CN106354929B - Bearing structure load transfer path method for visualizing based on stiffness variation principle - Google Patents
Bearing structure load transfer path method for visualizing based on stiffness variation principle Download PDFInfo
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Abstract
Bearing structure load transfer path method for visualizing based on stiffness variation principle, first calculate the U* of each point and its corresponding gradient vector in bearing structure, numerical integration is carried out using U* gradient vector of the fourth order Runge-Kutta numerical integration method to each point in bearing structure, obtained curve is the load path in bearing structure；Then since U* size is at zero, U* isopleth is extracted, fractograph analysis is done to each point on isopleth along each isopleth, extracts ridge point thereon, be sequentially connected with each ridge point to get the main load path based on stiffness variation is arrived；The present invention can specify the direction of transfer and distributional pattern of load path in the structure, provide guidance to accurately hold load transmission and Distribution dynamics in bearing structure.
Description
Technical field
The invention belongs to bearing structure design fields, and in particular to a kind of bearing structure based on stiffness variation principle
Load transfer path method for visualizing.
Technical background
Bearing structure is the important foundation component of industrial equipment, its main function is the other components of support, transmitting load
Lotus etc..In structured design phase, the visualization of load path for structural bearing efficiency assessment and material Optimum utilization also
It is very helpful.Principal stress trajectory method is a kind of method for the extraction load path being most widely used at present, it is answered extensively
For concrete structure cloth muscle and the configuration design of structure etc., the property of stress is identical at each point on principal stress trajectory, but
Its size is generally unequal, and principal stress trajectory is not to be connected to obligatory point from the position of load under normal circumstances, main
These properties of stress trajectory make its can not accurate description structure internal load transmission path.
Summary of the invention
In order to overcome the disadvantages of the above prior art, the purpose of the present invention is to provide a kind of based on stiffness variation principle
Bearing structure load transfer path method for visualizing can be explicitly shown the direction of transfer of load path in the structure and distribution shape
State provides guidance to accurately hold load transmission and Distribution dynamics in bearing structure.
To reach above-mentioned target, the technical scheme adopted by the invention is as follows:
Bearing structure load transfer path method for visualizing based on stiffness variation principle, comprising the following steps:
1) it solves the field U* of bearing structure: the U* value of each point in bearing structure being calculated by formula (1) and passes through interpolation
Method obtains U*, and the method for solving for the U* value that certain in bearing structure is put is as follows:
In formula, U is strain energy of the bearing structure under by primal constraints and load effect；U' is bearing structure in primal constraints
On the basis of load, separately add to the structural strain energy after target point staff cultivation；
2) load path is visualized: by the load path and main load path of U* determining bearing structures, specifically:
2.1) it generates load path: utilizing the U* U* gradients found out in bearing structure at each point obtained in step 1),
Numerical integration, obtained song are carried out using gradient vector of the fourth order Runge-Kutta numerical integration method to each point U* in bearing structure
Line is rigidity line, and rigidity line is load path in bearing structure；
2.2) it generates main load path: since U* size is at zero, extracting isopleth in U*；Along each isopleth
Fractograph analysis is done to each point on line, using the vertical plane of U* gradient as section, the maximum point of section upper curve is ridge point, is mentioned
Take the ridge point on each isopleth；It is sequentially connected with each ridge point and obtains U* crestal lines, crestal line is the main load based on stiffness variation
Path.
Using the field U* of finite element method bearing structure in the step 1), the specific steps are as follows:
1.1) finite element modeling: utilizing finite element method, to bearing structure modeling and grid division, obtains bearing structure
Finite element model, and then obtain the global stiffness matrix K of bearing structure；
1.2) strain energy when solution bearing structure is loaded: the finite element model that step 1.1) is obtained according to the actual situation
Apply constraint and load, obtains the modal displacement vector X of bearing structure using statics Analysis, and acquire modal displacement vector
Transposition XT, according to strain energy of formula (2) solution structure when loaded:
1.3) successively each node of staff cultivation and solve the strain energy of bearing structure: on the basis of step 1.2), successively it is complete about
Each node of beam object construction finite element model, the strain energy under solution bearing structure is loaded, when defining i-th of node of staff cultivation
Structural strain can be U'i；
1.4) field U* of bearing structure: the U* of i-th of node in bearing structure is solvediAre as follows:
According to formula (3), the U* value at each node is solved respectively, and the field U* of bearing structure is obtained by interpolation method.
The invention has the benefit that
Since the parameter U* used is the variation based on bearing structure overall situation strain energy, so final result has the overall situation
Property；Due to determining load path according to U*, so load path is necessarily connected with load(ing) point and obligatory point, meet the biography of load
Passing property；Due to using stiffness variation principle and using crestal line as load path, so that the load path arrived has clearly
Configuration.
Detailed description of the invention
Fig. 1 is the size and boundary condition schematic diagram of cantilever beam structure in embodiment.
Fig. 2 is the field the U* schematic diagram in embodiment comprising each point gradient vector.
Fig. 3 is the rigidity line and main load path schematic diagram of cantilever beam structure in embodiment.
Fig. 4 is U* distribution of contours figures and U* distributed in three dimensions surface charts, and wherein Fig. 4 (a) is U* distribution of contours
Schematic diagram, Fig. 4 (b) are U* distributed in three dimensions surface charts.
Fig. 5 is the schematic diagram that fractograph analysis method extracting ridges are utilized in embodiment.
Specific embodiment
Below with reference to the visual embodiment pair of load path under the cantilever beam structure loading conditions of 320mm*200mm*5mm
The present invention is described further.
Bearing structure load transfer path method for visualizing based on stiffness variation principle, comprising the following steps:
1) solve bearing structure field U*: the cantilever beam structure is modeled using finite element method, apply constraint with
Load, and the U* value of each node in bearing structure is calculated, U* then are obtained by interpolation, the U* value that certain in bearing structure is put
Method for solving it is as follows:
In formula, U is strain energy of the bearing structure under by primal constraints and load effect；U' is bearing structure in primal constraints
On the basis of load, separately add to the structural strain energy after target point staff cultivation；
Specific step is as follows:
1.1) finite element modeling: finite element method is utilized, to the cantilever beam structure grid division, used herein is four sections
Point shell unit, and definition material is structural steel, obtains the global stiffness matrix K of bearing structure；
1.2) solve bearing structure it is loaded when strain energy: the size of cantilever beam structure and boundary condition be such as in the present embodiment
Shown in Fig. 1, apply constraint and load, i.e. a column node of staff cultivation model left side according to Fig. 1, to section intermediate in right edge
Point applies downward load p, and P is 100 newton in this embodiment；Using statics Analysis obtain the modal displacement of bearing structure to
X is measured, and acquires the transposition X of modal displacement vectorT, according to the following formula solve obtain bearing structure it is loaded when strain energy:
1.3) successively each node of staff cultivation and solve the strain energy of bearing structure: on the basis of step 1.2), successively it is complete about
Each node of beam object construction finite element model, the strain energy under solution bearing structure is loaded, when defining i-th of node of staff cultivation
Structural strain can be U'i；
1.4) field U* of bearing structure: the U* value of the i-th node in bearing structure is solved are as follows:
According to above formula, the U* value at each node is solved respectively, and the field U* of bearing structure is obtained by interpolation method, such as scheme
Shown in 2；
2) load path: the load path of the U* as obtained in step 1) determining bearing structure and main load road is visualized
Diameter, specifically:
2.1) generate load path: the cloud charts of U* reflect inside configuration load transmission characteristic, gradient vector generation
The direction of table structure internal load transmitting, the present embodiment are found out in bearing structure at each point using U* obtained in step 1)
U* gradient vector, as shown in Figure 2；It is sweared using gradient of the fourth order Runge-Kutta numerical integration method to each point U* in bearing structure
Amount carries out numerical integration, and obtained curve is rigidity line, and rigidity line is load path in bearing structure, such as the thin reality in Fig. 3
Shown in line；
2.2) generate main load path: Fig. 4 (a) is the U* isopleth schematic diagram of certain two-dimensional structure, and corresponding U* is contour
Figure is as shown in Fig. 4 (b)；Dimensionless group U* is the rigidity size for representing each point in bearing structure, is become in U* value size with position
In the field U* of change, as shown in figure 4, crestal line is the main load path based on stiffness variation；
The position of crestal line is determined by the distribution of each point U* in bearing structure, carrys out extracting ridges using fractograph analysis method, such as
Shown in Fig. 5, the specific steps of crestal line extraction are as follows: since U* size is at zero, extract isopleth in U*；It is equivalent along each item
Each point does fractograph analysis on Line To Line, using the vertical plane of U* gradient as section in the present embodiment, the maximum of section upper curve
Point is ridge point, extracts the ridge point on each isopleth；It should be pointed out that when section is vertical with the direction of crestal line, section
The error of analytic approach extracting ridges is smaller, because crestal line is along the direction of gradient, this method will be made with the vertical plane of gradient
Maximum is analyzed for section；It is sequentially connected with each ridge point and obtains U* crestal lines, the i.e. main load path based on stiffness variation, such as
Shown in black heavy line in Fig. 3；
As shown in figure 3, the load road based on stiffness variation principle may finally be obtained using method proposed by the present invention
Diameter, it can be seen from the figure that load path gradually comes together in main load path from restrained end to load(ing) point；This is also absolutely proved
Main load path, that is, U* cloud charts crestal line plays bigger effect during load transmission；It is our as seen from Figure 3
Method has obtained clearly reflecting the load path of load direction of transfer and distributional pattern in the structure.
Claims (2)
1. the bearing structure load transfer path method for visualizing based on stiffness variation principle, which is characterized in that including following step
It is rapid:
1) it solves the field U* of bearing structure: the U* value of each point in bearing structure being calculated by formula (1) and passes through interpolation method
U* are obtained, the method for solving for the U* value that certain in bearing structure is put is as follows:
In formula, U is strain energy of the bearing structure under by primal constraints and load effect；U' is bearing structure in primal constraints and load
On the basis of lotus, separately add to the structural strain energy after target point staff cultivation；
2) load path is visualized: by the load path and main load path of U* determining bearing structures, specifically:
2.1) it generates load path: using the U* U* gradients found out in bearing structure at each point obtained in step 1), utilizing
Fourth order Runge-Kutta numerical integration method carries out numerical integration to the gradient vector of each point U* in bearing structure, and obtained curve is i.e.
For rigidity line, rigidity line is load path in bearing structure；
2.2) it generates main load path: since U* size is at zero, extracting isopleth in U*；Along each item equivalence Line To Line
Upper each point does fractograph analysis, and using the vertical plane of U* gradient as section, the maximum point of section upper curve is ridge point, extracts each
Ridge point on isopleth；It is sequentially connected with each ridge point and obtains U* crestal lines, crestal line is the main load path based on stiffness variation.
2. the bearing structure load transfer path method for visualizing according to claim 1 based on stiffness variation principle,
It is characterized in that: using the field U* of finite element method bearing structure in the step 1), the specific steps are as follows:
1.1) finite element modeling: utilizing finite element method, to bearing structure modeling and grid division, obtains the limited of bearing structure
Meta-model, and then obtain the global stiffness matrix K of bearing structure；
1.2) strain energy when solution bearing structure is loaded: the finite element model that step 1.1) obtains is applied according to the actual situation
Constraint and load, obtain the modal displacement vector X of bearing structure using statics Analysis, and acquire the transposition of modal displacement vector
XT, according to strain energy of formula (2) solution structure when loaded:
1.3) successively each node of staff cultivation and the strain energy of bearing structure is solved: on the basis of step 1.2), successively staff cultivation mesh
Each node of structural finite element model is marked, the strain energy under solution bearing structure is loaded defines knot when i-th of node of staff cultivation
Structure strain energy is U'i；
1.4) field U* of bearing structure: the U* of i-th of node in bearing structure is solvediAre as follows:
According to formula (3), the U* value at each node is solved respectively, and the field U* of bearing structure is obtained by interpolation method.
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| CN107563102A (en) * | 2017-10-11 | 2018-01-09 | 燕山大学 | A kind of power transmission skeleton method for visualizing of bearing structure |
| CN108536946A (en) * | 2018-04-02 | 2018-09-14 | 西安交通大学 | Operating condition Transfer Path Analysis Method of Automobile based on Landweber iterative methods |
| CN110096756B (en) * | 2019-04-08 | 2020-01-17 | 河海大学 | Free-form surface structure form creation method considering load uncertainty |
| CN114595612B (en) * | 2022-03-16 | 2024-05-10 | 上海核工程研究设计院股份有限公司 | Reinforcement calculation method and system for stress component based on entity unit integral path |
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