CN106096134B - Structural Metallic Fatigue fail-safe analysis and optimum design method based on damage mechanics - Google Patents
Structural Metallic Fatigue fail-safe analysis and optimum design method based on damage mechanics Download PDFInfo
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Abstract
The invention discloses a kind of Structural Metallic Fatigue fail-safe analysis and optimum design method based on damage mechanics.First against the easy key metal structure that fatigue occurs, utilize interval vector metrology structure and material and the uncertainty of impairment parameter, parametrization geometry and finite element model are established, fatigue life interval range is calculated in conjunction with interval Finite Element Method and damage mechanics finite element method；The Analysis on Fatigue Reliability of structure is further realized using non-probability interval interference theory；Finally using structure size as design variable, reliability is constraint condition, and construction weight realizes complete Optimized Iterative process by global optimization approach for objective function, and the optimal design variable result of output algorithm search is as final Optimal Structure Designing scheme.The fail-safe analysis and optimization method that the present invention establishes overcome scheme itself to the sensibility of design parameter, can reach requirement by important minimum and fatigue reliability under the conditions of structure meets and carries, design scheme is more economically reasonable.
Description
Technical field
The present invention relates to fatigue fracture and damage mechanics field, in particular to a kind of metal structure based on damage mechanics is tired
Labor fail-safe analysis and optimum design method, the invention are to consider that uncertain effect is lower based on damage mechanics finite element and non-general
Fatigue life reliability analysis and optimization design of the rate interval Finite Element Method in conjunction under.The invention can be engineering structure Anti fatigue Design
Reference is provided.
Background technique
In the various failure modes of structure, fatigue is one of main reason of structural failure and structural reliability
Test the main factor to be considered.In many cases, fatigue rupture can bring catastrophic consequence.Such as 1952
Year, the jet-propelled comet passenger plane of first comes into operation after taking a flight test more than 300 hours, and in 1954, awing accident was fallen suddenly
Enter Mediterranean, identified is as caused by the fatigue rupture of pressure chamber.Related document has been pointed out " since the eighties, since metal is tired
Fatal crass's major accident caused by labor is broken, 100 times every year on average ".It can be seen that carrying out analysis of fatigue to structure has weight
Want meaning.
When application damage mechanics FInite Element carries out analysis of fatigue, key step includes the determination of load, damage development
The determination of equation and the fitting of impairment parameter.But during calculating and the various influences useless in view of fatigue behaviour because
Element, for example, load level fluctuation, structure size effect, surface smoothness, process of surface treatment, temperature and hygrothermal environment and
Stress collection medium influence.These factors can be considered as the influence of material and structural uncertainty to fatigue life dispersibility.?
In conventional optimization process, load, structural parameters locating for structure and design requirement are treated as certainty form, however design
Obtained result is not often consistent with actual conditions, and scheme itself is very sensitive to design parameter.With uncertain structure point
The development of analysis method, the design concept of reliability optimization gradually replace traditional deterministic optimization, become Future Projects design
Inexorable trend.
Damage mechanics finite element and interval Finite Element Method are combined, it is established that meet the Optimized model needs of reliability index
Know load history range, geometrical parameters and impairment parameter range and the constant interval in relation to material property parameter.It is first
It is first to obtain fatigue life change according to load and geometry calculation stress strain response, then by material property application damage model
Change range, then Given Life design condition and calculated life span carry out Multidisciplinary systems analysis, finally realize knot
Structure optimization.Compared with the conventional method based on test, the calculating of finite element fatigue reliability can provide part life to be distributed, it
The quantity that experimental prototype can be reduced shortens the development cycle of product, and then reduces development cost, can greatly improve design effect
Rate.Therefore, the content of present invention has significant realistic meaning.
Summary of the invention
The technical problem to be solved by the present invention is overcoming the deficiencies of the prior art and provide a kind of gold based on damage mechanics
Belong to Fatigue Reliability Analysis and optimum design method.The present invention fully consider in Practical Project problem it is generally existing not really
Qualitative factor, analyzes uncertainty propagation problem with the non-probability interval vertex method of proposition, interferes mould according to non-probability interval
Type establishes reliability index, searches for obtain optimization design scheme by optimization algorithm.
The technical solution adopted by the present invention are as follows: a kind of Structural Metallic Fatigue fail-safe analysis based on damage mechanics and optimization
Design method realizes that steps are as follows:
Step 1: according to the geometrical characteristic of engineering structure, at the easy key position that fatigue occurs, for the length of rod piece
The size for spending the diameter D of l, the thickness B of plate, aperture or connecting shaft optimizes, and variable is denoted as x=(x1,x2,…xn),
Wherein xiIndicate that any one geometrical characteristic information, structure size allow to fluctuate in a certain range, i.e. xi∈[ximin,
ximax], i=1,2 ..., n, the value of each group of design variable correspond to a kind of design scheme, each dimension information is given just
Beginning design value；
Step 2: utilizing interval vector f=(f1,f2,…fm) rationally characterization structural parameters uncertain information, here not
Determine parameter fi, the bound section value of i=1,2 ..., m can indicate are as follows:
Wherein, subscript U represents the value upper bound of parameter, and subscript L represents the value lower bound of parameter, and subscript c represents parameter
Central value, subscript r represent the radius of parameter；
Step 3: establishing the geometrical model of structure, realized in Geometric Modeling when design variable changes in feasible region
When auto-building model, utilize CAD software it is macro record it is achievable based on design variable geometric parameterization modeling.Further will
CAD model gets up with CAE analysis software context, realizes parameterized mesh, cell attribute assignment, material based on finite element software
Expect attribute assignment, boundary condition setting.According to selected design variable, the update of entire set of parameters model is completed；
Step 4: selection damage evolution model, according to the fatigue test value of the material query criteria test specimen of optimized structure
It is fitted damage evolution equation parameter.General damage evolution equation can be expressed as form:
Wherein, D is the scalar injury tolerance changed between 0 to 1, and E is elasticity modulus, and N is fatigue life, σmaxFor unit
Equivalent stress, σthFor stress threshold value, b and m are the impairment parameters for needing to be fitted.By σmaxIt is regarded as the point on S-N curve with N,
σthFatigue stress limits intensity is taken, injury tolerance D is in 0 to 1 upper integral, then damage evolution equation can be expressed as:
There was only impairment parameter b and m in above formula is unknown quantity, enables a=EmThe both sides /b ((3/2) m+1) take residual error after logarithm
It may be expressed as:
Then n point on i.e. desirable S-N curve finds out corresponding impairment parameter with residual error minimum；
Step 5: damage mechanics FInite Element program is write using finite element secondary development, when relative damage degree is maximum
The injury tolerance accumulation of unit extracts structure fatigue life N and mass M to i.e. decision structure fatigue rupture after 1；
It is combined step 6: non-probability is not known vertex and propagates analytic approach with damage mechanics finite element, section is not true
Determine variable and substitute into the bound for obtaining fatigue life in structural fatigue finite element analysis, is expressed asNWithVertex, which is propagated, to be divided
Analysis method may be expressed as:
Wherein,The set of vertices conjunction value of uncertain variables is respectively indicated,fi WithRespectively
Indicate lower bound and the upper bound of uncertain variables；
Step 7: according to the structure Multidisciplinary systems model foundation Analysis on Fatigue Reliability index based on interval variable,
It interferes section that can indicate are as follows:
Wherein, fi IIndicate the interval range of i-th of uncertain variables, NIIt indicates containing uncertain damage mechanics finite element meter
Obtained service life interval range, SIThe design fatigue life range for indicating structure carries out section by the service ability of structure
Planning value obtains.M (R, S)=N-S=0 is taken for limiting condition plane, is failed by the non-Making by Probability Sets that Interference Model defines
Degree can be expressed as:
Wherein, FreliabilityIndicate Fatigue Reliability, δNWith δSRespectively indicate the standardization of mathematic(al) expectation and projected life
Space δN=(N-Nc)/NrWith δS=(S-Sc)/Sr, SSecurity domainIndicate the area of security domain, SAlwaysIndicate the gross area；
Step 8:, using weight as optimization aim, constructing engineering knot for design variable using reliability as constraint condition
Structure fatigue life mathematical optimization models.Complete Optimized Iterative process is realized with global optimization approach, until algorithm stop criterion is full
Foot, i.e., reach convergence in global optimizing, and the optimal design variable result of output algorithm search is set as final structure optimization
Meter scheme.
Wherein, structure size allows to fluctuate in a certain range in the first step, which is generally dependent on engineering
Experience and project cost, the size cannot change the geometrical characteristic of structure.
Wherein, it also may indicate that in the second step using the uncertainty of interval vector characterization structural parameters are as follows:
F=[fL,fU]=[fc-fr,fc+fr]
=fc+fr[-1,1]
=fc+fr×e
Wherein, uncertain parameter fi, i=1,2 ..., m can indicate structure size, elasticity modulus of materials, density, load
With the Damage Parameter of damage evolution equation etc..e∈Ξm, ΞmIt is defined as m dimensional vector set of all elements in [- 1,1],
Symbol "×" is defined as the operator that each corresponding element of two vectors is multiplied, and product is still the vector that dimension is m.
Wherein, the least square method that impairment parameter is fitted in the 4th step can be adapted for arbitrary damaged metal and develop
Equation, the selection of damage evolution equation is generally according to the type of attachment of structure and load situation.
Wherein, when carrying out damage mechanics finite element analysis in the 5th step, it should by the initial damage degree of all units
It is disposed as zero, and the maximum equivalent using the unit Vonmises stress being calculated as unit under external applied load.Meter
Continuous accumulation superpositing unit injury tolerance during calculating, thinks fatigue destruction when judging any cell injury tolerance to 1.
Wherein, the vertex scheme that interval propagation analysis is introduced in the 6th step, selects the vertex bound of uncertain parameter
It carries out non-probabilistic uncertainty and propagates analysis, must assure that the problem of studied is single when introducing vertex scheme and carrying out and propagate analysis
It adjusts, for damage mechanics finite element analysis fatigue life as the increase injury tolerance of the number of iterations and service life are monotonic increases
's.
Wherein, tired Multidisciplinary systems index is defined in the 7th step, utilizes the volume of structure security domain and basic
The ratio between the total volume in interval variable domain is measured as structural reliability, realizes the Multidisciplinary systems analysis and optimization of constraint condition
Design.
The advantages of the present invention over the prior art are that:
(1), perfect researchs of the damage mechanics in terms of uncertainty of the present invention establish damage mechanics and calculate the tired longevity
Order non-probability interval Reliability Analysis Theory.
(2), the present invention realizes the Anti-Fatigue Optimization Design to engineering structure by global optimization approach, can mention for design
For instructing and referring to, Structural Design and experimentation cost are saved.
(3), the present invention had both considered the uncertain of material parameter, it is contemplated that the uncertainty of damage model, for tired
The research of labor dispersibility more refines, and rationally expresses structural parameters to the influence degree of fatigue life.
(4), the non-probability interval vertex analysis method that the present invention uses can be for all damage evolution models, relatively
It is more convenient that uncertain propagation problem is analyzed in the probabilistic method for needing clear expression formula traditional.
Detailed description of the invention
Fig. 1 is the present invention for Structural Metallic Fatigue fail-safe analysis and optimum design method process based on damage mechanics
Figure；
Fig. 2 is flow chart of the present invention about impairment parameter fitting；
Fig. 3 is the non-probability Interference Model schematic diagram of the present invention；
Fig. 4 is the standardised space schematic diagram that the present invention is directed to reliability of service life model, wherein Fig. 4 (a) is critical shape
State, Fig. 4 (b) are interference region；
Fig. 5 is the size of initial designs containing orifice plate and structural schematic diagram in the embodiment of the present invention；
Fig. 6 is to optimize structural schematic diagram in Isight software in the embodiment of the present invention；
Fig. 7 is plate a quarter finite element model figure in the embodiment of the present invention；
Fig. 8 is the iteration convergence curve that the present invention is directed to embodiment optimization process.
Specific embodiment
With reference to the accompanying drawing and specific embodiment further illustrates the present invention.
As shown in Figure 1, the Structural Metallic Fatigue fail-safe analysis that the invention proposes a kind of based on damage mechanics and optimization
Design method, comprising the following steps:
(1) according to the geometrical characteristic of engineering structure, at the easy key position that fatigue occurs, such as length l, the plate of rod piece
Thickness B, aperture or connecting shaft diameter D equidimension optimize, variable is denoted as x=(x1,x2,…xn), wherein xi
Indicate any one geometrical characteristic information.In general, structure size allows to fluctuate in a certain range, i.e. xi∈[ximin,
ximax], i=1,2 ..., n, the value of each group of design variable correspond to a kind of design scheme, each dimension information is given just
Beginning design value；
(2) interval vector f=(f is utilized1,f2,…fm) rationally characterization structural parameters uncertain information, do not know here
Parameter fi, the bound section value of i=1,2 ..., m can indicate are as follows:
Wherein, subscript U represents the value upper bound of parameter, and subscript L represents the value lower bound of parameter, and subscript c represents parameter
Central value, subscript r represent the radius of parameter；
(3) geometrical model for establishing structure realizes the mould when design variable changes in feasible region in Geometric Modeling
Type automatically generates, and records the achievable geometric parameterization modeling based on design variable using CAD software is macro.Further by CAD mould
Type gets up with CAE analysis software context, realizes parameterized mesh, cell attribute assignment, material category based on finite element software
Property assignment, boundary condition setting.According to selected design variable, the update of entire set of parameters model is completed；
(4) damage evolution model is selected, is fitted according to the fatigue test value of the material query criteria test specimen of optimized structure
Damage evolution equation parameter.General damage evolution equation can be expressed as form:
Wherein, D is the scalar injury tolerance changed between 0 to 1, and E is elasticity modulus, and N is fatigue life, σmaxFor unit
Equivalent stress, σthFor stress threshold value, b and m are the impairment parameters for needing to be fitted.By σmaxIt is regarded as the point on S-N curve with N,
σthFatigue stress limits intensity is taken, injury tolerance D is in 0 to 1 upper integral, then damage evolution equation can be expressed as:
There was only impairment parameter b and m in above formula is unknown quantity, enables α=EmThe both sides /b ((3/2) m+1) take residual error after logarithm
It may be expressed as:
Then n point on i.e. desirable S-N curve finds out corresponding impairment parameter, detailed process such as Fig. 2 institute with residual error minimum
Show；
(5) damage mechanics FInite Element program is write using finite element secondary development, when the maximum unit of relative damage degree
Injury tolerance accumulation to i.e. decision structure fatigue rupture after 1, extract structure fatigue life N and mass M；
(6) non-probability is not known vertex propagation analytic approach to combine with damage mechanics finite element, by the uncertain change in section
Amount substitutes into the bound that fatigue life is obtained in structural fatigue finite element analysis, is expressed asNWithPropagate analytic approach in vertex
It may be expressed as:
Wherein,The set of vertices conjunction value of uncertain variables is respectively indicated,fi WithRespectively
Indicate lower bound and the upper bound of uncertain variables；
(7) it according to the structure Multidisciplinary systems model foundation Analysis on Fatigue Reliability index based on interval variable, does
Relating to section can indicate are as follows:
Wherein, fi IIndicate the interval range of i-th of uncertain variables, NIIt indicates containing uncertain damage mechanics finite element meter
Obtained service life interval range, SIThe design fatigue life range for indicating structure, can generally pass through the service ability of structure
Interval Programming value is carried out to obtain.M (R, S)=N-S=0 is taken for limiting condition plane, the non-probability defined by Interference Model
Set failure degree can be expressed as:
Wherein, FreliabilityIndicate Fatigue Reliability, δNWith δSRespectively indicate the standardization of mathematic(al) expectation and projected life
Space δN=(N-Nc)/NrWith δS=(S-Sc)/Sr, SSecurity domainIndicate the area of security domain, SAlwaysIndicate the gross area, Fig. 3 illustrates whole
A non-probability interval Interference Model, Fig. 4 illustrate the area ratio calculation method of reliability；
(8) tired for design variable building engineering structure using weight as optimization aim using reliability as constraint condition
Labor life optimization design model.Complete Optimized Iterative process is realized with global optimization approach, until algorithm stop criterion meets, i.e.,
Reach convergence in global optimizing, the optimal design variable result of output algorithm search is as final Optimal Structure Designing side
Case.
Embodiment:
The characteristics of in order to more fully illustrate the invention, the present invention are directed to standard metal fatigue structural member mould shown in fig. 5
Type is carried out based on the non-probability interval fail-safe analysis of damage mechanics and optimization design.The rectangular slab material is LY12CZ aluminium alloy,
Material chemical composition is as shown in table 1 below.Initial designs size length and width, the center hole diameter of plate be respectively 210mm,
100mm, 10mm, load are that both ends 150MPa is evenly distributed with tensile stress, stress ratio 0.2.FEM meshing is as shown in Figure 7.It presses
According to the content of foregoing invention description, with plate with a thickness of design variable, reliability is greater than 0.95 and is used as constraint condition, plate matter
Minimum objective function is measured, analysis is iterated with the optimization process application ASA global optimization approach of Fig. 6.
Table 1
The laboratory manual of query criteria obtains the S-N curve of respective material, the expression formula of curve be N=6.997421 ×
107(S-124)-1.274268, infinite life corresponding stress value is 127MPa.The damage being fitted according to method shown in Fig. 2
EVOLUTION EQUATION parameter, and it is as shown in table 2 below to the uncertain information of model and impairment parameter.
Table 2
The embodiment has carried out fail-safe analysis and optimization design to the hardened structure containing 4 parameter uncertainty information,
Fig. 8 illustrates the convergence curve of Optimized Iterative process, finally obtained optimal solution are as follows: and 1.74 millimeters of thickness, reliability 0.9505,
With 27.467 grams of quality.In conclusion the present invention utilizes the uncertain information of section process characterization parameter, section vertex is introduced not
It determines that the analysis that spreads through sex intercourse has obtained service life interval range, and introduces Multidisciplinary systems analysis method, calculated by global optimization
Method has obtained the optimal design thickness of plate.
The above is only specific steps of the invention, are not limited in any way to protection scope of the present invention；Its is expansible to answer
Structural life-time field, all technical sides formed using equivalent transformation or equivalent replacement are predicted for uncertain damage mechanics
Case is all fallen within rights protection scope of the present invention.
Part of that present invention that are not described in detail belong to the well-known technology of those skilled in the art.
Claims (7)
1. Structural Metallic Fatigue fail-safe analysis and optimum design method based on damage mechanics, it is characterised in that realize step such as
Under:
Step 1: according to the geometrical characteristic of engineering structure, at the easy key position that fatigue occurs, for rod piece length l,
The size of the diameter D of the thickness B of plate, aperture or connecting shaft optimize, and variable is denoted as x=(x1,x2,…xn), wherein
xiIndicate that any one geometrical characteristic information, structure size allow to fluctuate in a certain range, i.e. xi∈[ximin,ximax], i
=1,2 ..., n, the value of each group of design variable correspond to a kind of design scheme, each dimension information gives initial designs
Value；
Step 2: utilizing interval vector f=(f1,f2,…fm) rationally characterization structural parameters uncertain information, do not know here
Parameter fi, the bound section value of i=1,2 ..., m can indicate are as follows:
Wherein, subscript U represents the value upper bound of parameter, and subscript L represents the value lower bound of parameter, and subscript c represents the center of parameter
Value, subscript r represent the radius of parameter；
Step 3: establishing the geometrical model of structure, the mould when design variable changes in feasible region is realized in Geometric Modeling
Type automatically generates, and the achievable geometric parameterization modeling based on design variable is recorded using CAD software is macro, further by CAD mould
Type gets up with CAE analysis software context, realizes parameterized mesh, cell attribute assignment, material category based on finite element software
Property assignment, boundary condition setting the update of entire set of parameters model completed according to selected design variable；
Step 4: selection damage evolution model, is fitted according to the fatigue test value of the material query criteria test specimen of optimized structure
Damage evolution equation parameter, damage evolution equation can be expressed as form:
Wherein, D is the scalar injury tolerance changed between 0 to 1, and E is elasticity modulus, and N is fatigue life, σmaxIt is equivalent for unit
Stress, σthFor stress threshold value, b and m are the impairment parameters for needing to be fitted, by σmaxThe point on S-N curve, σ are regarded as with NthIt takes
Fatigue stress limits intensity, injury tolerance D is in 0 to 1 upper integral, then damage evolution equation can be expressed as:
There was only impairment parameter b and m in above formula is unknown quantity, enables a=EmThe both sides /b ((3/2) m+1) take residual error after logarithmIt can indicate
Are as follows:
Then n point on i.e. desirable S-N curve finds out corresponding impairment parameter with residual error minimum；
Step 5: damage mechanics FInite Element program is write using finite element secondary development, when the maximum unit of relative damage degree
Injury tolerance accumulation to i.e. decision structure fatigue rupture after 1, extract structure fatigue life N and mass M；
It is combined step 6: non-probability is not known vertex and propagates analytic approach with damage mechanics finite element, by the uncertain change in section
Amount substitutes into the bound that fatigue life is obtained in structural fatigue finite element analysis, is expressed asNWithPropagate analytic approach in vertex
It may be expressed as:
Wherein,The set of vertices conjunction value of uncertain variables is respectively indicated,fi WithIt respectively indicates under uncertain variables
Boundary and the upper bound, i=1,2 ..., m；
Step 7: being done according to the structure Multidisciplinary systems model foundation Analysis on Fatigue Reliability index based on interval variable
Relating to section can indicate are as follows:
Wherein, fi IIndicate the interval range of i-th of uncertain variables, NIIt indicates to obtain containing uncertain damage mechanics FEM calculation
The service life interval range arrived, SIThe design fatigue life range for indicating structure carries out Interval Programming by the service ability of structure
Value obtains, and takes M (N, S)=N-S=0 for limiting condition plane, can by the non-Making by Probability Sets failure degree that Interference Model defines
Expression are as follows:
Wherein, FreliabilityIndicate Fatigue Reliability, δNWith δSRespectively indicate the standardised space δ of mathematic(al) expectation and projected lifeN
=(N-Nc)/NrWith δS=(S-Sc)/Sr, SSecurity domainIndicate the area of security domain, SAlwaysIndicate the gross area；
Step 8: using reliability as constraint condition, it is tired for design variable building engineering structure using weight as optimization aim
Labor life optimization design model realizes complete Optimized Iterative process with global optimization approach, until algorithm stop criterion meets, i.e.,
Reach convergence in global optimizing, the optimal design variable result of output algorithm search is as final Optimal Structure Designing side
Case.
2. the Structural Metallic Fatigue fail-safe analysis and optimum design method according to claim 1 based on damage mechanics,
It is characterized by: structure size allows to fluctuate in a certain range in the first step, the range depend on engineering experience with
And project cost, the size cannot change the geometrical characteristic of structure.
3. the Structural Metallic Fatigue fail-safe analysis and optimum design method according to claim 1 based on damage mechanics,
It is characterized by: also may indicate that in the second step using the uncertainty of interval vector characterization structural parameters are as follows:
F=[fL,fU]=[fc-fr,fc+fr]
=fc+fr[-1,1]
=fc+fr×e
Wherein, uncertain parameter fi, i=1,2 ..., m can indicate structure size, elasticity modulus of materials, density, load and damage
The Damage Parameter of EVOLUTION EQUATION, e ∈ Ξm, ΞmIt is defined as m dimensional vector set of all elements in [- 1,1], symbol "×"
It is defined as the operator that each corresponding element of two vectors is multiplied, product is still the vector that dimension is m.
4. the Structural Metallic Fatigue fail-safe analysis and optimum design method according to claim 1 based on damage mechanics,
It is characterized by: the least square method that impairment parameter is fitted in the 4th step can be adapted for arbitrary damaged metal evolution side
Journey, the selection of damage evolution equation is according to the type of attachment and load situation of structure.
5. the Structural Metallic Fatigue fail-safe analysis and optimum design method according to claim 1 based on damage mechanics,
It is characterized by: when carrying out damage mechanics finite element analysis in the 5th step, it should which the initial damage degree of all units is equal
It is set as zero, and the maximum equivalent using the unit Vonmises stress being calculated as unit under external applied load；It calculates
Continuous accumulation superpositing unit injury tolerance in the process, thinks fatigue destruction when judging any cell injury tolerance to 1.
6. the Structural Metallic Fatigue fail-safe analysis and optimum design method according to claim 1 based on damage mechanics,
It is characterized by: in the 6th step introduce interval propagation analysis vertex scheme, select the vertex bound of uncertain parameter into
Row non-probabilistic uncertainty propagates analysis, must assure that the problem of studied is dull when introducing vertex scheme and carrying out and propagate analysis
, for damage mechanics finite element analysis fatigue life as the increase injury tolerance of the number of iterations and service life are monotonic increases
's.
7. the Structural Metallic Fatigue fail-safe analysis and optimum design method according to claim 1 based on damage mechanics,
It is characterized by: defining tired Multidisciplinary systems index, volume and base region using structure security domain in the 7th step
Between the ratio between the total volume of scope of a variable measured as structural reliability, realize that the Multidisciplinary systems analysis and optimization of constraint condition is set
Meter.
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| CN113111562B (en) * | 2021-05-19 | 2022-12-23 | 中国船舶重工集团海装风电股份有限公司 | Wind turbine generator main frame optimization design method based on deformation technology |
| CN114492145B (en) * | 2022-03-31 | 2022-08-09 | 江铃汽车股份有限公司 | Structural member static strength analysis method and system based on CAE |
| CN117709171A (en) * | 2024-02-06 | 2024-03-15 | 中南大学 | High cycle fatigue failure numerical simulation method and system |
| CN117876053B (en) * | 2024-03-11 | 2024-05-28 | 浙江立兴造价师事务所有限责任公司 | Intelligent mapping method and system for engineering cost |
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| CN105653794A (en) * | 2015-12-30 | 2016-06-08 | 北京航空航天大学 | Time-variant reliability design method for rectangular plate structure with initial defects |
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| JP2010009595A (en) * | 2008-06-24 | 2010-01-14 | Livermore Software Technology Corp | Sampling strategy using genetic algorithm (ga) for optimizing engineering design |
| CN103344514A (en) * | 2013-07-05 | 2013-10-09 | 北京航空航天大学 | High-cycle fatigue and low-intensity impact coupled damage calculation method based on nominal stress method |
| CN105653794A (en) * | 2015-12-30 | 2016-06-08 | 北京航空航天大学 | Time-variant reliability design method for rectangular plate structure with initial defects |
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