CN109284574A - A kind of series connection truss structure system Multidisciplinary systems analysis method - Google Patents
A kind of series connection truss structure system Multidisciplinary systems analysis method Download PDFInfo
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Abstract
The invention discloses a kind of series connection truss structure system Multidisciplinary systems analysis methods, comprising steps of the power function of one, determining series connection each failure mode of truss structure system；Two, the multidimensional ellipsoidal model for describing uncertain variable is established；Three, the multidimensional for obtaining uncertain variable normalizes ellipsoidal model of equal value；Four, the hyper-sphere model of uncertain variable is obtained；Five, the volume of unit of account hyper-sphere model；Six, the wide boundary of the failure domain total volume of series connection truss structure system is obtained；Seven, the narrow boundary of the failure domain total volume of series connection truss structure system is obtained；Eight, the value range of the non-probability failure degree of series connection truss structure system is calculated；Nine, the value range of the non-probability decision degree of series connection truss structure system is calculated.The present invention considerably reduces the workload solved in the non-probability decision degree of series connection truss structure system by the width boundary interval estimation of the failure domain total volume of series connection truss structure system, provides relatively accurate reasonable estimated value.
Description
Technical field
The invention belongs to truss Multidisciplinary systems analysis technical fields, and in particular to a kind of series connection truss structure system is non-
Probability and reliability analysis method.
Background technique
The truss structure that truss is made of many rod pieces is evenly distributed with its internal force, reduces material consumption and structure certainly
The advantages that heavy and light and be widely used in the fields such as mechanical, building, building and aerospace.In Truss Design and manufacturing process,
Often there is uncertain informations relevant to load, material property, geometric dimension and boundary condition etc., need giving for science
Consider.Analysis method for reliability is one of the effective way for handling above-mentioned uncertain information, therefore probabilistic reliability method obtains
It is widely applied.However, in many engineering practical structures problems, for determining the distribution parameter or probability of probabilistic reliability model
What the sample information of density function was usually a lack of, in this context, it is only necessary to know boundary or the variation model of uncertain parameter
The Multidisciplinary systems analysis method of security evaluation can be carried out to it by, which enclosing, is gradually proposed.Existing structure Multidisciplinary systems
It is for single failure mode that analysis is mostly, and such as Once approximate method and quadratic approximation, and truss structure is a typical tandem junction
Structure multi-invalidation mode system, in theory, Monte Carlo can provide the Multidisciplinary systems point of series connection truss structure system
The accurate solution of analysis, but it causes solution efficiency lower because amount of calculation is huge, therefore nowadays lacks a kind of effective string
Copula frame structural body system Multidisciplinary systems analysis method.
Summary of the invention
In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is that providing a kind of series connection truss
Structural system Multidisciplinary systems analysis method passes through the width boundary section of the failure domain total volume of series connection truss structure system
Estimation considerably reduces the workload solved in the non-probability decision degree of series connection truss structure system, and it is relatively accurate reasonable to provide
Estimated value, give the structural system Multidisciplinary systems analysis for more meeting actual requirement of engineering as a result, widely applicable and answer
It is extensive with prospect, convenient for promoting the use of.
In order to solve the above technical problems, the technical solution adopted by the present invention is that: a kind of non-probability of series connection truss structure system
Analysis method for reliability, which is characterized in that method includes the following steps:
Step 1: determining the power function of series connection each failure mode of truss structure system: using truss structure failure criteria
Determine the power function g of series connection each failure mode of truss structure systemi(X), wherein i is the number of structural system failure mode
And i=1,2 ..., I, I are the number of structural system failure mode, X is uncertain variable vector and X=(X1,X2,...,
Xm)T, m is the dimension that uncertain variable number and m are equal to the uncertain variable vector X,
XlFor first of uncertain variable, l is that the value range of positive integer and l are 1~m,Indicate first of uncertain variable Xl
The section of value,Xl For uncertain variable XlLower bound,For uncertain variable XlThe upper bound；
Step 2: establishing the multidimensional ellipsoidal model for describing uncertain variable: being become using data processor to uncertainty
Amount establishes multidimensional ellipsoidal model, obtains multidimensional ellipsoidal model
Wherein, vector X0For multidimensional ellipsoid do not know domain central point vector and It is not true for first
Qualitative variable XlValue interval midpoint, ΩxFor for determining the eigenmatrix of the shape of multidimensional ellipsoid and the multidimensional ellipsoid in direction
AndZllFirst of uncertainty when to determine multidimensional ellipsoidal model according to NATAF method
Variable XlWith first of uncertain variable XlCovariance, RmFor the real number field of m dimension；
Step 3: the multidimensional for obtaining uncertain variable normalizes ellipsoidal model of equal value, process is as follows:
The normalized of step 301, uncertain variable vector: according to formulaIt obtains uncertain
The uncertain variable normalized vector U of property variable vector X, wherein U=(U1,U2,...,Um)T, UlFor first of uncertainty
Variable XlCorresponding normalization variable,For first of uncertain variable XlSection radius and
Step 302, the multidimensional for constructing uncertain variable normalize ellipsoidal model of equal value: using data processor to uncertain
Property variable normalized vector U construct the multidimensional of uncertain variable and normalize ellipsoidal model of equal value
ΩuFor uncertain variable normalized vector U normalization space u in determine multidimensional ellipsoid eigenmatrix and For withDiagonal matrix is tieed up for the m of diagonal element；
Step 4: obtaining the hyper-sphere model of uncertain variable, process is as follows:
Step 401, to uncertain variable normalized vector U normalization space u in determine multidimensional ellipsoid spy
Levy matrix ΩuCholeskey decomposition is carried out, i.e.,Wherein, L0Lower three angular moment decomposed for Choleskey
Battle array；
Step 402 is normalized ellipsoidal model of equal value and converts to obtain uncertain variable and exists using data processor to multidimensional
Unit hyper-sphere model E in the space normed space δδ=δ | δTδ≤1,δ∈Rm, wherein δ be uncertain variable normalize to
Measure U the space normed space δ standardized vector and
The dimension in the space normed space δ is m, δlTo normalize variable UlStandardized variable in the space normed space δ；
Obtain the relationship between the standardized vector δ in uncertain variable vector X and the space normed space δ:
To the power function g of series connection each failure mode of truss structure systemi(X) it is deformed in the space normed space δ
Processing, obtains the Structural functional equation g of the failure mode in the space normed space δi(δ)；
Step 5: according to formulaUnit of account hyper-sphere model EδVolume VAlways, wherein Γ () is
Gamma function；
Step 6: obtaining the wide boundary of the failure domain total volume of series connection truss structure system: in normed space, when i-th
The Structural functional equation g of a failure modeiThe curved surface and unit hyper-sphere model E that (δ) is constitutedδIt is empty using normed space δ when intersection
Between failure mode Structural functional equation giPoint and unit hyper-sphere model E on the curved surface that (δ) is constitutedδThe distance between origin is most
Small value calculates the Structural functional equation g of the failure mode in the space normed space δi(δ) corresponding failure domain volume Vi；
According to wide bound method formulaThe failure domain for calculating series connection truss structure system is overall
Product VF, alwaysWide boundary, wherein
Step 7: obtaining the narrow boundary of the failure domain total volume of series connection truss structure system: to failure domain volume ViMiddle I
The corresponding failure domain volume of failure mode carries out sorting from large to small adjustment, the failure domain volume W=(W after being adjusted1,
W2,...,WI)T, wherein W1~WIFor V1~VIIt is sorting from large to small as a result, i.e. W1>W2>...>WI, W1=max (Vi), WI=
min(Vi)；
According to narrow bound method formula
Calculate the failure domain total volume V of series connection truss structure systemF, alwaysNarrow boundary,It fails for the i-th failure mode and jth
The total failure domain of mode；
Step 8: calculating series connection truss structure system according to the narrow boundary of the failure domain total volume of series connection truss structure system
Non- probability failure degree value range ηs,F, wherein
Step 9: according to formula ηs,R=1- ηs,F, calculate the value model of the non-probability decision degree of series connection truss structure system
Enclose ηs,R。
Above-mentioned a kind of series connection truss structure system Multidisciplinary systems analysis method, it is characterised in that: described uncertain
Property variable number m be not less than 2；
As m=2, unit hyper-sphere model EδFor unit circle, the Structural functional equation of the failure mode in the space normed space δ
giThe two-dimentional arch surface that the curved surface and unit circle that (δ) is constituted are crossed to form, fail domain volume V at this timeiWith the area of two-dimentional arch surfaceIt indicates, wherein h is the height of two-dimentional arch surface；
As m=3, unit hyper-sphere model EδFor unit sphere, the structure function letter of the failure mode in the space normed space δ
Number giThe three-dimensional segment that the curved surface and unit sphere that (δ) is constituted are crossed to form, fail domain volume V at this timeiWith the volume of three-dimensional segmentIt indicates, wherein h' is the height of three-dimensional segment；
As m >=4, unit hyper-sphere model EδHypersphere, the structure function letter of the failure mode in the space normed space δ are tieed up for m
Number giThe m dimension hypersphere that curved surface and m the dimension hypersphere that (δ) is constituted are crossed to form lacks, and fail domain volume V at this timeiWith the scarce body of m dimension hypersphere
ProductIt indicates, wherein h " is that m ties up what hypersphere lacked
It is high.
A kind of above-mentioned series connection truss structure system Multidisciplinary systems analysis method, it is characterised in that: the series connection purlin
The power function g of each failure mode of frame structural body systemi(X)=0 it is known as failure critical surface, when series connection truss structure system respectively fails
The power function g of modei(X) < 0 when, series connection truss structure system failure；When the function of series connection each failure mode of truss structure system
It can function gi(X) >=0 when, series connection truss structure system safety.
Above-mentioned a kind of series connection truss structure system Multidisciplinary systems analysis method, it is characterised in that: described uncertain
Property variable includes dead load, dynamic loading, length, width, elasticity modulus.
A kind of above-mentioned series connection truss structure system Multidisciplinary systems analysis method, it is characterised in that: i-th failure
The total failure domain of mode and jth failure modeIt is acquired by numerical integration.
Compared with the prior art, the present invention has the following advantages:
1, the present invention is normalized by the multidimensional ellipsoidal model to uncertain variable, obtains uncertain change
The multidimensional of amount normalizes ellipsoidal model of equal value, solves when the magnitude difference in uncertain variable vector between each variable is larger
When, there is the problem of serious morbid state in the eigenmatrix of multidimensional ellipsoidal model, guarantees the essence of calculated result in numerical procedure
It is all having the same to guarantee that the multidimensional after normalized normalizes all elements in the eigenmatrix of ellipsoidal model of equal value for degree
Magnitude, convenient for promoting the use of.
2, the width boundary interval estimation that the present invention passes through the failure domain total volume of series connection truss structure system, wherein string
The wide boundary interval estimation of the failure domain total volume of copula frame structural body system fails domain volume by single failure mode to estimate to lose
Domain is imitated, then further consideration multi-mode fails domain the narrow boundary interval estimation of the failure domain total volume for truss structure system of connecting altogether
Narrower interval estimation range is given, corresponding Multidisciplinary systems Measure Indexes, reliable and stable, using effect are defined
It is good.
3, the method for the present invention step is simple, has fully considered engineering actual demand, has given and more meet actual requirement of engineering
The analysis of structural system Multidisciplinary systems as a result, widely applicable and application prospect is extensive, greatly simplifie series connection truss knot
The workload that structure system failure domain volume calculates effectively compensates for the prior art and is only capable of carrying out the structure under single failure mode
The deficiency of Multidisciplinary systems analysis, has expanded the range of structure Multidisciplinary systems analysis method, to the reliable of structural system
Property analysis have very important significance, convenient for promote the use of.
In conclusion width boundary interval estimation of the present invention by the failure domain total volume of series connection truss structure system,
The workload solved in the non-probability decision degree of series connection truss structure system is considerably reduced, relatively accurate reasonable estimation is provided
Value gives the structural system Multidisciplinary systems analysis for more meeting actual requirement of engineering as a result, widely applicable and application prospect
Extensively, convenient for popularization and use.
Below by drawings and examples, technical scheme of the present invention will be described in further detail.
Detailed description of the invention
Fig. 1 is method flow block diagram of the invention.
Fig. 2 is the structural schematic diagram of series connection truss structure system in the present embodiment.
Fig. 3 is the Structural functional equation g of the failure mode in the present embodiment Plays space space δi(δ) constitute curved surface with
Unit hyper-sphere model EδIntersect schematic diagram.
Specific embodiment
As shown in Figure 1 to Figure 3, a kind of series connection truss structure system Multidisciplinary systems analysis method of the invention, including
Following steps:
Step 1: determining the power function of series connection each failure mode of truss structure system: using truss structure failure criteria
Determine the power function g of series connection each failure mode of truss structure systemi(X), wherein i is the number of structural system failure mode
And i=1,2 ..., I, I are the number of structural system failure mode, X is uncertain variable vector and X=(X1,X2,...,
Xm)T, m is the dimension that uncertain variable number and m are equal to the uncertain variable vector X,
XlFor first of uncertain variable, l is that the value range of positive integer and l are 1~m,Indicate first of uncertain variable Xl
The section of value,Xl For uncertain variable XlLower bound,For uncertain variable XlThe upper bound；
In the present embodiment, the uncertainty variable includes dead load, dynamic loading, length, width, elasticity modulus.
In the present embodiment, the power function g of series connection each failure mode of truss structure systemi(X)=0 it is known as failure to face
Interface, as the power function g of series connection each failure mode of truss structure systemi(X) < 0 when, series connection truss structure system failure；When
The power function g for each failure mode of truss structure system of connectingi(X) >=0 when, series connection truss structure system safety.
Step 2: establishing the multidimensional ellipsoidal model for describing uncertain variable: being become using data processor to uncertainty
Amount establishes multidimensional ellipsoidal model, obtains multidimensional ellipsoidal model
Wherein, vector X0For multidimensional ellipsoid do not know domain central point vector and It is not true for first
Qualitative variable XlValue interval midpoint, ΩxFor for determining the eigenmatrix of the shape of multidimensional ellipsoid and the multidimensional ellipsoid in direction
AndZllFirst of uncertainty when to determine multidimensional ellipsoidal model according to NATAF method
Variable XlWith first of uncertain variable XlCovariance, RmFor the real number field of m dimension；
Step 3: the multidimensional for obtaining uncertain variable normalizes ellipsoidal model of equal value, process is as follows:
The normalized of step 301, uncertain variable vector: according to formulaIt obtains uncertain
The uncertain variable normalized vector U of property variable vector X, wherein U=(U1,U2,...,Um)T, UlFor first of uncertainty
Variable XlCorresponding normalization variable,For first of uncertain variable XlSection radius and
Step 302, the multidimensional for constructing uncertain variable normalize ellipsoidal model of equal value: using data processor to uncertain
Property variable normalized vector U construct the multidimensional of uncertain variable and normalize ellipsoidal model of equal value
ΩuFor uncertain variable normalized vector U normalization space u in determine multidimensional ellipsoid eigenmatrix and For withDiagonal matrix is tieed up for the m of diagonal element；
It should be noted that being normalized by the multidimensional ellipsoidal model to uncertain variable, obtain not really
The multidimensional of qualitative variable normalizes ellipsoidal model of equal value, solves when the magnitude difference in uncertain variable vector between each variable
When larger, there is the problem of serious morbid state in the eigenmatrix of multidimensional ellipsoidal model, guarantees calculated result in numerical procedure
Precision, guarantee that the multidimensional after normalized normalizes all elements in the eigenmatrix of ellipsoidal model of equal value and all has phase
Same magnitude, convenient for promoting the use of.
Step 4: obtaining the hyper-sphere model of uncertain variable, process is as follows:
Step 401, to uncertain variable normalized vector U normalization space u in determine multidimensional ellipsoid spy
Levy matrix ΩuCholeskey decomposition is carried out, i.e.,Wherein, L0Lower three angular moment decomposed for Choleskey
Battle array；
Step 402 is normalized ellipsoidal model of equal value and converts to obtain uncertain variable and exists using data processor to multidimensional
Unit hyper-sphere model E in the space normed space δδ=δ | δTδ≤1,δ∈Rm, wherein δ be uncertain variable normalize to
Measure U the space normed space δ standardized vector and
The dimension in the space normed space δ is m, δlTo normalize variable UlStandardized variable in the space normed space δ；
Obtain the relationship between the standardized vector δ in uncertain variable vector X and the space normed space δ:
To the power function g of series connection each failure mode of truss structure systemi(X) it is deformed in the space normed space δ
Processing, obtains the Structural functional equation g of the failure mode in the space normed space δi(δ)；
Step 5: according to formulaUnit of account hyper-sphere model EδVolume VAlways, wherein Γ () is
Gamma function；
Step 6: obtaining the wide boundary of the failure domain total volume of series connection truss structure system: in normed space, when i-th
The Structural functional equation g of a failure modeiThe curved surface and unit hyper-sphere model E that (δ) is constitutedδIt is empty using normed space δ when intersection
Between failure mode Structural functional equation giPoint and unit hyper-sphere model E on the curved surface that (δ) is constitutedδThe distance between origin is most
Small value calculates the Structural functional equation g of the failure mode in the space normed space δi(δ) corresponding failure domain volume Vi；
According to wide bound method formulaThe failure domain for calculating series connection truss structure system is overall
Product VF, alwaysWide boundary, wherein
In the present embodiment, the uncertainty variable number m is not less than 2；
As m=2, unit hyper-sphere model EδFor unit circle, the Structural functional equation of the failure mode in the space normed space δ
giThe two-dimentional arch surface that the curved surface and unit circle that (δ) is constituted are crossed to form, fail domain volume V at this timeiWith the area of two-dimentional arch surfaceIt indicates, wherein h is the height of two-dimentional arch surface；
As m=3, unit hyper-sphere model EδFor unit sphere, the structure function letter of the failure mode in the space normed space δ
Number giThe three-dimensional segment that the curved surface and unit sphere that (δ) is constituted are crossed to form, fail domain volume V at this timeiWith the volume of three-dimensional segmentIt indicates, wherein h' is the height of three-dimensional segment；
As m >=4, unit hyper-sphere model EδHypersphere, the structure function letter of the failure mode in the space normed space δ are tieed up for m
Number giThe m dimension hypersphere that curved surface and m the dimension hypersphere that (δ) is constituted are crossed to form lacks, and fail domain volume V at this timeiWith the scarce body of m dimension hypersphere
ProductIt indicates, wherein h " is that m ties up what hypersphere lacked
It is high.
Step 7: obtaining the narrow boundary of the failure domain total volume of series connection truss structure system: to failure domain volume ViMiddle I
The corresponding failure domain volume of failure mode carries out sorting from large to small adjustment, the failure domain volume W=(W after being adjusted1,
W2,...,WI)T, wherein W1~WIFor V1~VIIt is sorting from large to small as a result, i.e. W1>W2>...>WI, W1=max (Vi), WI=
min(Vi)；
According to narrow bound method formula
Calculate the failure domain total volume V of series connection truss structure systemF, alwaysNarrow boundary,It fails for the i-th failure mode and jth
The total failure domain of mode；
In the present embodiment, the total failure domain of i-th failure mode and jth failure modePass through numerical integration
It acquires.
It should be noted that the width boundary interval estimation of the failure domain total volume by series connection truss structure system,
In, the wide boundary interval estimation of the failure domain total volume for truss structure system of connecting fails domain volume by single failure mode to estimate
Meter failure domain, the narrow boundary interval estimation of the failure domain total volume for truss structure system of connecting then further consider that multi-mode is lost altogether
Effect domain gives narrower interval estimation range, defines corresponding Multidisciplinary systems Measure Indexes, reliable and stable, uses effect
Fruit is good.
Step 8: calculating series connection truss structure system according to the narrow boundary of the failure domain total volume of series connection truss structure system
Non- probability failure degree value range ηs,F, wherein
Step 9: according to formula ηs,R=1- ηs,F, calculate the value model of the non-probability decision degree of series connection truss structure system
Enclose ηs,R。
As shown in Fig. 2, in the present embodiment, it is not true there are three in 5 bar truss structures by taking plane 5 rods truss structure as an example
Determine variable X1、X2And X3, three uncertain variables X1、X2And X3It is load, the allowable stress of No. 1 bar is 240kN, No. 2 bars
Allowable stress is 200kN, and the allowable stress of No. 3 bars is 280kN, and the allowable stress of No. 4 bars is 280kN, the allowable stress of No. 5 bars
For 180kN, three uncertain variables X1、X2And X3Related coefficientWith0.2 is taken, three uncertain
Variable X1、X2And X3Value table it is as shown in table 1.
Table 1
The power function g of the failure mode of 5 bars is determined in MATLAB using truss structure failure criteriai(X), wherein
The power function of the failure mode of No. 1 bar
The power function of the failure mode of No. 2 bars
The power function of the failure mode of No. 3 bars
The power function of the failure mode of No. 4 bars
The power function of the failure mode of No. 5 bars
The eigenmatrix of the multidimensional ellipsoid of uncertain variable vector X is determined according to NATAF method
Then multidimensional ellipsoidal model
In order to effectively overcome interference caused by eigenmatrix pathosis, multidimensional ellipsoidal model is normalized, is obtainedTo uncertain variable normalized vector U normalization space u in feature
Matrix ΩuCholeskey decomposition is carried out, i.e.,
Matrix after decomposition is substituted into multidimensional to normalize in ellipsoidal model of equal value, is obtained
Then, unit hyper-sphere model of the uncertain variable in the space normed space δ is represented by
Deformation process is carried out in the space normed space δ to uncertain variable normalized vector U, is obtained
To the power function g of series connection each failure mode of truss structure systemi(X) it is deformed in the space normed space δ
Processing, obtains the Structural functional equation of the failure mode of No. 1 bar in the space normed space δ
The bar of the space normed space δ 2
The Structural functional equation of failure modeNormed space
The Structural functional equation of the failure mode of No. 3 bars in the space δ
Standard null
Between No. 4 bars in the space δ failure mode Structural functional equation
Standard null
Between No. 5 bars in the space δ failure mode Structural functional equation
Unit hyper-sphere model EδVolume
M takes 3 in the present embodiment, unit hyper-sphere model EδFor unit sphere, the structure of the failure mode in the space normed space δ
Power function giThe three-dimensional segment that the plane and unit sphere that (δ) is constituted are crossed to form, fail domain volume V at this timeiWith three-dimensional segment
VolumeIt indicates, wherein h' is the height of three-dimensional segment；
By the Structural functional equation g of the failure mode in the space normed space δiThe curved surface and unit hyper-sphere model E that (δ) is constitutedδ
Intersected, utilizes the Structural functional equation g of the failure mode in the space normed space δiPoint and unit are super on the curved surface that (δ) is constituted
Spherical model EδThe distance between origin minimum value calculates the Structural functional equation g of the failure mode in the space normed space δi(δ) is corresponding
Failure domain volume Vi, ginseng is shown in Table 2.
Table 2
| Failure mode | Segment radius r | The high h' of segment | Fail domain volume |
| gδ1 | 1 | 0.1458 | 0.0635 |
| gδ2 | 1 | 0.2648 | 0.2007 |
| gδ3 | 1 | 0.5254 | 0.7150 |
| gδ4 | 1 | 0.3893 | 0.4143 |
| gδ5 | 1 | 0.3656 | 0.3686 |
According to wide bound method formulaThe failure domain for calculating series connection truss structure system is overall
Product VF, alwaysWide boundaryMust fail domain total volume VF, alwaysWide boundary are as follows: 0.7150≤VF, always≤
1.7621。
To failure domain volume ViThe corresponding failure domain volume of middle I failure mode carries out sorting from large to small adjustment, obtains
Failure domain volume W=(W adjusted1,W2,...,WI)T=(0.7150,0.4143,0.3686,0.2007,0.0635)T, root
According to narrow bound method formulaCalculate series connection purlin
The failure domain total volume V of frame structural body systemF, alwaysNarrow boundary, must fail domain total volume VF, alwaysNarrow boundary are as follows: 0.8654≤VF, always
≤0.9115。
The non-general of series connection truss structure system is calculated according to the narrow boundary of the failure domain total volume of series connection truss structure system
The value range of rate failure degreeObtain 19.35%≤ηs,F≤ 20.38%, therefore, in the present embodiment, truss of connecting
The value range η of the non-probability decision degree of structural systems,RAre as follows: 79.62%≤ηs,R≤ 80.65%.
The present invention gives the structural body for more meeting actual requirement of engineering in use, fully considered engineering actual demand
It is Multidisciplinary systems analysis as a result, widely applicable and application prospect is extensive, greatly simplifies series connection truss structure system and lose
The workload that domain volume calculates is imitated, effectively compensating for that the prior art is only capable of carrying out non-probability to the structure under single failure mode can
By the deficiency of property analysis, the range of structure Multidisciplinary systems analysis method has been expanded, has been had to the fail-safe analysis of structural system
There is very important meaning, convenient for promoting the use of.
The above is only presently preferred embodiments of the present invention, is not intended to limit the invention in any way, it is all according to the present invention
Technical spirit any simple modification to the above embodiments, change and equivalent structural changes, still fall within skill of the present invention
In the protection scope of art scheme.
Claims (5)
1. a kind of series connection truss structure system Multidisciplinary systems analysis method, which is characterized in that method includes the following steps:
Step 1: determining the power function of series connection each failure mode of truss structure system: being determined using truss structure failure criteria
The power function g for each failure mode of truss structure system of connectingi(X), wherein i is the number and i=of structural system failure mode
1,2 ..., I, I are the number of structural system failure mode, and X is uncertain variable vector and X=(X1,X2,...,Xm)T, m
For uncertain variable number and m is equal to the dimension of the uncertain variable vector X,XlIt is
L uncertain variable, l are that the value range of positive integer and l are 1~m,Indicate first of uncertain variable XlValue
Section,Xl For uncertain variable XlLower bound,For uncertain variable XlThe upper bound；
Step 2: establishing the multidimensional ellipsoidal model for describing uncertain variable: being built using data processor to uncertain variable
Vertical multidimensional ellipsoidal model, obtains multidimensional ellipsoidal modelIts
In, vector X0For multidimensional ellipsoid do not know domain central point vector and For first of uncertainty
Variable XlValue interval midpoint, ΩxFor for determine the shape of multidimensional ellipsoid and the multidimensional ellipsoid in direction eigenmatrix andZllFirst of uncertain change when to determine multidimensional ellipsoidal model according to NATAF method
Measure XlWith first of uncertain variable XlCovariance, RmFor the real number field of m dimension；
Step 3: the multidimensional for obtaining uncertain variable normalizes ellipsoidal model of equal value, process is as follows:
The normalized of step 301, uncertain variable vector: according to formulaObtain uncertain become
Measure the uncertain variable normalized vector U of vector X, wherein U=(U1,U2,...,Um)T, UlFor first of uncertain variable
XlCorresponding normalization variable,For first of uncertain variable XlSection radius and
Step 302, the multidimensional for constructing uncertain variable normalize ellipsoidal model of equal value: using data processor to uncertain variable
The multidimensional that normalized vector U constructs uncertain variable normalizes ellipsoidal model of equal value
ΩuFor uncertain variable normalized vector U normalization space u in determine multidimensional ellipsoid eigenmatrix and For withDiagonal matrix is tieed up for the m of diagonal element；
Step 4: obtaining the hyper-sphere model of uncertain variable, process is as follows:
Step 401, to uncertain variable normalized vector U normalization space u in determine multidimensional ellipsoid feature square
Battle array ΩuCholeskey decomposition is carried out, i.e.,Wherein, L0The lower triangular matrix decomposed for Choleskey；
Step 402 converts to obtain uncertain variable in standard to multidimensional normalization ellipsoidal model of equal value using data processor
Unit hyper-sphere model E in the space δ of spaceδ=δ | δTδ≤1,δ∈Rm, wherein δ is uncertain variable normalized vector U
The space normed space δ standardized vector and
The dimension in the space normed space δ is m, δlTo normalize variable UlStandardized variable in the space normed space δ；
Obtain the relationship between the standardized vector δ in uncertain variable vector X and the space normed space δ:
To the power function g of series connection each failure mode of truss structure systemi(X) deformation process is carried out in the space normed space δ,
Obtain the Structural functional equation g of the failure mode in the space normed space δi(δ)；
Step 5: according to formulaUnit of account hyper-sphere model EδVolume VAlways, wherein Γ () is
Gamma function；
Step 6: obtaining the wide boundary of the failure domain total volume of series connection truss structure system: in normed space, being lost when i-th
The Structural functional equation g of effect modeiThe curved surface and unit hyper-sphere model E that (δ) is constitutedδWhen intersection, the space normed space δ is utilized
The Structural functional equation g of failure modeiPoint and unit hyper-sphere model E on the curved surface that (δ) is constitutedδThe distance between origin minimum value
Calculate the Structural functional equation g of the failure mode in the space normed space δi(δ) corresponding failure domain volume Vi；
According to wide bound method formulaCalculate the failure domain total volume of series connection truss structure system
VF, alwaysWide boundary, wherein
Step 7: obtaining the narrow boundary of the failure domain total volume of series connection truss structure system: to failure domain volume ViMiddle I failure
The corresponding failure domain volume of mode carries out sorting from large to small adjustment, the failure domain volume W=(W after being adjusted1,W2,...,
WI)T, wherein W1~WIFor V1~VIIt is sorting from large to small as a result, i.e. W1>W2>...>WI, W1=max (Vi), WI=min
(Vi)；
According to narrow bound method formulaIt calculates
The failure domain total volume V for truss structure system of connectingF, alwaysNarrow boundary,For the i-th failure mode and jth failure mode
Total failure domain；
Step 8: calculating the non-of series connection truss structure system according to the narrow boundary of the failure domain total volume of series connection truss structure system
The value range η of probability failure degrees,F, wherein
Step 9: according to formula ηs,R=1- ηs,F, calculate the value range of the non-probability decision degree of series connection truss structure system
ηs,R。
2. a kind of series connection truss structure system Multidisciplinary systems analysis method described in accordance with the claim 1, it is characterised in that:
The uncertainty variable number m is not less than 2；
As m=2, unit hyper-sphere model EδFor unit circle, the Structural functional equation g of the failure mode in the space normed space δi(δ)
The two-dimentional arch surface that the curved surface and unit circle of composition are crossed to form, fail domain volume V at this timeiWith the area of two-dimentional arch surfaceIt indicates, wherein h is the height of two-dimentional arch surface；
As m=3, unit hyper-sphere model EδFor unit sphere, the Structural functional equation g of the failure mode in the space normed space δi
The three-dimensional segment that the curved surface and unit sphere that (δ) is constituted are crossed to form, fail domain volume V at this timeiWith the volume of three-dimensional segmentIt indicates, wherein h' is the height of three-dimensional segment；
As m >=4, unit hyper-sphere model EδHypersphere, the Structural functional equation g of the failure mode in the space normed space δ are tieed up for mi
The m dimension hypersphere that curved surface and m the dimension hypersphere that (δ) is constituted are crossed to form lacks, and fail domain volume V at this timeiWith the scarce volume of m dimension hypersphereIt indicates, wherein h " is that m ties up what hypersphere lacked
It is high.
3. a kind of series connection truss structure system Multidisciplinary systems analysis method described in accordance with the claim 1, it is characterised in that:
The power function g of series connection each failure mode of truss structure systemi(X)=0 it is known as failure critical surface, when series connection truss structure
The power function g of each failure mode of systemi(X) < 0 when, series connection truss structure system failure；When series connection truss structure system is respectively lost
The power function g of effect modei(X) >=0 when, series connection truss structure system safety.
4. a kind of series connection truss structure system Multidisciplinary systems analysis method described in accordance with the claim 1, it is characterised in that:
The uncertainty variable includes dead load, dynamic loading, length, width, elasticity modulus.
5. a kind of series connection truss structure system Multidisciplinary systems analysis method described in accordance with the claim 1, it is characterised in that:
The total failure domain of i-th failure mode and jth failure modeIt is acquired by numerical integration.
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