CN115828690A - Method for distributing quality of structural finite element model - Google Patents

Method for distributing quality of structural finite element model Download PDF

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CN115828690A
CN115828690A CN202211544600.5A CN202211544600A CN115828690A CN 115828690 A CN115828690 A CN 115828690A CN 202211544600 A CN202211544600 A CN 202211544600A CN 115828690 A CN115828690 A CN 115828690A
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mass
distribution
quality
matrix
position information
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刘凯
付志超
田海涛
苑凯华
程萌
刘燚
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Beijing Electromechanical Engineering Research Institute
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Abstract

The invention provides a method for distributing structural finite element model quality, which comprises the steps of obtaining the quality after distribution according to the quality data before distribution and the quality data after distribution
Figure DDA0003979395820000011
2. Mass after distribution
Figure DDA0003979395820000012
Divided into two groups, positive mass
Figure DDA0003979395820000013
And negative mass
Figure DDA0003979395820000014
Respectively record the position informationInformation; 3. solving for new C according to positive and negative mass nodes aa And A ab Also according to the formula
Figure DDA0003979395820000015
Will be provided with
Figure DDA0003979395820000016
Mass distribution to step4 Positive Mass
Figure DDA0003979395820000017
On a node, the negative quality record after allocation is
Figure DDA0003979395820000018
4. Using a formula
Figure DDA0003979395820000019
Acquisition culling
Figure DDA00039793958200000110
New mass arrays after the mass point; 5. repeating two to four times until
Figure DDA00039793958200000111
Mass in (2) has no negative mass. The invention can obviously improve the quality distribution efficiency, reduce the complexity of the finite element model, improve the simulation analysis precision of the finite element model and facilitate the engineering application.

Description

Method for distributing quality of structural finite element model
Technical Field
The invention belongs to the technical field of aeroelasticity, and relates to a mass distribution method of a structural finite element model.
Background
The aeroelastic technology is a comprehensive discipline for researching the interaction between aerodynamics and structural elastic deformation in a regular grade and is mainly used for researching the influence of an aircraft under the combined action of elastic force, inertia force and aerodynamic force.
An accurate and efficient structural finite element model is the analysis basis for developing aeroelasticity mechanics, the mass characteristic of the finite element model is one of the original data of modal and inertia force calculation, and the reliability of the finite element model has important influence on the calculation result. Traditional mass distribution needs a large amount of manual operation and adjustment, is low in efficiency and inconsistent in output result, needs a large amount of connecting units to connect the mass to the finite element model, and increases the scale and complexity of the finite element model.
Disclosure of Invention
The present invention is directed to solving at least one of the problems of the prior art.
Therefore, the invention provides a structural finite element model quality distribution method.
The technical solution of the invention is as follows: a method for distributing the mass of a structural finite element model is provided, which comprises the following steps:
determining quality data before distribution and quality data after distribution, wherein the quality data before distribution comprises quality and corresponding node position information, and the quality data after distribution comprises the node position information of the quality after distribution;
secondly, determining parameters of an influence area based on the distributed quality node information;
thirdly, acquiring a corresponding matrix C before quality distribution according to the node position information before distribution and the parameters of the affected area aa (ii) a Acquiring a corresponding matrix A after quality distribution according to the distributed node position information and the parameters of the affected area ab ；
Step four, according to the matrix C aa Matrix A ab And the quality data quality to be distributed solves the distributed quality
Figure BDA0003979395800000021
Step five, distributing the quality
Figure BDA0003979395800000022
Divided into two groups, positive mass
Figure BDA0003979395800000023
And negative mass
Figure BDA0003979395800000024
Respectively recording node position information;
step six, according to the negative mass
Figure BDA0003979395800000025
Calculating new matrix C by corresponding node position information and influence area parameters aa (ii) a According to mass
Figure BDA0003979395800000026
Solving new matrix A by corresponding node position information and influence area parameters ab ；
Step seven, according to the new matrix C aa 、A ab And a negative mass
Figure BDA0003979395800000027
Solving for redistributed negative masses
Figure BDA0003979395800000028
To connect the negative mass
Figure BDA0003979395800000029
Mass distribution to positive mass in step five
Figure BDA00039793958000000210
On a node;
step eight, according to positive mass
Figure BDA00039793958000000211
And negative mass
Figure BDA00039793958000000212
Acquisition culling
Figure BDA00039793958000000213
New mass arrays after the mass point;
step nine, repeating the step five to the step eight until
Figure BDA00039793958000000214
Mass in (2) has no negative mass.
Further, determining an area of influence parameter based on the node information of the allocated quality by:
determining the distance r of two nodes with the farthest distance according to the node information of the distributed quality max ；
Based on said distance r by max Determining an area of influence parameter rr:
rr＝r max /5。
further, the corresponding matrix C before quality distribution is obtained according to the node position information before distribution and the parameters of the influence area aa The method comprises the following steps:
acquiring a pre-distribution radial basis function according to the pre-distribution node position information and the influence area parameters;
acquiring a corresponding matrix C before quality distribution according to the radial basis function before distribution and the node position information before distribution aa 。
Further, a pre-allocation radial basis function is obtained according to the pre-allocation node position information and the affected area parameter by the following formula:
Figure BDA0003979395800000031
wherein (x) ai ,y ai ,z ai ) Pre-node location information is assigned for the quality,
Figure BDA0003979395800000032
the pre-assignment radial basis functions.
Further, acquiring a corresponding matrix C before quality distribution according to the radial basis function before distribution and node position information before distribution by the following formula aa ：
Figure BDA0003979395800000033
Further, the corresponding matrix A after quality distribution is obtained according to the distributed node position information and the parameters of the influence area ab The method comprises the following steps:
acquiring a distributed radial basis function according to the distributed node position information and the parameters of the influence area;
acquiring a corresponding matrix A after quality distribution according to the distributed radial basis functions and the distributed node position information ab 。
Further, the distributed radial basis functions are obtained according to the distributed node position information and the parameters of the affected area through the following formula:
Figure BDA0003979395800000034
wherein (x) bi ,y bi ,z bi ) The post-node location information is assigned for the quality,
Figure BDA0003979395800000041
is the post-assignment radial basis function.
Further, obtaining a corresponding matrix A after quality distribution according to the distributed radial basis function and the distributed node position information by the following formula ab ：
Figure BDA0003979395800000042
Further, according to the matrix C by aa Matrix A ab And solving the pre-allocated mass to the post-allocated mass
Figure BDA0003979395800000043
Figure BDA0003979395800000044
Wherein the content of the first and second substances,
Figure BDA0003979395800000045
is the pre-distribution mass;
according to the new matrix C by aa 、A ab And a negative mass
Figure BDA0003979395800000046
Solving for redistributed negative masses
Figure BDA0003979395800000047
Figure BDA0003979395800000048
Further, according to the positive mass by the following formula
Figure BDA0003979395800000049
And negative mass
Figure BDA00039793958000000410
Acquisition culling
Figure BDA00039793958000000411
New mass array after mass point
Figure BDA00039793958000000412
Figure BDA00039793958000000413
The technical scheme adopts a virtual work principle interpolation method to ensure the consistency of the mass and the mass center before and after distribution, and simultaneously designs a negative mass elimination redistribution method to avoid the occurrence of negative mass after distribution; the redistributed mass is attached to the nodes of the existing model, so that the mass distribution efficiency can be obviously improved, the complexity of the finite element model can be reduced, the simulation analysis precision of the finite element model can be improved, and the engineering application is facilitated.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
FIG. 1 is a schematic flow chart of a method according to an embodiment of the present invention.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The relative arrangement of the components and steps, the numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless specifically stated otherwise. Meanwhile, it should be understood that the sizes of the respective portions shown in the drawings are not drawn in an actual proportional relationship for the convenience of description. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate. In all examples shown and discussed herein, any particular value should be construed as merely illustrative, and not limiting. Thus, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures.
In one embodiment of the present invention, as shown in fig. 1, there is provided a method for assigning mass to a finite element model of a structure, the method comprising:
determining quality data before distribution and quality data after distribution, wherein the quality data before distribution comprises quality and corresponding node position information (three-coordinate position of a mass center corresponding to the quality), and the quality data after distribution comprises the node position information of the quality after distribution;
secondly, determining parameters of an influence area based on the node information of the distributed quality;
thirdly, acquiring a corresponding matrix C before quality distribution according to the node position information before distribution and the parameters of the affected area aa (ii) a Acquiring a corresponding matrix A after quality distribution according to the distributed node position information and the parameters of the affected area ab ；
Step four, according to the matrix C aa Matrix A ab And the quality of the quality data needing to be distributed solves the distributed quality
Figure BDA0003979395800000061
Step five, distributing the quality
Figure BDA0003979395800000062
Divided into two groups, positive mass
Figure BDA0003979395800000063
And negative mass
Figure BDA0003979395800000064
Respectively recording node position information;
step six, according to the negative mass
Figure BDA0003979395800000065
Calculating new matrix C by corresponding node position information and influence area parameters aa (ii) a According to mass
Figure BDA0003979395800000066
Solving new matrix A by corresponding node position information and influence area parameters ab ；
Step seven, according to the new matrix C aa 、A ab And a negative mass
Figure BDA0003979395800000067
Solving for redistributed negative masses
Figure BDA0003979395800000068
To connect the negative mass
Figure BDA0003979395800000071
Mass distribution to positive mass in step five
Figure BDA0003979395800000072
On a node;
step eight, according to positive mass
Figure BDA0003979395800000073
And negative mass
Figure BDA0003979395800000074
Acquisition culling
Figure BDA0003979395800000075
New mass arrays after the mass point;
step nine, repeating the step five to the step eight until
Figure BDA0003979395800000076
Mass in (2) has no negative mass.
That is, the new quality array obtained in the step eight is continuously transferred to the step five for processing, the new quality array is divided into two groups, the subsequent steps are continuously executed,up to
Figure BDA0003979395800000077
Medium mass has no negative mass, and finally the final product
Figure BDA0003979395800000078
And outputting the corresponding node coordinates to finish the quality distribution.
In the embodiment of the invention, the consistency of the mass and the mass center before and after distribution can be ensured by the virtual work principle according to the following steps:
Figure BDA0003979395800000079
formula (1) is a formula for ensuring consistency of mass and mass center before and after mass distribution, wherein M i For the mass before mass distribution, x i Is M i A position coordinate corresponding to the mass; m j For the mass after mass distribution, x j Is M j Position coordinates corresponding to the mass.
The formula for conservation of force and moment is:
Figure BDA00039793958000000710
equation (2) is a formula for conservation of force and moment before and after interpolation, where F i For the force before interpolation, x i Is F i The point of action of the corresponding force; f j For interpolated force, x j Is F j The point of action of the force.
The force interpolation adopts a virtual work principle, so that the establishment of the formula (2) can be ensured, and the formula (1) is completely consistent with the formula (2), so that the quality and the mass center before and after distribution can be ensured to be consistent by applying the virtual work principle.
The virtual work principle is that the virtual work done on the interface displacement before and after interpolation is equal, i.e. the virtual work is equal
Figure BDA0003979395800000081
In the above formula, δ W is the imaginary work;
Figure BDA0003979395800000082
to interpolate the front force matrix, δ u a Virtual displacement before interpolation;
Figure BDA0003979395800000083
to interpolate the rear force matrix, δ u b And (4) performing virtual displacement after interpolation.
Introducing an RBF interpolation function and a definite solution condition thereof, and converting the formula of a mass matrix M instead of a force matrix F into a matrix form:
Figure BDA0003979395800000084
wherein
Figure BDA0003979395800000085
Figure BDA0003979395800000086
Figure BDA0003979395800000087
In order to assign a pre-quality matrix,
Figure BDA0003979395800000088
to assign the post-quality matrix, (x) ai ,y ai ,z ai ),(x bi ,y bi ,z bi ) The position information before and after the mass is allocated,
Figure BDA0003979395800000089
for the radial basis function, the expression is as follows:
Figure BDA00039793958000000810
in the formula (4)
Figure BDA00039793958000000811
C aa And A ab As is known, a post-allocation quality matrix can be derived
Figure BDA00039793958000000812
Because the virtual work principle can only ensure that the quality and the mass center before and after the quality distribution are consistent, the quality after the distribution is not negative, and the negative quality points need to be removed and redistributed, the embodiment of the invention adopts a virtual work principle interpolation method to ensure the consistency of the quality and the mass center before and after the distribution, and simultaneously designs a method (five to nine steps) for removing and redistributing the negative quality to avoid the occurrence of the negative quality after the distribution.
Therefore, the embodiment of the invention adopts a virtual work principle interpolation method to ensure the consistency of the mass and the mass center before and after distribution, and simultaneously designs a method for eliminating negative mass and redistributing to avoid the occurrence of negative mass after distribution; the redistributed mass depends on the nodes of the existing model, so that the mass distribution efficiency can be obviously improved, the complexity of the finite element model can be reduced, the simulation analysis precision of the finite element model can be improved, and the engineering application is facilitated.
In the above embodiment, the impact area parameter is determined based on the node information of the post-allocation quality by:
determining the distance r of two nodes with the farthest distance according to the node information of the distributed quality max ；
Based on said distance r by max Determining an area of influence parameter rr:
rr＝r max /5。
in the above embodiment, the obtaining of the pre-quality-distribution corresponding matrix C according to the node position information before distribution and the affected area parameter aa The method comprises the following steps:
acquiring a pre-distribution radial basis function according to the pre-distribution node position information and the influence area parameters;
according to the aboveObtaining a pre-quality-distribution corresponding matrix C by using a pre-distribution radial basis function and pre-distribution node position information aa 。
In the embodiment of the invention, the pre-distribution radial basis function is obtained according to the pre-distribution node position information and the influence area parameter by the following formula:
Figure BDA0003979395800000091
wherein (x) ai ,y ai ,z ai ) Pre-node location information is assigned for the quality,
Figure BDA0003979395800000092
the pre-radial basis functions are assigned.
In the embodiment of the invention, the corresponding matrix C before quality distribution is obtained according to the radial basis function before distribution and the node position information before distribution by the following formula aa ：
Figure BDA0003979395800000101
In the above embodiment, the corresponding matrix a after quality distribution is obtained according to the distributed node position information and the parameters of the affected area ab The method comprises the following steps:
acquiring a distributed radial basis function according to the distributed node position information and the parameters of the influence area;
acquiring a corresponding matrix A after quality distribution according to the distributed radial basis functions and the distributed node position information ab 。
In the embodiment of the invention, the distributed radial basis function is obtained according to the distributed node position information and the influence area parameter by the following formula:
Figure BDA0003979395800000102
wherein (x) bi ,y bi ,z bi ) Is divided by massAfter the position information of the nodes is matched,
Figure BDA0003979395800000103
is the post-assignment radial basis function.
In the embodiment of the invention, the corresponding matrix A after quality distribution is obtained according to the distributed radial basis functions and the distributed node position information by the following formula ab ：
Figure BDA0003979395800000104
It can be seen that the matrix C can be derived from aa Matrix A ab And solving the quality after distribution for the quality before distribution
Figure BDA0003979395800000105
Figure BDA0003979395800000106
Wherein the content of the first and second substances,
Figure BDA0003979395800000111
is the pre-dispense mass.
Furthermore, for solving a new matrix C aa And a new matrix A ab According to the mass of the load
Figure BDA0003979395800000112
Solving a new matrix C for corresponding node location information aa The specific solving method refers to the formula (4), and is not described in detail herein; in the same way, can be based on quality
Figure BDA0003979395800000113
Solving new matrix A according to the node position information (namely positive and negative node position information) ab 。
It can be seen that the new matrix C can be derived from aa 、A ab And a negative mass
Figure BDA0003979395800000114
Solving for redistributed negative masses
Figure BDA0003979395800000115
Figure BDA0003979395800000116
In the above embodiment, the positive mass is determined by the following equation
Figure BDA0003979395800000117
And negative mass
Figure BDA0003979395800000118
Acquisition culling
Figure BDA0003979395800000119
New mass array after mass point
Figure BDA00039793958000001110
Figure BDA00039793958000001111
That is, using the formula
Figure BDA00039793958000001112
Can obtain and reject
Figure BDA00039793958000001113
And (5) new quality arrays after the quality points.
In summary, the method for distributing the mass of the finite element model provided by the embodiment of the invention adopts the virtual work principle interpolation method to ensure the consistency of the mass and the mass center before and after distribution and the method of eliminating and redistributing the negative mass to avoid the occurrence of the negative mass after distribution; the redistributed mass is attached to the nodes of the existing model, so that the mass distribution efficiency can be obviously improved, the complexity of the finite element model can be reduced, and the simulation analysis precision of the finite element model can be improved.
Features that are described and/or illustrated above with respect to one embodiment may be used in the same way or in a similar way in one or more other embodiments and/or in combination with or instead of the features of the other embodiments.
It should be emphasized that the term "comprises/comprising" when used herein, is taken to specify the presence of stated features, integers, steps or components but does not preclude the presence or addition of one or more other features, integers, steps, components or groups thereof.
The above methods of the present invention may be implemented by hardware, or may be implemented by hardware in combination with software. The present invention relates to a computer-readable program which, when executed by a logic section, enables the logic section to implement the apparatus or constituent parts described above, or to implement various methods or steps described above. The present invention also relates to a storage medium such as a hard disk, a magnetic disk, an optical disk, a DVD, a flash memory, or the like, for storing the above program.
The many features and advantages of these embodiments are apparent from the detailed specification, and thus, it is intended by the appended claims to cover all such features and advantages of these embodiments which fall within the true spirit and scope thereof. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the embodiments of the invention to the exact construction and operation illustrated and described, and accordingly, all suitable modifications and equivalents may be resorted to, falling within the scope thereof.
The invention has not been described in detail and is in part known to those of skill in the art.

Claims (10)

1. A method for assigning mass to a finite element model of a structure, the method comprising:
determining quality data before distribution and quality data after distribution, wherein the quality data before distribution comprises quality and corresponding node position information, and the quality data after distribution comprises the node position information of the quality after distribution;
secondly, determining parameters of an influence area based on the distributed quality node information;
thirdly, acquiring a corresponding matrix C before quality distribution according to the node position information before distribution and the parameters of the affected area aa (ii) a Acquiring a corresponding matrix A after quality distribution according to the distributed node position information and the parameters of the affected area ab ；
Step four, according to the matrix C aa Matrix A ab And the quality of the quality data needing to be distributed solves the distributed quality
Figure FDA0003979395790000011
Step five, distributing the quality
Figure FDA0003979395790000012
Divided into two groups, positive mass
Figure FDA0003979395790000013
And negative mass
Figure FDA0003979395790000014
Respectively recording node position information;
step six, according to the negative mass
Figure FDA0003979395790000015
Calculating new matrix C by corresponding node position information and influence area parameters aa (ii) a According to mass
Figure FDA0003979395790000016
Solving new matrix A by corresponding node position information and influence area parameters ab ；
Step seven, according to the new matrix C aa 、A ab And a negative mass
Figure FDA0003979395790000017
Solving for redistributed negative masses
Figure FDA0003979395790000018
To connect the negative mass
Figure FDA0003979395790000019
Mass distribution to positive mass in step five
Figure FDA00039793957900000110
On a node;
step eight, according to positive mass
Figure FDA00039793957900000111
And negative mass
Figure FDA00039793957900000112
Acquisition culling
Figure FDA00039793957900000113
New mass arrays after the mass point;
step nine, repeating the step five to the step eight until
Figure FDA00039793957900000114
Mass in (2) has no negative mass.
2. The method of claim 1, wherein the parameters of the region of influence are determined based on the node information of the assigned mass by:
determining the distance r of two nodes with the farthest distance according to the node information of the distributed quality max ；
Based on said distance r by max Determining an area of influence parameter rr:
rr＝r max /5。
3. a structural finite element according to claim 1 or 2The model quality distribution method is characterized in that the corresponding matrix C before quality distribution is obtained according to the node position information before distribution and the influence area parameters aa The method comprises the following steps:
acquiring a pre-distribution radial basis function according to the pre-distribution node position information and the influence area parameters;
acquiring a corresponding matrix C before quality distribution according to the radial basis function before distribution and the node position information before distribution aa 。
4. The method of claim 3, wherein the pre-distribution radial basis functions are obtained from the pre-distribution node location information and the affected area parameters according to the following formula:
Figure FDA0003979395790000021
wherein (x) ai ,y ai ,z ai ) Pre-node location information is assigned for the quality,
Figure FDA0003979395790000022
the pre-assignment radial basis functions.
5. The method as claimed in claim 4, wherein the pre-quality-distribution correspondence matrix C is obtained from the pre-distribution radial basis function and the pre-distribution node position information according to the following formula aa ：
Figure FDA0003979395790000023
6. The method as claimed in claim 3, wherein the step of obtaining the after-quality-distribution correspondence matrix A according to the distributed node position information and the parameters of the affected area ab The method comprises the following steps:
acquiring a distributed radial basis function according to the distributed node position information and the parameters of the influence area;
acquiring a corresponding matrix A after quality distribution according to the distributed radial basis functions and the distributed node position information ab 。
7. The method of claim 6, wherein the assigned radial basis functions are obtained from the assigned node location information and the affected area parameters according to the following formula:
Figure FDA0003979395790000031
wherein (x) bi ,y bi ,z bi ) The post-node location information is assigned for the quality,
Figure FDA0003979395790000032
is the post-assignment radial basis function.
8. The method of claim 7, wherein the matrix A corresponding to the distributed quality is obtained according to the distributed radial basis functions and the distributed node position information by the following formula ab ：
Figure FDA0003979395790000033
9. A method as claimed in claim 1, wherein said method comprises calculating said matrix C from said matrix C by aa Matrix A ab And solving the pre-allocated mass to the post-allocated mass
Figure FDA0003979395790000034
Figure FDA0003979395790000035
Wherein the content of the first and second substances,
Figure FDA0003979395790000036
is the pre-distribution mass;
according to the new matrix C by aa 、A ab And a negative mass
Figure FDA0003979395790000037
Solving for redistributed negative masses
Figure FDA0003979395790000038
Figure FDA0003979395790000039
10. A method of mass distribution for a finite element model of a structure as set forth in claim 9, wherein the mass distribution is based on positive mass by the following equation
Figure FDA00039793957900000310
And negative mass
Figure FDA00039793957900000311
Acquisition culling
Figure FDA00039793957900000312
New mass array after mass point
Figure FDA00039793957900000313
Figure FDA00039793957900000314
CN202211544600.5A 2022-12-04 2022-12-04 Method for distributing quality of structural finite element model Pending CN115828690A (en)

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