Structural finite element model mass distribution method

Abstract

The application provides a structural finite element model quality distribution method, comprising the following steps: 1, obtaining the quality after distribution according to the quality data before distribution and the quality data after distribution; 2, distributing the quality after distribution into two groups, positive quality and negative quality, and recording the position information of the positive quality and the negative quality respectively; 3, solving new C aa and A ab , and distributing the quality to the positive quality node in step 4 according to the formula, recording the negative quality after distribution; 4, obtaining the new quality matrix after removing the quality point by using the formula; 5, repeating steps 2-4 until there is no negative quality in the quality. The application can significantly 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 engineering application.

Description

Technical Field

[0001] This invention belongs to the field of aeroelasticity technology and relates to a method for mass allocation in a structural finite element model. Background Technology

[0002] Aeroelasticity is a comprehensive discipline that studies the laws governing the interaction between aerodynamics and structural elastic deformation, as well as its applications. It mainly studies the effects of the combined action of elastic forces, inertial forces, and aerodynamic forces on aircraft.

[0003] An accurate and efficient structural finite element model is the foundation for aeroelasticity analysis. The mass characteristics of the finite element model are one of the raw data for modal and inertial force calculations, and its reliability has a significant impact on the calculation results. Traditional mass allocation requires a lot of manual operation and adjustment, which is inefficient and produces inconsistent output results. It also requires a large number of connection elements to connect the mass to the finite element model, increasing the size and complexity of the finite element model. Summary of the Invention

[0004] The present invention aims to solve at least one of the technical problems existing in the prior art.

[0005] Therefore, the present invention provides a method for mass allocation in a structural finite element model.

[0006] The technical solution of this invention is as follows: A method for mass allocation in a structural finite element model is provided, the method comprising:

[0007] Step 1: Determine the quality data before allocation and the quality data after allocation. The quality data before allocation includes the quality and the corresponding node position information, and the quality data after allocation includes the node position information of the quality after allocation.

[0008] Step 2: Determine the parameters of the affected area based on the node information of the allocated quality;

[0009] Step 3: Obtain the matrix C corresponding to the quality allocation before the node position information and the influence area parameters. aa Based on the allocated node location information and the influence region parameters, obtain the matrix A corresponding to the quality allocation. ab ;

[0010] Step 4: Based on the matrix C aa Matrix A ab And the quality data to be allocated, the quality solution after allocation

[0011] Step 5: Distribute the allocated mass Divided into two groups, positive mass and negative mass Record the node location information respectively;

[0012] Step Six: Based on negative mass The new matrix C is calculated based on the corresponding node location information and the parameters of the affected area. aa According to quality The new matrix A is obtained by solving for the corresponding node location information and influence area parameters. ab ;

[0013] Step 7: Based on the new matrix C aa A ab and negative mass Solving for negative mass after redistribution To reduce negative mass The mass is allocated to the positive mass in step five. On the node;

[0014] Step 8: Based on positive mass and negative mass Get Removal The new mass matrix after the mass point;

[0015] Step 9: Repeat steps 5 through 8 until... There is no negative mass in the mass.

[0016] Furthermore, the parameters of the affected region are determined based on the node information of the allocated quality in the following manner:

[0017] The distance r between the two farthest nodes is determined based on the node information of the allocated quality. max ;

[0018] Based on the distance r, the following formula is used max Determine the parameter rr for the affected area:

[0019] rr = r max / 5.

[0020] Furthermore, the step of obtaining the corresponding matrix C before quality allocation based on the node position information before allocation and the influence region parameters... aa ,include:

[0021] Obtain the radial basis function before allocation based on the node location information and the parameters of the affected area before allocation;

[0022] Based on the radial basis function and node position information before allocation, obtain the corresponding matrix C before mass allocation. aa .

[0023] Furthermore, the radial basis function before allocation is obtained based on the node position information and the parameters of the affected region, using the following formula:

[0024]

[0025] Among them, (x ai ,y ai ,z ai () represents the node location information before quality allocation. For the radial basis functions before assignment.

[0026] Furthermore, the matrix C corresponding to the mass allocation before allocation is obtained using the following formula based on the radial basis function before allocation and the node position information before allocation. aa :

[0027]

[0028] Furthermore, the step of obtaining the corresponding matrix A after quality allocation based on the allocated node position information and the influence region parameters... ab ,include:

[0029] The radial basis function after allocation is obtained based on the node position information and the parameters of the affected area.

[0030] Based on the allocated radial basis function and the allocated node position information, obtain the matrix A corresponding to the mass allocation. ab .

[0031] Furthermore, the radial basis function after allocation is obtained based on the node position information and the parameters of the affected region using the following formula:

[0032]

[0033] Among them, (x bi ,y bi ,z bi () represents the node location information after quality allocation. These are the radial basis functions after allocation.

[0034] Furthermore, the matrix A corresponding to the mass allocation is obtained based on the allocated radial basis function and the allocated node position information using the following formula. ab :

[0035]

[0036] Furthermore, based on the matrix C, the following formula is used... aa Matrix A ab And the mass before allocation, and the mass after allocation.

[0037]

[0038] in, For the mass before allocation;

[0039] Based on the new matrix C using the following formula aa A ab and negative mass Solving for negative mass after redistribution

[0040]

[0041] Furthermore, based on the following formula according to positive mass and negative mass Get Removal New mass array after mass point

[0042]

[0043] The above technical solution uses the virtual work principle interpolation method to ensure the consistency of mass and centroid before and after allocation. At the same time, a method for eliminating and redistributing negative mass is designed to avoid the occurrence of negative mass after allocation. The redistributed mass is attached to the nodes of the existing model, which can significantly improve the efficiency of mass allocation and reduce the complexity of the finite element model, improve the accuracy of finite element model simulation analysis, and facilitate engineering applications. Attached Figure Description

[0044] The accompanying drawings, which form part of this specification, are provided to further illustrate embodiments of the invention and, together with the textual description, explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0045] Figure 1 This is a schematic diagram of the method flow of an embodiment of the present invention. Detailed Implementation

[0046] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0048] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0049] like Figure 1 As shown, in one embodiment of the present invention, a method for mass allocation in a structural finite element model is provided, the method comprising:

[0050] Step 1: Determine the mass data before allocation and the mass data after allocation. The mass data before allocation includes the mass and the corresponding node position information (the three-coordinate position of the centroid corresponding to the mass). The mass data after allocation includes the node position information of the mass after allocation.

[0051] Step 2: Determine the parameters of the affected area based on the node information of the allocated quality;

[0052] Step 3: Obtain the matrix C corresponding to the quality allocation before the node position information and the influence area parameters. aa Based on the allocated node location information and the influence region parameters, obtain the matrix A corresponding to the quality allocation. ab ;

[0053] Step 4: Based on the matrix C aa Matrix A ab And the quality data to be allocated, the quality solution after allocation

[0054] Step 5: Distribute the allocated mass Divided into two groups, positive mass and negative mass Record the node location information respectively;

[0055] Step Six: Based on negative mass The corresponding node location information and influence area parameters are used to calculate a new matrix C. aa According to quality The new matrix A is obtained by solving for the corresponding node location information and influence area parameters. ab ;

[0056] Step 7: Based on the new matrix C aa A ab and negative mass Solving for negative mass after redistribution To reduce negative mass The mass is allocated to the positive mass in step five. On the node;

[0057] Step 8: Based on positive mass and negative mass Get Removal The new mass matrix after the mass point;

[0058] Step 9: Repeat steps 5 through 8 until... There is no negative mass in the mass.

[0059] That is, after obtaining the new mass matrix in step eight, the process continues to step five, where the new mass matrix is ​​divided into two groups, and subsequent steps are performed until... The quality in the middle has no negative quality, and the final result will be Output the corresponding node coordinates to complete the quality allocation.

[0060] In this embodiment of the invention, the principle of virtual work can be used to ensure that the mass and center of mass are consistent before and after the distribution, based on the following:

[0061]

[0062] Formula (1) is the formula to ensure that the mass and center of mass are consistent before and after mass distribution, where M i For the mass before mass allocation, x i For M i The position coordinates corresponding to the mass; M j For the mass after mass allocation, x j For M j The position coordinates corresponding to the mass.

[0063] The formulas for the conservation of force and torque are:

[0064]

[0065] Formula (2) is the formula for the conservation of force and torque before and after interpolation, where F i The force before interpolation, x i For F i Point of application of stress; F j The force after interpolation, x j For F j The point of application of stress.

[0066] Force interpolation uses the principle of virtual work, which can ensure that formula (2) holds true. Formula (1) and formula (2) are completely consistent. Therefore, by applying the principle of virtual work, we can also ensure that the mass and center of mass are consistent before and after distribution.

[0067] The principle of virtual work is: the virtual work done on the interface displacement before and after interpolation is equal, that is...

[0068]

[0069] In the above formula, δW represents virtual work; Let δu be the force matrix before interpolation. a Virtual shift before interpolation; The force matrix after interpolation, δu b Virtual shift after interpolation.

[0070] Introducing the RBF interpolation function and its boundary conditions, and replacing the force matrix F with the mass matrix M, the above formula is transformed into matrix form:

[0071]

[0072] in

[0073]

[0074]

[0075] To assign the mass matrix before distribution, For the assigned mass matrix, (x ai ,y ai ,z ai ),(x bi ,y bi ,z bi This represents the positional information before and after quality allocation. The radial basis functions are expressed as follows:

[0076]

[0077] In formula (4) C aa and A ab Given that the mass matrix after allocation can be obtained, we can calculate it.

[0078] Since the principle of virtual work can only guarantee that the mass and the center of mass are consistent before and after mass allocation, it cannot guarantee that the mass after allocation is not negative. Negative mass points need to be removed and redistributed. Therefore, this embodiment of the invention uses the virtual work principle interpolation method to ensure the consistency of mass and the center of mass before and after allocation, while designing a method for removing and redistributing negative mass (steps five to nine) to avoid the occurrence of negative mass after allocation.

[0079] As can be seen, the embodiments of the present invention use the virtual work principle interpolation method to ensure the consistency of mass and centroid before and after allocation, and at the same time design a method for negative mass removal and redistribution to avoid the occurrence of negative mass after allocation; the redistributed mass is attached to the nodes of the existing model, which can significantly improve the efficiency of mass allocation and reduce the complexity of the finite element model, improve the accuracy of finite element model simulation analysis, and facilitate engineering applications.

[0080] In the above embodiments, the parameters of the affected region are determined based on the node information of the allocated quality in the following manner:

[0081] The distance r between the two farthest nodes is determined based on the node information of the allocated quality. max ;

[0082] Based on the distance r, the following formula is used max Determine the parameter rr for the affected area:

[0083] rr = r max / 5.

[0084] In the above embodiment, the step of obtaining the corresponding matrix C before quality allocation based on the node position information before allocation and the influence region parameters is described. aa ,include:

[0085] Obtain the radial basis function before allocation based on the node location information and the parameters of the affected area before allocation;

[0086] Based on the radial basis function and node position information before allocation, obtain the corresponding matrix C before mass allocation. aa .

[0087] In this embodiment of the invention, the radial basis function before allocation is obtained based on the node position information and the influence region parameters before allocation using the following formula:

[0088]

[0089] Among them, (x ai ,y ai ,z ai () represents the node location information before quality allocation. For the radial basis functions before assignment.

[0090] In this embodiment of the invention, the matrix C corresponding to the mass allocation before allocation is obtained by the following formula based on the radial basis function before allocation and the node position information before allocation. aa :

[0091]

[0092] In the above embodiment, the step of obtaining the matrix A corresponding to the quality allocation based on the allocated node position information and the influence region parameters is described. ab ,include:

[0093] The radial basis function after allocation is obtained based on the node position information and the parameters of the affected area.

[0094] Based on the allocated radial basis function and the allocated node position information, obtain the matrix A corresponding to the mass allocation. ab .

[0095] In this embodiment of the invention, the radial basis function after allocation is obtained based on the node position information and the influence region parameters using the following formula:

[0096]

[0097] Among them, (x bi ,y bi ,z bi () represents the node location information after quality allocation. These are the radial basis functions after allocation.

[0098] In this embodiment of the invention, the matrix A corresponding to the mass allocation is obtained based on the allocated radial basis function and the allocated node position information using the following formula. ab :

[0099]

[0100] It can be seen that the matrix C can be obtained by the following formula. aa Matrix A ab And the mass before allocation, the mass after allocation.

[0101]

[0102] in, This refers to the mass before allocation.

[0103] Furthermore, for solving the new matrix C aa And the new matrix A ab According to negative mass Solve for the new matrix C using the corresponding node position information. aaThe specific solution method is given in formula (4), and will not be elaborated further here; similarly, it can be determined based on the mass. The new matrix A is solved using the corresponding node position information (i.e., the positive and negative node position information). ab .

[0104] It can be seen that the new matrix C can be obtained through the following formula. aa A ab and negative mass Solving for negative mass after redistribution

[0105]

[0106] In the above embodiments, the following formula is used based on the positive mass. and negative mass Get Removal New mass array after mass point

[0107]

[0108] That is, using the formula You can get the removal The new mass matrix after the mass point.

[0109] In summary, the finite element model mass allocation method proposed in this embodiment of the invention uses the virtual work principle interpolation method to ensure the consistency of mass and centroid before and after allocation, and the method of eliminating and redistributing negative mass avoids the occurrence of negative mass after allocation; the redistributed mass is attached to the nodes of the existing model, which can significantly improve the efficiency of mass allocation and reduce the complexity of the finite element model, thereby improving the accuracy of finite element model simulation analysis.

[0110] The features described and / or illustrated above with respect to one embodiment may be used in the same or similar manner in one or more other embodiments, and / or in combination with or in lieu of features in other embodiments.

[0111] It should be emphasized that the term "including / comprises" as used herein refers to the presence of a feature, whole, step, or component, but does not exclude the presence or addition of one or more other features, wholes, steps, components, or combinations thereof.

[0112] The methods described above in this invention can be implemented in hardware or in combination with software. This invention relates to computer-readable programs that, when executed by a logic component, enable the logic component to implement the aforementioned apparatus or constituent parts, or to implement the various methods or steps described above. This invention also relates to storage media for storing the above programs, such as hard disks, magnetic disks, optical disks, DVDs, flash memory, etc.

[0113] Many features and advantages of these embodiments are apparent from this detailed description, and therefore the appended claims are intended to cover all such features and advantages of these embodiments that fall within their true spirit and scope. Furthermore, since many modifications and alterations will readily occur to those skilled in the art, the embodiments of the invention are not intended to be limited to the precise structures and operations illustrated and described, but rather to encompass all suitable modifications and equivalents falling within their scope.

[0114] The parts of this invention not described in detail are techniques known to those skilled in the art.

Claims

1. A method for mass allocation in a structural finite element model, characterized in that, The method includes: Step 1: Determine the quality data before allocation and the quality data after allocation. The quality data before allocation includes the quality and the corresponding node position information, and the quality data after allocation includes the node position information of the quality after allocation. Step 2: Determine the parameters of the affected area based on the node information of the allocated quality; Step 3: Obtain the matrix C corresponding to the quality allocation before the node position information and the influence area parameters. aa Based on the allocated node location information and the influence region parameters, obtain the matrix A corresponding to the quality allocation. ab ; Step 4: Based on the matrix C aa Matrix A ab And the quality data to be allocated, the quality solution after allocation Step 5: Distribute the allocated mass Divided into two groups, positive mass and negative mass Record the node location information respectively; Step Six: Based on negative mass The new matrix C is calculated based on the corresponding node location information and the parameters of the affected area. aa According to quality The new matrix A is obtained by solving for the corresponding node location information and influence area parameters. ab ; Step 7: Based on the new matrix C aa A ab and negative mass Solving for negative mass after redistribution To reduce negative mass The mass is allocated to the positive mass in step five. On the node; Step 8: Based on positive mass and negative mass Get Removal The new mass matrix after the mass point; Step 9: Repeat steps 5 through 8 until... There is no negative mass in the mass.

2. The method for mass allocation in a structural finite element model according to claim 1, characterized in that, The parameters of the affected region are determined based on the node information of the allocated quality in the following manner: The distance r between the two farthest nodes is determined based on the node information of the allocated quality. max ; Based on the distance r, the following formula is used max Determine the parameter rr for the affected area: rr＝r max / 5。 3. A method for mass allocation in a structural finite element model according to claim 1 or 2, characterized in that, The matrix C corresponding to the quality allocation before the allocation is obtained based on the node position information before allocation and the influence area parameters. aa ,include: Obtain the radial basis function before allocation based on the node location information and the parameters of the affected area before allocation; Based on the radial basis function and node position information before allocation, obtain the corresponding matrix C before mass allocation. aa .

4. The method for mass allocation in a structural finite element model according to claim 3, characterized in that, The radial basis function before allocation is obtained using the following formula based on the node position information and the parameters of the affected region before allocation: Among them, (x ai ,y ai ,z ai () represents the node location information before quality allocation. For the radial basis functions before assignment.

5. The method for mass allocation in a structural finite element model according to claim 4, characterized in that, The matrix C corresponding to the mass allocation before allocation is obtained by using the radial basis function and node position information before allocation according to the following formula. aa :

6. The method for mass allocation in a structural finite element model according to claim 3, characterized in that, The matrix A corresponding to the quality allocation is obtained based on the allocated node position information and the influence region parameters. ab ,include: The radial basis function after allocation is obtained based on the node position information and the parameters of the affected area. Based on the allocated radial basis function and the allocated node position information, obtain the matrix A corresponding to the mass allocation. ab .

7. The method for mass allocation in a structural finite element model according to claim 6, characterized in that, The radial basis function after allocation is obtained using the following formula based on the node position information and the parameters of the affected region: Among them, (x bi ,y bi ,z bi () represents the node location information after quality allocation. These are the radial basis functions after allocation.

8. The method for mass allocation in a structural finite element model according to claim 7, characterized in that, The matrix A corresponding to the mass allocation is obtained by using the following formula based on the allocated radial basis function and the allocated node position information. ab :

9. The method for mass allocation in a structural finite element model according to claim 1, characterized in that, Based on the matrix C using the following formula aa Matrix A ab And the mass before allocation, the mass after allocation. in, For the mass before allocation; Based on the new matrix C using the following formula aa A ab and negative mass Solving for negative mass after redistribution 10. The method for mass allocation in a structural finite element model according to claim 9, characterized in that, Based on the following formula, positive mass and negative mass Get Removal New mass array after mass point

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