CN108304642A - A kind of stiffened cylindrical shell dynamic buckling is to Static Buckling equivalent method - Google Patents
A kind of stiffened cylindrical shell dynamic buckling is to Static Buckling equivalent method Download PDFInfo
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- CN108304642A CN108304642A CN201810082444.2A CN201810082444A CN108304642A CN 108304642 A CN108304642 A CN 108304642A CN 201810082444 A CN201810082444 A CN 201810082444A CN 108304642 A CN108304642 A CN 108304642A
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Abstract
The present invention provides a kind of stiffened cylindrical shell dynamic bucklings to Static Buckling equivalent method, belongs to Dynamic Buckling of Structures and structural static buckling field in structural mechanics, including：(1) stiffened cylindrical shell power and Static Buckling parametric modeling and calculating obtain buckling mode, critical load and payload remainder coefficient.(2) Static Buckling mode and dynamic buckling mode similarity calculation.(3) with the highest Static Buckling mode intelligent search algorithm of dynamic buckling mode vectors correlation degree.(4) the equivalent static(al) load calculation method consistent with dynamic buckling mode and payload remainder coefficient.Stiffened cylindrical shell dynamic buckling provided by the invention can determine equivalent basic load to Static Buckling equivalent method according to dynamic buckling mode is consistent with payload remainder coefficient, the load can instruct to carry out related Static Buckling experiment in the case where dynamic buckling experiment condition limits, and reduce experimental cost and experiment condition requirement.
Description
Technical field
The present invention provides a kind of stiffened cylindrical shell dynamic bucklings to Static Buckling equivalent method, belongs to structural mechanics
Middle Dynamic Buckling of Structures and structural static buckling field, and in particular to be stiffened cylindrical shell dynamic buckling to Static Buckling
It is equivalent.
Background technology
Power is to the equivalent structure for being most used in civil engineering under earthquake loading early in the 1980s of static(al)
In design and optimization.Commonly determine that the method for basic load is that the quality of system is multiplied by a reference acceleration in engineering
Obtain required load.Haftka and Gurdal is in its works《Elements ofStructural Optimization》In
It one coefficient of impact is multiplied by instead of dynamic load(loading) to basic load carries out and is load-optimised, the results showed that this power is to static(al) etc.
It is desirable to imitate thought.Power determines that problem has close contact, researcher to be frequently necessary to from sight to the equivalent and load of static(al)
The load suffered by structural response pushing-out structure observed.However it is to connect that this problem, which has ambiguity, the response of actually structure,
Continuous, and the response of finite number node can only be defined when calculating, this results in equivalent load unstable.So in order to find really
Fixed solution, it is often necessary to load be carried out it is assumed that such as assuming load space distribution form or load loading position.Choi and
Park proposes equivalent static(al) bearing method (equivalent static load, abbreviation ESL), is used for structural optimization analysis,
But equivalent basic load is only intended to structure optimization in the static(al) equivalent method, equivalent static(al) is that the intermediate of structure optimization becomes
Amount, there is no actual meanings, are difficult to instruct static trial.
Structure has dynamic buckling once being acted on by dynamic impact load.Compared with Static Buckling problem, move
The introducing of power load-time parameter leads to Dynamic Buckling of Structures complication.But by the shadow of experiment condition and experiment fees
It rings, it is difficult to carry out dynamic load(loading) experimental evaluation to structure especially large scale structure, this, which is significantly limited, causes dynamic buckling
Structural response and destruction prediction ability.Static trial is simple and practicable, and the manpower and materials of cost are less, but lack at this stage
It is a kind of by dynamic load(loading) to basic load equivalent method.It is therefore desirable to propose that dynamic buckling, should to Static Buckling equivalent method
Method can instruct to carry out equivalent Static Buckling experiment, and be forecast to dynamic buckling mode and critical load, reduce cost
Greatly, high dynamic buckling is required to test, and existing power is only intended to the optimization of structure to static(al) equivalent method, does not relate to
And buckling problem.
Invention content
The present invention provides a kind of stiffened cylindrical shell dynamic bucklings to Static Buckling equivalent method, it is therefore intended that by net
Lattice Cylindrical Shell dynamic buckling is equivalent to Static Buckling, and guides and carries out the experiment of equivalent Static Buckling, to reduce cost it is big,
It is required that high dynamic buckling experiment.The object of the present invention is achieved like this：
A kind of stiffened cylindrical shell dynamic buckling includes the following steps to Static Buckling equivalent method：
1, the dynamic load(loading) P changed over time is loaded to stiffened cylindrical shellIt is dynamic(t).By PIt is dynamic(t) it is decomposed intoWhereinFor load amplitude, fIt is dynamic(t) it is that load function, amplitude 1 is normalized.
2, it is f to change over time rule to stiffened cylindrical shell applicationIt is dynamic(t), different loads amplitude AIt is dynamicDynamic loading, meter
Calculation obtains dynamic buckling critical loadDynamic buckling modeAnd dynamic load(loading) residual coefficientExtract the modal displacement matrix M of cylindrical shell coveringIt is dynamic。
3, according to dynamic buckling mode to equivalent Static Buckling load distribution form fIt is quietCarry out spatial distribution constraint, fIt is quietCharacterization
The spatial variations of basic load, maximum value 1 calculate different loads distribution form fIt is quietLower stiffened cylindrical shell Static Buckling faces
Boundary's load amplitudeObtain Static Buckling critical loadStatic Buckling mode
4, extraction cylindrical shell covering modal displacement matrix MIt is quiet, it is based onFormula calculates quiet
Power buckling modeWith dynamic buckling modeSimilarity degree η, e be Euler's numbers, m and n are matrix MIt is dynamicAnd MIt is quietLine number with
Row number.
5, using particle cluster algorithm search and dynamic buckling modeThe maximum Static Buckling mode of similarityAt this time
Maximum similarity is ηmax, Static Buckling modeCorresponding to basic load distribution form isThe critical load of corresponding Static Buckling
Lotus amplitude isStatic Buckling critical load isSo far dynamic buckling is converted to equivalent static(al) and bends
Song, i.e. κ consistent with Static Buckling payload remainder coefficient according to dynamic bucklingIt is dynamic=κIt is quietIt obtainsStatic(al)
Load isPIt is dynamic(t) according to dynamic buckling to Static Buckling it is equivalent obtain its equivalent basic load be PIt is quiet。
Compared with prior art, advantage of the invention is that：A kind of stiffened cylindrical shell power provided by the invention is bent
Song can determine equivalent basic load to Static Buckling equivalent method according to dynamic buckling mode and critical load, in dynamic buckling
Experiment condition carries out the buckling mode equivalent Static Buckling experiment consistent with payload remainder coefficient in the case of limiting, have important
Engineering significance.
Description of the drawings
Fig. 1 is stiffened cylindrical shell power to Static Buckling Equivalent Calculation flow chart；
Fig. 2 is stiffened cylindrical shell structural schematic diagram；
Fig. 3 goes through curve when being stiffened cylindrical shell dynamic buckling assumed (specified) load；
Fig. 4 is stiffened cylindrical shell dynamic buckling assumed (specified) load spatial distribution schematic diagram；
Fig. 5 is stiffened cylindrical shell dynamic buckling circumferential direction mode；
Fig. 6 is stiffened cylindrical shell Static Buckling assumed (specified) load spatial distribution schematic diagram；
Fig. 7 is the stiffened cylindrical shell Static Buckling circumferential direction mode after particle cluster algorithm is searched for.
Specific implementation mode
Method provided by the invention is described in more detail below in conjunction with the accompanying drawings：
When 1, calculating beginning, the attached grid reinforcement circle shown in Fig. 2 of ABAQUS secondary exploitation technologies based on PYTHON language
Pole-shell structure carries out parametric modeling.By dynamic load(loading) PIt is dynamic(t) it is decomposed intoWhereinFor load amplitude,
fIt is dynamic(t) it is load function after normalizing, characterizes dynamic load(loading) and change over time rule, the dynamic load(loading) applied is at any time and empty
Between changing rule as shown in attached drawing 3 and attached drawing 4, i.e., dynamic load(loading) be uniformly be applied to structural outer surface, at any time be in symmetrical three
The dynamic load(loading) of angle wave.Use ABAQUS/Explicit assumed (specified) loads form for fIt is dynamic(t) make stiffened cylindrical shell power bend
Bent critical load amplitudeObtain stiffened cylindrical shell dynamic buckling circumferential direction modeAs shown in Fig. 5, cylinder is extracted
The modal displacement matrix M of shell coveringIt is dynamic, define dynamic load(loading) residual coefficient
2, after the completion of stiffened cylindrical shell dynamic buckling calculates, Static Buckling point is carried out to it using ABAQUS arc-length methods
Analysis, according to gained stiffened cylindrical shell dynamic buckling modeCertain restrictions is carried out to basic load, it is believed that basic load is in
Piecewise linearity is distributed, therefore determines fIt is quietThe parameter of distribution is each section of peak value T of piecewise linear functioni(i=1~8), grid reinforcement circle
Column shell Static Buckling assumed (specified) load spatial distribution schematic diagram is as shown in Fig. 6, and Static Buckling calculates all parameter T when startingiJust
Beginning turns to 1, calculates Static Buckling mode under the basic loadAnd extract cylindrical shell covering modal displacement matrix MIt is quiet。
3, it is based on formulaCalculate Static Buckling modeWith dynamic buckling mode
Similarity degree η, wherein e is Euler's numbers, and m and n are matrix MIt is quietWith MIt is dynamicLine number and row number.When dynamic buckling modeWith it is quiet
Power buckling modeWhen essentially equal, MIt is quietAnd MIt is dynamicEach element in matrix is identical, and η is 1 at this time.
4, the basic load parameter T applied is determined using particle swarm optimization algorithmi, step 2 and 3 is repeated, it is secondary until calculating
Number reaches predefined max calculation times N.It searches out and dynamic buckling modeThe highest Static Buckling mode of similarityStiffened cylindrical shell Static Buckling circumferential direction mode is as shown in Fig. 7 after particle cluster algorithm is searched for, corresponding static(al)
Load distribution form isEach section of amplitude of corresponding piecewise linear function beCorresponding Static Buckling critical load isSo far dynamic buckling is equivalent to Static Buckling according to mode is equal.
5, after the completion of particle group optimizing, according to Static Buckling critical loadAnd dynamic load(loading) residual coefficient with it is quiet
Equal (the κ of power payload remainder coefficientIt is dynamic=κIt is quiet), obtaining basic load isSo far according to dynamic buckling with
Static Buckling mode is equal and dynamic load(loading) residual coefficient is equal with basic load residual coefficient, and the power changed over time is carried
Lotus PIt is dynamic(t) it is equivalent to basic load
Claims (4)
1. a kind of stiffened cylindrical shell dynamic buckling is to Static Buckling equivalent method, it is characterised in that：Include the following steps,
(1) the dynamic load(loading) P changed over time is loaded to stiffened cylindrical shellIt is dynamic(t), by PIt is dynamic(t) it is decomposed into
WhereinFor load amplitude, fIt is dynamic(t) it is that load function, amplitude 1 is normalized；(2) to stiffened cylindrical shell apply with
Time Change is fIt is dynamic(t), different loads amplitude AIt is dynamicDynamic loading, dynamic buckling critical load is calculatedPower
Buckling modeAnd dynamic load(loading) residual coefficient κIt is dynamic, extract the modal displacement matrix M of cylindrical shell coveringIt is dynamic；(3) according to dynamic
Power buckling mode is to equivalent Static Buckling load distribution form fIt is quietCarry out spatial distribution constraint, fIt is quietThe space for characterizing basic load becomes
Change, maximum value 1, calculates different loads distribution form fIt is quietLower stiffened cylindrical shell Static Buckling critical load amplitude
To Static Buckling critical loadStatic Buckling mode(4) extraction cylindrical shell covering modal displacement matrix MIt is quiet,
Calculate Static Buckling modeWith dynamic buckling modeSimilarity degree η；(5) particle cluster algorithm search is used to be bent with power
Bent modeThe maximum Static Buckling mode of similarityMaximum similarity is η at this timemax, Static Buckling modeIt is corresponding
Basic load distribution form isCorresponding to Static Buckling critical load amplitude isStatic Buckling critical load isSo far dynamic buckling is converted to equivalent Static Buckling, surplus according to dynamic buckling and Static Buckling load
Remaining coefficient is consistent, i.e. κIt is dynamic=κIt is quietIt obtainsBasic load isPIt is dynamic(t) it is bent according to power
Song is to equivalent its equivalent basic load that obtains of Static Buckling for PIt is quiet。
2. a kind of stiffened cylindrical shell dynamic buckling according to claim 1 is to Static Buckling equivalent method, feature
It is：Dynamic load(loading) P described in step (1)It is dynamic(t) it is uniformly to be applied to structural outer surface, be at any time symmetric triangular wave
Dynamic load(loading).
3. a kind of stiffened cylindrical shell dynamic buckling according to claim 1 is to Static Buckling equivalent method, feature
It is：Dynamic buckling critical load described in step (2)Calculation formula beWherein fIt is dynamic(t)
For load function after normalization,To use ABAQUS/Explicit assumed (specified) loads form for fIt is dynamic(t) make grid reinforcement justify
Column shell dynamic buckling critical load amplitude；The power payload remainder coefficient κIt is dynamicIt is defined asWhereinFor load
Amplitude.
4. a kind of stiffened cylindrical shell dynamic buckling according to claim 1 is to Static Buckling equivalent method, feature
It is：Static Buckling mode described in step (4)With dynamic buckling modeSimilarity degree η be based on formulaIt calculates, wherein e is Euler's numbers, and m and n are matrix MIt is quietWith MIt is dynamicLine number and row number.
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| CN201810082444.2A CN108304642B (en) | 2018-01-29 | 2018-01-29 | Equivalent method for buckling of grid reinforced cylindrical shell from dynamic buckling direction to static buckling direction |
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| CN201810082444.2A CN108304642B (en) | 2018-01-29 | 2018-01-29 | Equivalent method for buckling of grid reinforced cylindrical shell from dynamic buckling direction to static buckling direction |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110727997A (en) * | 2019-09-20 | 2020-01-24 | 湖北省工业建筑集团有限公司 | Method for calculating stability of metal cylindrical shell |
| CN111753455A (en) * | 2020-06-30 | 2020-10-09 | 仲恺农业工程学院 | Method for quickly calculating dynamic buckling of slender metal arch structure by considering geometric defects |
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| CN105258585A (en) * | 2015-10-29 | 2016-01-20 | 大连理工大学 | Method for designing hybrid fiber composite anti-explosion tank |
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| WO2009008572A1 (en) * | 2007-07-10 | 2009-01-15 | Industry-University Cooperation Foundation Hanyang University | Method of calculating nonlinear dynamic response structural optimal solution using equivalent static loads |
| CN104614262A (en) * | 2015-02-06 | 2015-05-13 | 西安科技大学 | Electromagnetic integrated system for monitoring, recording and applying dynamic and static loads |
| CN105258585A (en) * | 2015-10-29 | 2016-01-20 | 大连理工大学 | Method for designing hybrid fiber composite anti-explosion tank |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110727997A (en) * | 2019-09-20 | 2020-01-24 | 湖北省工业建筑集团有限公司 | Method for calculating stability of metal cylindrical shell |
| CN111753455A (en) * | 2020-06-30 | 2020-10-09 | 仲恺农业工程学院 | Method for quickly calculating dynamic buckling of slender metal arch structure by considering geometric defects |
| CN111753455B (en) * | 2020-06-30 | 2023-07-04 | 仲恺农业工程学院 | Method for rapidly calculating dynamic buckling of slender metal arch structure by considering geometric defects |
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