return to step 202.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610670679.4A CN106295021B (en) | 2016-08-15 | 2016-08-15 | A kind of Forecasting Methodology for facing the strain of hydrogen heavy wall cylindrical shell elastic stress |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610670679.4A CN106295021B (en) | 2016-08-15 | 2016-08-15 | A kind of Forecasting Methodology for facing the strain of hydrogen heavy wall cylindrical shell elastic stress |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106295021A CN106295021A (en) | 2017-01-04 |
| CN106295021B true CN106295021B (en) | 2018-05-29 |
Family
ID=57670685
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610670679.4A Active CN106295021B (en) | 2016-08-15 | 2016-08-15 | A kind of Forecasting Methodology for facing the strain of hydrogen heavy wall cylindrical shell elastic stress |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106295021B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR102085134B1 (en) * | 2018-06-01 | 2020-03-05 | 경희대학교 산학협력단 | A method for determining average radial stress and pressure vs. volume relationship of a compressible material |
| CN110727997B (en) * | 2019-09-20 | 2020-06-23 | 湖北省工业建筑集团有限公司 | Method for calculating stability of metal cylindrical shell |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2002342694A (en) * | 2001-05-17 | 2002-11-29 | Araco Corp | Method and device for structural analysis of elastic material |
| CN101323247A (en) * | 2008-07-11 | 2008-12-17 | 清华大学 | Dilution device for fuel battery passenger car discharging hydrogen concentration |
| CN102141466A (en) * | 2010-12-21 | 2011-08-03 | 浙江大学 | Boundary simulation device and method for thin-walled cylindrical shell structure experiment |
| 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 |
-
2016
- 2016-08-15 CN CN201610670679.4A patent/CN106295021B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2002342694A (en) * | 2001-05-17 | 2002-11-29 | Araco Corp | Method and device for structural analysis of elastic material |
| CN101323247A (en) * | 2008-07-11 | 2008-12-17 | 清华大学 | Dilution device for fuel battery passenger car discharging hydrogen concentration |
| 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 |
Non-Patent Citations (1)
| Title |
|---|
| 多层不等厚组合圆柱壳屈曲数值模拟分析;陈志平 等;《浙江大学学报（工学版）》;20090930;第43卷(第9期);第1679-1683页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106295021A (en) | 2017-01-04 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Wu et al. | A phase-field regularized cohesive zone model for hydrogen assisted cracking | |
| Wierzbicki et al. | Homogenized mechanical properties for the jellyroll of cylindrical Lithium-ion cells | |
| Greve et al. | Mechanical testing and macro-mechanical finite element simulation of the deformation, fracture, and short circuit initiation of cylindrical Lithium ion battery cells | |
| Jivkov et al. | Pore space and brittle damage evolution in concrete | |
| CN106295021B (en) | A kind of Forecasting Methodology for facing the strain of hydrogen heavy wall cylindrical shell elastic stress | |
| Bradford et al. | The Bree problem with different yield stresses on-load and off-load and application to creep ratcheting | |
| CN106372273B (en) | One kind faces hydrogen heavy wall cylindrical shell elastic limit loading prediction method | |
| Liu et al. | Effects of reeling on pipe structural performance—Part II: Analysis | |
| Ando et al. | Comparison and assessment of the creep-fatigue evaluation methods with notched specimen made of Mod. 9Cr-1Mo steel | |
| Zheng et al. | Damage performance analysis of prestressed concrete containments following a loss of coolant accident considering different external temperatures | |
| Hwang et al. | Evaluation of flow stresses of tubular materials considering anisotropic effects by hydraulic bulge tests | |
| Hagihara et al. | Finite element analysis for creep failure of coolant pipe in light water reactor due to local heating under severe accident condition | |
| CN105205342A (en) | Method of determining limit load of high temperature pressure pipeline | |
| Kwon et al. | Optimization of gap sizes for the high performance of annular nuclear fuels | |
| Jinjin et al. | Hydrogen-induced attractive force between two partials of edge dislocation in nickel | |
| Fatemi et al. | End boundary effects on local buckling response of high strength linepipe | |
| CN109800458A (en) | A method of assessment reactor safety operation | |
| Qin et al. | Thermal Stress Modeling and Analysis of Packed-bed Thermocline Energy Storage Tank for INL Thermal Energy Distribution System (TEDS) | |
| RU2526856C1 (en) | Imitator of fuel element of nuclear reactor | |
| Jiang et al. | A noncyclic method for determination of accumulated strain in stainless steel 304 pressure vessels | |
| Perl | Thermal simulation of an arbitrary residual stress field in a fully or partially autofrettaged thick-walled spherical pressure vessel | |
| Nicolici et al. | Experimental and numerical testing of an innovative steam generator tube plugging procedure | |
| Kuroda et al. | Dynamics and generation of stress waves in cracked graphite moderator bricks | |
| Abdelmeguid et al. | Modeling Sequence of Earthquakes and Aseismic Slip (SEAS) in Complex Faults Zones Using a Computationally Efficient Numerical Algorithm | |
| Nie et al. | Nonlinear seismic correlation analysis of the JNES/NUPEC large-scale piping system tests |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |