CN104392130B - The definite method and its application for most damaging loading direction of non-proportional loading - Google Patents
The definite method and its application for most damaging loading direction of non-proportional loading Download PDFInfo
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- CN104392130B CN104392130B CN201410677398.2A CN201410677398A CN104392130B CN 104392130 B CN104392130 B CN 104392130B CN 201410677398 A CN201410677398 A CN 201410677398A CN 104392130 B CN104392130 B CN 104392130B
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Abstract
The present invention discloses the definite method for most damaging loading direction of non-proportional loading, carries out as follows：S1, specified point and search space are determined in cell surface, and determines stress of the specified point in described search space under each searching coordinates system, strain tensor course；S2, accumulated damage or safety coefficient of the specified point under each searching coordinates system are calculated using tired algorithm according to the stress and strain tensor course determined in step S1；S3, the accumulated damage or safety coefficient of all searching coordinates systems of comparison, the direction output by accumulated damage maximum or safety coefficient minimum respective loads is most to damage loading direction.Present invention may determine that the most damage loading direction of unit, reduces the blindness of search, reduces calculation amount, improve search speed.
Description
Technical field
The present invention relates to the definite methods for most damaging loading direction, and in particular to non-proportional loading most damages loading direction
Determine method.
Background technology
Due to structure bear in itself multiaxis combined load synchronous or asynchronous effect or structure itself it is complex-shaped,
So that even if local under uniaxial stress be still present with multi-axis stress state, so in Practical Project, disproportional non-proportional loading
The phenomenon that being a kind of universal.For disproportional multiaxial loading, principal stress often changes over time, so as to cause the side of fatigue damage
To being not easy to find.Effective strain method, energy method have ignored the directionality of fatigue damage in existing non-proportional loading analysis method, face
For interface method to bear the plane of maximum shear strain as critical plane, this method thinks the cycling shear strain in maximum shear strain plane
It is to cause the factor of fatigue damage with normal direction normal strain, although it is contemplated that cause the dangerous surface of damage, but in load history
The situation of shear strain and the direction random fluctuation of normal direction normal strain is cycled, can not provide and most damage direction.It is not inconsistent simultaneously for those
The situation that maximum shear strain is critical plane is closed, this critical plane approach will be unable to be applicable in.
The content of the invention
Goal of the invention：Present invention aims at, provide to be accurately positioned disproportional Multiaxial damages in view of the deficiencies of the prior art
Direction, adapt to stress random fluctuation situation non-proportional loading most damage loading direction definite method.
Technical solution：The definite method for most damaging loading direction of non-proportional loading of the present invention, carries out as follows：
S1, specified point and search space are determined in cell surface, and determines that the specified point is every in described search space
Stress, strain tensor course under one searching coordinates system；
S2, the specified point is calculated every using tired algorithm according to the stress and strain tensor course determined in step S1
Accumulated damage or safety coefficient under a searching coordinates system；
S3, the accumulated damage or safety coefficient of all searching coordinates systems of comparison, by accumulated damage is maximum or safety coefficient most
The direction output of small corresponding load is most to damage loading direction.
The technical solution of the present invention is further defined as when being scanned for the scope of freedom of unit, it is definite in step S1
Specified point is the central point on each scope of freedom, and definite search space is to be determined according to predetermined region of search and search density.
Further, when being scanned for the scope of freedom of unit, stress, strain in step S1 to each scope of freedom central point
The calculation procedure of tensor course is as follows：
Zy1, the measuring coordinate system o-xyz for extracting scope of freedom central point and scope of freedom central point are in the measuring coordinate system
Under ess-strain course, determine ess-strain tensor of each course point scope of freedom central point in measuring coordinate system；
Zy2, search space is determined：Extract default region of search parameter θ and Δ θ and search density parameter Δ α, shape
Into search space o-x_s-x_e, wherein to be o-xyz coordinate systems turn the search start bit that θ angles obtain around z-axis in o points by x_s, y_s
Put reference axis, x_e, y_e are o-x_s, y_s, and z_s coordinate systems turn the search final position that Δ θ angles obtain around z-axis in o points and sit
Parameter, search space are using o-x_s and o-x_e as border, using Δ α as N number of coordinate series of increment；
Zy3, the direction cosines for calculating each coordinate system in search space and each axis of measuring coordinate system；
Zy4, stress of the scope of freedom center under n-th of searching coordinates system, strain tensor course are calculated.
Further, when being scanned for the given side of unit, in step S1, definite specified point is appointing in given side
Meaning point, definite search space are to be determined according to search face, region of search and search density.
Further, when being scanned for the given side of unit, stress, strain tensor course in step S1 to specified point
Calculation procedure it is as follows：
The ess-strain course of Zd1, the original coordinate system and specified point o of extraction specified point o under original coordinate system, really
Specified point o is in the ess-strain tensor of the original coordinate system in fixed each course；
Zd2, search space is determined：Given side coordinate system o-xyz is extracted as measuring coordinate system, according to the default field of search
Field parameter θ and Δ θ and search density parameter Δ α, forms search space o-x_s-x_e, wherein x_s, y_s is o-xyz coordinates
It ties up to o points and turns the search starting position coordinates axis that θ angles obtain around z-axis, x_e, y_e are o-x_s, and y_s, z_s coordinate systems are in o points
Turn the search final position reference axis that Δ θ angles obtain around z-axis, search space is using o-x_s and o-x_e as border, with Δ α
For N number of coordinate series of increment；
Zd3, each searching coordinates system in search space and the direction cosines of each axis of original coordinate system are calculated；
Zd4, ess-strain tensor course of the o points under n-th of searching coordinates system is calculated.
Advantageous effect：The definite method for most damaging loading direction of non-proportional loading provided by the invention, by calculating fatigue
The accumulated damage or safety coefficient of all searching coordinates systems of method computing unit, the most damage loading direction of effective determination unit；
Meanwhile search face may be selected in the present invention, improves the flexibility of search；The controllable damage field setting of the present invention, reduces search
Blindness reduces calculation amount, improves search speed, meanwhile, the setting of controllable search density can be fast according to search density selection
Speed search or high-precision are searched for；The applicable ability of the present invention is strong, germinates the fatigue endurance performance in stage for structural crack and changes
There is very important effect into structure design.
Description of the drawings
Fig. 1 is the flow chart of the localization method for most damaging direction for the unit scope of freedom non-proportional loading that embodiment 1 provides；
Fig. 2 is the flow chart of the localization method for most damaging direction for the unit given side non-proportional loading that embodiment 2 provides；
Fig. 3 is the coordinate of ess-strain tensor of each course point scope of freedom central point in measuring coordinate system in embodiment 1
It is schematic diagram；
Fig. 4 is that each coordinate system in search space and the coordinate system of the direction cosines of measuring coordinate system each axis show in embodiment 1
It is intended to.
Specific embodiment
Technical solution of the present invention is described in detail below by attached drawing, but protection scope of the present invention is not limited to
The embodiment.
Actual phenomenon in surface is often germinated according to the crackle of structure, in the search that Free Surface is controllably set,
By scanning the damage accumulation of region of search, the Impact direction of " most damaging " is provided, while it is arbitrarily flat to provide structure any position
The search in face can find the most damage direction of any position in structure, and " most damaging " direction is for understanding the crack initiation stage
Fatigue endurance performance and the improved structure design of structure have very important effect.
The tired algorithm of present invention application provides the definite method for most damaging loading direction of non-proportional loading, as follows
It carries out：
S1, specified point and search space are determined in cell surface, and determines that the specified point is every in described search space
Stress, strain tensor course under one searching coordinates system；
S2, the specified point is calculated every using tired algorithm according to the stress and strain tensor course determined in step S1
Accumulated damage or safety coefficient under a searching coordinates system；
S3, the accumulated damage or safety coefficient of all searching coordinates systems of comparison, by accumulated damage is maximum or safety coefficient most
The direction output of small corresponding load is most to damage loading direction.
The positioning for most damaging direction that non-proportional loading is carried out with reference to the scope of freedom of unit and given side carries out respectively in detail
It states.
Embodiment 1：
The present embodiment is scanned for for the scope of freedom of unit, and flow chart is as shown in Figure 1, be as follows：
S1, specified point and search space are determined in cell surface, and determines that the specified point is every in described search space
Stress, strain tensor course under one searching coordinates system；
When being scanned for the scope of freedom of unit, in step S1, definite specified point is the central point on each scope of freedom, is determined
Search space be according to predetermined region of search and search density determine.
The calculation procedure of stress, strain tensor course to each scope of freedom central point is as follows：
Zy1, the measuring coordinate system o-xyz for extracting scope of freedom central point and scope of freedom central point are in the measuring coordinate system
Under ess-strain course, determine ess-strain tensor of each course point scope of freedom central point in measuring coordinate system.
Ess-strain course is as shown in table 1：
Table 1：
In coordinate system schematic diagram such as Fig. 3 of ess-strain tensor of each course point scope of freedom central point in measuring coordinate system
It is shown.
Zy2, search space is determined：Extract default region of search parameter θ and Δ θ and search density parameter Δ α, shape
Into search space o-x_s-x_e, wherein to be o-xyz coordinate systems turn the search start bit that θ angles obtain around z-axis in o points by x_s, y_s
Put reference axis, x_e, y_e are o-x_s, y_s, and z_s coordinate systems turn the search final position that Δ θ angles obtain around z-axis in o points and sit
Parameter, search space are using o-x_s and o-x_e as border, using Δ α as N number of coordinate series of increment；
Zy3, the direction cosines for calculating each coordinate system in search space and each axis of measuring coordinate system, all directions cosine such as table 2
Shown, coordinate system schematic diagram is as shown in Figure 4.
Table 2：
| Included angle cosine | X | y | z |
| x_n | Ln11 | Ln12 | Ln13 |
| y_n | Ln21 | Ln22 | Ln23 |
| z_n | Ln31 | Ln32 | Ln33 |
By taking n-th of searching coordinates system as an example, direction cosines are as shown in table 3：
Zy4, stress of the scope of freedom center under n-th of searching coordinates system, strain tensor course are calculated, as shown in table 4：
Table 4：
S2, the specified point is calculated using tired algorithm according to the stress and strain tensor s_n courses determined in step S1
Accumulated damage Damage or safety coefficient Safety factor under each searching coordinates system.
Judge whether to complete the corresponding fatigue behaviour of ess-strain course institute under all searching coordinates systems to calculate, if do not had
Have, repeat the above steps, calculated until completing the corresponding fatigue behaviour of ess-strain course institute under all searching coordinates systems.
S3, the accumulated damage Damage of all searching coordinates systems of comparison or safety coefficient Safety Factor damage accumulation
The searching coordinates for hindering Damage maximums or the minimum corresponding loads of safety coefficient Safety Factor are corresponding y_n directions output
Most to damage loading direction.
Embodiment 2：
The present embodiment is scanned for for the given side of unit, and flow chart is as shown in Fig. 2, be as follows：
S1, specified point and search space are determined on the surface of unit, and determines the specified point in described search space
Stress, strain tensor course under each searching coordinates system.
Definite specified point is the arbitrary point in given side, definite search space be according to search face, region of search and
Search density determines.
Stress, the calculation procedure of strain tensor course to specified point is as follows：
The ess-strain course of Zd1, the original coordinate system and specified point o of extraction specified point o under original coordinate system, really
Specified point o is in the ess-strain tensor of the original coordinate system in fixed each course.
This is as shown in table 5 in the ess-strain tensor of the original coordinate system in each course：
Table 5：
Zd2, search space is determined：Given side coordinate system o-xyz is extracted as measuring coordinate system, according to the default field of search
Field parameter θ and Δ θ and search density parameter Δ α, forms search space o-x_s-x_e, wherein x_s, y_s is o-xyz coordinates
It ties up to o points and turns the search starting position coordinates axis that θ angles obtain around z-axis, x_e, y_e are o-x_s, and y_s, z_s coordinate systems are in o points
Turn the search final position reference axis that Δ θ angles obtain around z-axis, search space is using o-x_s and o-x_e as border, with Δ α
For N number of coordinate series of increment.
Zd3, each searching coordinates system in search space and the direction cosines of each axis of original coordinate system are calculated, as shown in table 6：
Table 6：
| Included angle cosine | xn | yn | zn |
| 11 | 12 | 13 | |
| 21 | 22 | 23 | |
| 31 | 32 | 33 |
Zd4, stress of the o points under n-th of searching coordinates system, strain tensor course are calculated, as shown in table 7：
Table 7：
S2, the specified point is calculated using tired algorithm according to the stress and strain tensor s_n courses determined in step S1
Accumulated damage Damage or safety coefficient Safety factor under each searching coordinates system.
Judge whether to complete the corresponding fatigue behaviour of ess-strain course institute under all searching coordinates systems to calculate, if do not had
Have, repeat the above steps, calculated until completing the corresponding fatigue behaviour of ess-strain course institute under all searching coordinates systems.
S3, the accumulated damage Damage of all searching coordinates systems of comparison or safety coefficient Safety Factor damage accumulation
The searching coordinates for hindering Damage maximums or the minimum corresponding loads of safety coefficient Safety Factor are corresponding y_n directions output
Most to damage loading direction.
As described above, although the present invention has been represented and described with reference to specific preferred embodiment, must not explain
For to the limitation of itself of the invention.It, can be right under the premise of the spirit and scope of the present invention that appended claims define are not departed from
Various changes can be made in the form and details for it.
Claims (3)
1. the definite method for most damaging loading direction of non-proportional loading, which is characterized in that carry out as follows：
S1, specified point and search space are determined in cell surface, and determines that the specified point is each in described search space and search
Stress, strain tensor course under rope coordinate system；
S2, searched according to the stress and strain tensor course determined in step S1 using the tired algorithm calculating specified point each
Accumulated damage or safety coefficient under rope coordinate system；
S3, the accumulated damage or safety coefficient of all searching coordinates systems of comparison, accumulated damage maximum or safety coefficient is minimum
Direction output as most damages loading direction；
When being scanned for the scope of freedom of unit, in step S1, definite specified point is the central point on each scope of freedom, and definite searches
Rope space is to be determined according to predetermined region of search and search density, stress, strain in step S1 to each scope of freedom central point
The calculation procedure of tensor course is as follows：
Zy1, the measuring coordinate system o-xyz for extracting scope of freedom central point and scope of freedom central point are under the measuring coordinate system
Ess-strain course determines ess-strain tensor of each course point scope of freedom central point in measuring coordinate system；
Zy2, search space is determined：It extracts default region of search parameter θ and Δ θ and search density parameter Δ α, formation is searched
Rope space o-x_s-x_e, wherein x_s are o-xyz coordinate systems turns the search starting position coordinates that θ angles obtain around z-axis in o points
Axis, x_e are o-x_s, y_s, and z_s coordinate systems turn the search final position reference axis that Δ θ angles obtain around z-axis in o points, and search is empty
Between be using o-x_s and o-x_e as border, using Δ α as N number of coordinate series of increment；
Zy3, the direction cosines for calculating each coordinate system in search space and each axis of measuring coordinate system；
Zy4, stress of the scope of freedom center under n-th of searching coordinates system, strain tensor course are calculated.
2. the definite method for most damaging loading direction of non-proportional loading according to claim 1, which is characterized in that unit
Given side when scanning for, in step S1, definite specified point is the arbitrary point in given side, and definite search space is root
It is determined according to search face, region of search and search density.
3. the definite method for most damaging loading direction of non-proportional loading according to claim 2, which is characterized in that unit
Given side when scanning for, it is as follows to the calculation procedure of the stress of specified point, strain tensor course in step S1：
The ess-strain course of Zd1, the original coordinate system and specified point o of extraction specified point o under original coordinate system, determines each
Specified point o is in the ess-strain tensor of the original coordinate system in a course；
Zd2, search space is determined：Given side coordinate system o-xyz is extracted as measuring coordinate system, according to default region of search
Parameter θ and Δ θ and search density parameter Δ α, form search space o-x_s-x_e, wherein x_s is o-xyz coordinate systems in o
The search starting position coordinates axis for turning θ angles around z-axis and obtaining is put, x_e is o-x_s, y_s, and z_s coordinate systems turn Δ in o points around z-axis
The search final position reference axis that θ angles obtain, search space are using o-x_s and o-x_e as border, using Δ α as the N of increment
A coordinate series；
Zd3, each searching coordinates system in search space and the direction cosines of each axis of original coordinate system are calculated；
Zd4, ess-strain tensor course of the o points under n-th of searching coordinates system is calculated.
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| CN111398019B (en) * | 2020-04-22 | 2021-03-02 | 中国科学院武汉岩土力学研究所 | Method for rapidly judging relative size of rock damage under loads with different strain rates |
| CN111950101A (en) * | 2020-08-07 | 2020-11-17 | 中铁轨道交通装备有限公司 | Tensor-based multi-axial fatigue analysis method |
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