CN113361001A - Solar wing structure optimization method and device combining finite element method and gradient method and storage medium - Google Patents

Solar wing structure optimization method and device combining finite element method and gradient method and storage medium Download PDF

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CN113361001A
CN113361001A CN202110458926.5A CN202110458926A CN113361001A CN 113361001 A CN113361001 A CN 113361001A CN 202110458926 A CN202110458926 A CN 202110458926A CN 113361001 A CN113361001 A CN 113361001A
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杨林
王岩松
魏磊
胡自强
徐拓奇
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Shandong University
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Abstract

The invention relates to a solar wing structure optimization method, equipment and a storage medium combining a finite element method and a gradient method, wherein the method comprises the following steps: step 1: establishing a solar wing finite element model, generating a modal analysis working condition, and generating a file with an extension name of. bdf, namely a bdf file, required by the computation of the nartran software; step 2: parameterizing a solar wing finite element model, setting the density of a finite element grid, the installation position of a hinge and the position of a compaction point as variable variables, setting the density of the finite element grid, setting the sizes of two directions of a finite element grid unit, defining the position of a coordinate origin at the first node position at the lower left corner of the finite element grid, generating finite element grid information by using matlab software, and updating; and step 3: optimizing the installation position of the solar wing hinge; and 4, step 4: and optimizing the position of the solar wing pressing point. The invention can improve the natural frequency of the solar wing structure, greatly improve the efficiency of the solar wing structure design and reduce the workload of designers.

Description

Solar wing structure optimization method and device combining finite element method and gradient method and storage medium
Technical Field
The invention relates to a solar wing structure optimization method, solar wing structure optimization equipment and a storage medium combining a finite element method and a gradient method, and belongs to the technical field of spacecraft structure design.
Background
The solar wing is also called as a solar sailboard and is an important component of a satellite power supply subsystem. The solar cell on the solar wing converts solar energy into electric energy through a photoelectric effect, and then the electric energy is stored in spacecrafts such as satellites and the like to provide necessary energy for satellite payloads and instruments and equipment of various subsystems of the satellites. In the process of launching the satellite, the solar wings are usually in a folded state, and are subjected to the vibration mechanical load transmitted to the satellite by the carrier rocket at the moment, so that the vibration mechanical load on the solar wings is transmitted. When the natural frequency of the solar wing is close to the natural frequency of the satellite body, acceleration response with a large amplitude is generated on the solar wing, the maximum value of the acceleration response can reach dozens of g or even hundreds of g, and the solar cell is damaged in serious conditions. When the satellite runs in orbit, the solar wing is in an unfolded state, if the fundamental frequency of the sailboard is too low, the sailboard is easily coupled with the attitude control frequency of the satellite, the control precision and stability of the satellite are affected, the micro-vibration problem of the satellite can be aggravated, and the performance indexes of instruments for satellite imaging, communication, measurement and the like are reduced. Therefore, by optimally designing the structure of the solar wing, the natural frequency of the solar wing is improved, the vibration response in the launching process of the solar wing and the micro-vibration response of the satellite in the on-orbit state are reduced, and the method has important significance for improving the working environment of the satellite, improving the performance index of the satellite and better completing the specified task.
Many researchers at home and abroad develop the optimization design research of the solar wing structure. Document 1[ smart, great lucmin, puhailing ] solar wing substrate structure optimization using OptiStruct software, spacecraft engineering.2011, 20 (06): 63-68], and carrying out topology optimization and size optimization design on the solar wing sailboard by using finite element software OptiStruct. Document 2[ wushipei, liuqiong, songbei, rongeli, xinpengfei ] structural optimization of UltraFlex solar cell array, astronavigation report 2020, 41 (11): 1378 + 1384] to improve the stability and natural frequency of the unfolding process of the circular solar cell array as the optimization target, and to optimize the structure of the circular solar cell array by using finite element software SAMCEF by using the UltraFlex solar cell array as a model. Most of the existing solar wing structure optimization methods carry out topology or size optimization on the solar wing structure through finite element software, and on one hand, the method depends on the design experience of engineers and needs larger workload; on the other hand, due to the limitation of the overall dimension of the satellite and the required power, the design space of the overall dimension of the solar wing structure is small, and certain design difficulty is achieved.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a solar wing structure optimization method combining a finite element method and a gradient method, which is characterized in that a finite element parameterized model of a solar wing structure is established, and the position of a solar wing hinge and the position of a compression point are automatically optimized by combining a finite element software through the gradient method so as to improve the natural frequency of the solar wing structure. The method can increase the structural rigidity of the solar wing as much as possible under the conditions of not increasing the structural mass and not changing the overall dimension of the solar wing, thereby achieving the aim of optimizing the design. By the method, the design efficiency is improved, and the design workload is reduced. In the prior art, no relevant description is available.
The invention also provides computer equipment and a storage medium.
Interpretation of terms:
1. the nanostran software is structural finite element analysis software developed by American MSC company, and is widely applied to the field of aerospace structural static and dynamic analysis.
2. matlab software is a commercial mathematical software produced by the MathWorks corporation in the united states, and can realize the functions of mathematical computation, data analysis, image processing, signal processing and the like by writing programs.
3. A solar wing hinge is an unfolding and locking mechanism on a satellite solar wing, the solar wing is stretched from a folded state to an unfolded state by utilizing mechanical energy stored by a spring and is kept in a locked state, and two solar wing hinges are usually adopted to be matched for use.
4. The solar wing pressing device is a device for forming a fastening state between a satellite and a solar wing, and the fastening state is released when the solar wing pressing device is released. The solar wing pressing point is the position of the solar wing pressing device.
5. bdf File is a file format generated by commercial finite element software and readable by nanostran software, only one file is needed, and file naming can be set arbitrarily
The technical scheme of the invention is as follows:
a solar wing structure optimization method combining a finite element method and a gradient method comprises the following specific steps:
step 1: according to the external dimension and the material property of the solar wing structure, a solar wing finite element model is established by utilizing commercial finite element software to generate a modal analysis working condition, wherein a finite element grid is a two-dimensional rectangular grid, and a file with an extension name of. bdf, namely a bdf file, required by the computation of the nartran software is generated; the file name can be arbitrarily set, such as xx.
Step 2: parameterizing a finite element model of the solar wing: setting the installation position of the hinge and the position of the compaction point as variable variables, and setting the density of the finite element grid, namely setting the sizes of two directions of the finite element grid unit as delta x and delta y respectively; given that the length and width dimensions of the solar wing are l and h respectively, defining m as l/Δ x, and n as h/Δ y, the number of elements of the finite element grid is m · n, the number of nodes in the finite element grid is (m +1) (n +1), defining the coordinate origin to be located at the first node position at the lower left corner of the finite element grid, the x axis points from left to right, the y axis points from bottom to top, and the z axis is determined according to the right-hand rule;
generating finite element mesh information by utilizing a matlab software writing program, wherein the finite element mesh information comprises coordinate information of nodes and node composition information of finite element mesh units; replacing the finite element mesh information in the bdf file generated in the step 1, wherein the finite element mesh information comprises the coordinate information of nodes and the node composition information of units;
and step 3: optimizing the installation position of the solar wing hinge;
and 4, step 4: and optimizing the position of the solar wing pressing point.
Further preferably, the dimensions in both directions are less than 100 mm.
According to the optimization of the invention, in the step 3, the installation position of the solar wing hinge is optimized, and the specific implementation steps are as follows:
step 3.1: setting initial hinge installation positions, wherein the two hinges comprise a first hinge and a second hinge, the first hinge and the second hinge are both positioned on the lower bottom edge of the solar wing, the first hinge installation position selects any node N1 on the lower bottom edge of the solar wing, the second hinge installation positions N2 and N1 are symmetrically distributed along the midpoint of the lower bottom edge, and the two nodes both restrict six degrees of freedom, wherein the six degrees of freedom comprise translation along the x axis, translation along the y axis, translation along the z axis, rotation around the x axis, rotation around the y axis and rotation around the z axis;
modifying the constraint condition in the bdf file by using matlab software, calling the nanostran software to perform modal analysis to obtain a result file with the extension name of f06, namely an f06 file, and extracting a first-order natural frequency f in the f06 file by using the matlab software;
step 3.2: changing the constraint working condition, wherein the constraint point selects a first node N1L1 on the left side of N1 and a node N2R1 which is symmetrically distributed with N1L1 along the midpoint of the lower bottom edge; utilizing matlab software to modify the constraint condition in bdf files, calling nanostran software to perform modal analysis to obtain f06 files, and utilizing a matlab software writing program to extract a first-order natural frequency f in the f06 filesL；
Step 3.3: changing the constraint condition, selecting a first node N1R1 on the right side of the N1 and a node N2L1 symmetrically distributed with the N1R1 along the midpoint of the lower bottom edge as constraint points; modifying the constraint condition in the bdf file by using matlab software, calling the nanostran software to perform modal analysis to obtain an f06 file, and extracting the first-order natural frequency f in the f06 file by using the matlab softwareR；
Step 3.4: comparing f with fLAnd fRWhen f is large or small<fLWhen the installation position of the first hinge is updated to be the node N1L1, the installation position of the second hinge is updated to be the node N2R1, and the steps 3.1 to 3.3 are repeated; when f is<fRWhen the installation position of the first hinge is updated to be the node N1R1, the installation position of the second hinge is updated to be the node N2L1, and the steps 3.1 to 3.3 are repeated; when f is>＝fLAnd f>＝fRAnd then, terminating the iteration, wherein the mounting position of the first hinge and the mounting position of the second hinge are the optimal positions.
Preferably, according to the present invention, the coordinate information of the ith node is defined as follows:
Figure BDA0003041535040000031
GRID is a coordinate identification symbol of a node, xi ═ mod (i-1, m +1) ×, yi ═ floor ((i-1)/(m +1)) × Δ y, a function mod (i-1, m +1) represents that i-1 is divided by m +1 to obtain a remainder, and a function floor ((i-1)/(m +1)) represents that a maximum integer smaller than (i-1)/(m +1) is obtained;
the node composition information of the jth finite element mesh unit is defined as follows:
Figure BDA0003041535040000032
wherein CQUAD4 is a type of finite element mesh element.
According to the optimization of the invention, the position of the solar wing compaction point is optimized, and the specific implementation steps are as follows:
step 4.1: under the constraint condition of keeping the optimal positions of the two hinges, setting the initial position of a compaction point, selecting any node N3 on the finite element model of the solar wing at the initial position of the compaction point, wherein the coordinates of N3 are (x, y), and constraining six degrees of freedom; modifying the constraint condition in the bdf file by using matlab software, calling the nanostran software to perform modal analysis to obtain an f06 file, and extracting a first-order natural frequency f' in the f06 file by using the matlab software;
step 4.2: changing constraint conditions, keeping the constraint condition conditions of the optimal positions of the two hinges, selecting left, right, upper and lower adjacent nodes N3L1, N3R1, N3U1 and N3D1 of N3 for constraint points respectively, modifying the constraint conditions in a bdf file under the four constraint points by matlab software, calling nartran software to perform modal analysis on a finite element model under the four constraint points to obtain an f06 file, and extracting first-order natural frequency in the f06 file by the matlab software respectivelyfL’、fR’、fU' and fD’；
Step 4.3: calculating the gradient of the first order natural frequency
Figure BDA0003041535040000041
Step 4.4: calculating the optimized direction of the compaction point according to the formula (1), wherein the coordinates (x ', y') of the new compaction point are shown in the formula (1):
Figure BDA0003041535040000042
in the formula (1), alpha is a step length;
step 4.5: when in use
Figure BDA0003041535040000043
When the vector is not zero, the compaction point is updated to the node closest to the coordinate (x ', y'), and the steps from 4.1 to 4.4 are repeated; when in use
Figure BDA0003041535040000044
And when the vector is zero, terminating the iteration, and setting the compaction point as the optimal position.
Further preferably, the step size range is (max (delta x, delta y))2～5(max(Δx,Δy))2And (max (Δ x, Δ y)) represents the maximum value of Δ x and Δ y.
Further preferably, the gradient of the first order natural frequency is calculated according to equation (2)
Figure BDA0003041535040000045
Figure BDA0003041535040000046
In the formula (2), the reaction mixture is,
Figure BDA0003041535040000047
a computer arrangement comprising a memory storing a computer program and a processor implementing the steps of a method for solar wing structure optimization combining a finite element method and a gradient method when executing the computer program.
A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the solar wing structure optimization method in combination with the finite element method and the gradient method.
The invention has the beneficial effects that:
the invention provides an automatic optimization method for a solar wing compression point on the premise of not increasing the structural quality of a solar wing, not changing the external dimension and other states of the solar wing, establishes a finite element parameterized model of the solar wing structure, and automatically optimizes the hinge position and the compression point position of the solar wing by combining a gradient method with finite element software, thereby improving the natural frequency of the solar wing structure, improving the working efficiency of the optimal design of the solar wing structure and reducing the workload of the structural design of the solar wing.
Drawings
FIG. 1 is a schematic flow chart of a solar wing structure optimization method combining a finite element method and a gradient method according to the present invention;
FIG. 2 is a schematic representation of the solar wing geometry of an embodiment;
FIG. 3 is a schematic diagram of a solar wing hinge position optimization path;
FIG. 4 is a schematic view of an iteration curve of a first order natural frequency of a finite element model of a solar wing as a function of hinge position;
FIG. 5 is a schematic diagram of a solar wing compaction point position optimization path;
FIG. 6 is an iterative curve diagram of the variation of the first-order natural frequency of the solar wing finite element model with the position of the compaction point.
The specific implementation mode is as follows:
the present invention will be described in detail below with reference to the accompanying drawings. The embodiment is implemented on the premise of the technical scheme of the invention, and a detailed implementation mode is given.
Example 1
A solar wing structure optimization method combining a finite element method and a gradient method is shown in figure 1, and comprises the following specific steps:
step 1: according to the external dimension and the material property of the solar wing structure, a solar wing finite element model is established by utilizing commercial finite element software to generate a modal analysis working condition, wherein a finite element grid is a two-dimensional rectangular grid, and a file with an extension name of. bdf, namely a bdf file, required by the computation of the nartran software is generated; the file name can be arbitrarily set, such as xx.
Step 2: parameterizing a finite element model of the solar wing: setting the installation position of the hinge and the position of the compaction point as variable variables, and setting the density of the finite element grid, namely setting the sizes of two directions of the finite element grid unit as delta x and delta y respectively; given that the length and width dimensions of the solar wing are l and h respectively, defining m as l/Δ x, and n as h/Δ y, the number of elements of the finite element grid is m · n, the number of nodes in the finite element grid is (m +1) (n +1), defining the coordinate origin to be located at the first node position at the lower left corner of the finite element grid, the x axis points from left to right, the y axis points from bottom to top, and the z axis is determined according to the right-hand rule;
generating finite element mesh information by utilizing a matlab software writing program, wherein the finite element mesh information comprises coordinate information of nodes and node composition information of finite element mesh units; replacing the finite element mesh information in the bdf file generated in the step 1, wherein the finite element mesh information comprises the coordinate information of nodes and the node composition information of units;
and step 3: optimizing the installation position of the solar wing hinge;
and 4, step 4: and optimizing the position of the solar wing pressing point.
Example 2
A method for optimizing a solar wing structure by combining a finite element method and a gradient method according to embodiment 1, which is different from the method comprising the following steps:
the dimensions in both directions are less than 100 mm.
In the step 3, the installation position of the solar wing hinge is optimized, and the specific implementation steps are as follows:
step 3.1: setting initial hinge installation positions, wherein the two hinges comprise a first hinge and a second hinge, the first hinge and the second hinge are both positioned on the lower bottom edge of the solar wing, the first hinge installation position selects any node N1 on the lower bottom edge of the solar wing, the second hinge installation positions N2 and N1 are symmetrically distributed along the midpoint of the lower bottom edge, and the two nodes both restrict six degrees of freedom, wherein the six degrees of freedom comprise translation along the x axis, translation along the y axis, translation along the z axis, rotation around the x axis, rotation around the y axis and rotation around the z axis;
modifying the constraint condition in the bdf file by using matlab software, calling the nanostran software to perform modal analysis to obtain a result file with the extension name of f06, namely an f06 file, and extracting a first-order natural frequency f in the f06 file by using the matlab software;
the matlab software is used to modify bdf the constraint conditions in the file, the format is as follows:
Figure BDA0003041535040000061
where SPC1 is the constraint condition designation, 123456 represents constraint x-axis translation, y-axis translation, z-axis translation, x-axis rotation, y-axis rotation, and z-axis rotation for 6 degrees of freedom.
Calling the nanostran software to perform modal analysis, and obtaining a result file with an extension name of f06, namely an f06 file, wherein the file name of xx.f06 calling the nanostran software is a section of program command, and a user can write a program by himself; the modal analysis of the nanostran software is the prior art; the f06 file nastran modal analysis generates only one result file, the file name is the same as bdf, and if the file name of bdf is xx.bdf, a file xx.f06 is generated after calculation.
Step 3.2: changing the constraint working condition, wherein the constraint point selects a first node N1L1 on the left side of N1 and a node N2R1 which is symmetrically distributed with N1L1 along the midpoint of the lower bottom edge; utilizing matlab software to modify the constraint condition in bdf files, calling nanostran software to perform modal analysis to obtain f06 files, and utilizing a matlab software writing program to extract a first-order natural frequency f in the f06 filesL；
Step 3.3: changing the constraint condition, selecting a first node N1R1 on the right side of the N1 and a node N2L1 symmetrically distributed with the N1R1 along the midpoint of the lower bottom edge as constraint points; utilizing matlab softwareModifying the constraint condition in bdf files, calling nanostran software to perform modal analysis to obtain f06 files, and extracting the first-order natural frequency f in the f06 files by utilizing matlab softwareR；
Step 3.4: comparing f with fLAnd fRWhen f is large or small<fLWhen the installation position of the first hinge is updated to be the node N1L1, the installation position of the second hinge is updated to be the node N2R1, and the steps 3.1 to 3.3 are repeated; when f is<fRWhen the installation position of the first hinge is updated to be the node N1R1, the installation position of the second hinge is updated to be the node N2L1, and the steps 3.1 to 3.3 are repeated; when f is>＝fLAnd f>＝fRAnd then, terminating the iteration, wherein the mounting position of the first hinge and the mounting position of the second hinge are the optimal positions.
The coordinate information of the ith node is defined as follows:
Figure BDA0003041535040000071
GRID is a coordinate identification symbol of a node, xi ═ mod (i-1, m +1) ×, yi ═ floor ((i-1)/(m +1)) × Δ y, a function mod (i-1, m +1) represents that i-1 is divided by m +1 to obtain a remainder, and a function floor ((i-1)/(m +1)) represents that a maximum integer smaller than (i-1)/(m +1) is obtained;
the node composition information of the jth finite element mesh unit is defined as follows:
Figure BDA0003041535040000072
wherein CQUAD4 is a type of finite element mesh element.
The method optimizes the position of the solar wing compaction point and specifically comprises the following steps:
step 4.1: under the constraint condition of keeping the optimal positions of the two hinges, setting the initial position of a compaction point, selecting any node N3 on the finite element model of the solar wing at the initial position of the compaction point, wherein the coordinates of N3 are (x, y), and constraining six degrees of freedom;
the matlab software is used to modify bdf the constraint conditions in the file, the format is as follows:
Figure BDA0003041535040000073
calling the nanostran software to perform modal analysis to obtain an f06 file, and extracting a first-order natural frequency f' in the f06 file by using matlab software;
step 4.2: changing constraint conditions, keeping the constraint condition conditions of the optimal positions of the two hinges, selecting left, right, upper and lower adjacent nodes N3L1, N3R1, N3U1 and N3D1 of N3 for constraint points respectively, modifying the constraint conditions in a bdf file under the four constraint points by matlab software, calling nartran software to perform modal analysis on a finite element model under the four constraint points to obtain an f06 file, and extracting first-order natural frequency f in the f06 file by the matlab software respectivelyL’、fR’、fU' and fD’；
Step 4.3: calculating the gradient of the first order natural frequency
Figure BDA0003041535040000074
Step 4.4: calculating the optimized direction of the compaction point according to the formula (1), wherein the coordinates (x ', y') of the new compaction point are shown in the formula (1):
Figure BDA0003041535040000075
in the formula (1), alpha is a step length;
step 4.5: when in use
Figure BDA0003041535040000076
When the vector is not zero, the compaction point is updated to the node closest to the coordinate (x ', y'), and the steps from 4.1 to 4.4 are repeated; when in use
Figure BDA0003041535040000077
And when the vector is zero, terminating the iteration, and setting the compaction point as the optimal position.
Step sizeThe setting can be carried out according to the grid size, the selection of the step length influences the optimization speed, but does not influence the final result, and the value range of the step length is (max (delta x, delta y))2～5(max(Δx,Δy))2And (max (Δ x, Δ y)) represents the maximum value of Δ x and Δ y.
Calculating the gradient of the first order natural frequency according to equation (2)
Figure BDA0003041535040000081
Figure BDA0003041535040000082
In the formula (2), the reaction mixture is,
Figure BDA0003041535040000083
example 3
Taking a certain type of satellite solar wing as an example, the geometric shape of the solar wing is shown in fig. 2, the geometric dimension of the solar wing is 700mm multiplied by 1100mm multiplied by 24mm, and the sailboard substrate adopts a honeycomb sandwich structure.
The solar wing structure optimization method combining the finite element method and the gradient method of the embodiment specifically comprises the following implementation steps:
step 1: according to the external dimension and the material property of the solar wing structure, a solar wing finite element model is established by utilizing commercial finite element software, and an bdf file required by the calculation of the nartran software is generated, wherein the file name is test1. bdf.
Step 2: parameterizing a finite element model of the solar wing, and setting the installation position of the hinge and the position of the compaction point as variable variables. Setting the density and the number of the finite element grids, and setting the sizes of the finite element grid units in two directions as follows: length 50mm, width 50mm, then m equals 14, n equals 22, total number of nodes 345, finite element mesh element number 308. Defining the coordinate origin to be positioned at the first node position at the lower left corner of the finite element grid, pointing the x axis from left to right, pointing the y axis from bottom to top, determining the z axis according to the right-hand rule, generating the finite element grid information by using matlab software, and replacing the finite element grid information generated in bdf file in the step 1.
The coordinate information of the nodes is as follows:
Figure BDA0003041535040000084
the node composition information of the cell is defined as follows:
Figure BDA0003041535040000085
Figure BDA0003041535040000091
and step 3: and optimizing the installation position of the solar wing hinge.
Step 3.1: setting an initial hinge installation position, selecting a node 2 at a first hinge installation position, selecting a node 14 at a second hinge installation position, and constraining six degrees of freedom at the two nodes. The matlab software is used to modify bdf the constraint conditions in the file, the format is as follows:
Figure BDA0003041535040000092
calling the nastran software for modal analysis to obtain an f06 file with the file name of test1.f06, and extracting the first-order natural frequency f in the f06 file to be 4.51Hz by using matlab software.
Step 3.2: changing the constraint working condition, selecting a node 1 on the left side of the node 2 and a node 15 symmetrical to the node 1 by a constraint point; modifying bdf file displacement constraint condition by matlab software, carrying out modal analysis on finite element model by using nastran software, and extracting first-order natural frequency f by using matlab softwareL＝3.44Hz。
Step 3.3: changing the constraint working condition, selecting a node 3 on the right side of the node 2 and a node 13 symmetrical to the node 3 by a constraint point; modifying bdf file displacement constraint condition by matlab software, and performing modal classification on finite element model by using nastran softwareAnalyzing, extracting the first-order natural frequency f by matlab softwareR＝4.74Hz。
Step 3.4: comparing f with fLAnd fRDue to the size of f<fRThen, the position of the first hinge is changed into the node 3, the position of the second hinge is changed into the node 13, and the steps 3.1-3.3 are repeated; through a plurality of iterations up to f>＝fLAnd f>＝fRAt this time, the optimal position of the first hinge is node 4, the coordinates are (150, 0), the optimal position of the second hinge is node 12, the coordinates are (550, 0), the optimized iteration path of the hinge position is shown in fig. 3, and the iteration curve of the first-order natural frequency of the finite element model of the solar wing changing along with the hinge position is shown in fig. 4.
And 4, step 4: and optimizing the position of the solar wing pressing point.
Step 4.1: on the premise of keeping the constraint node 4 and the node 12, an initial position of a compaction point is set, the initial position of the compaction point is selected to be a node 33, coordinates are (100 ), and six degrees of freedom are constrained. And modifying bdf the displacement constraint conditions in the file by utilizing matlab software.
The format is as follows:
Figure BDA0003041535040000093
modal analysis is carried out on the solar wing finite element model by using the nartran software to obtain an f06 file, and the matlab software is used for extracting the first-order natural frequency f' in the calculation result f06 file to be 5.91 Hz.
Step 4.2: changing constraint conditions, keeping and keeping constraint nodes 4 and 12, respectively selecting left, right, upper and lower adjacent nodes of the compression point in the step 4.1 by the third constraint point, modifying displacement constraint conditions in bdf files under four conditions by matlab software, performing modal analysis on four finite element models by using nartran software to obtain f06 files, and respectively extracting first-order natural frequency f in f06 files by using matlab softwareL’＝5.69Hz、fR’＝6.16Hz、fU' -6.22 Hz and fD’＝5.61Hz。
Step 4.3: calculating first order natural frequency according to equation (1)Gradient of gradient
Figure BDA0003041535040000101
Step 4.4: calculating the optimized direction of the compaction point according to the formula (2), and setting the step length alpha to be 4 delta x210000, new compacting point position coordinate is
Figure BDA0003041535040000102
Setting the new compaction point as the node 49 closest to the coordinate (x ', y'), and repeating the steps 4.1-4.2; through several iterations until
Figure BDA0003041535040000103
And when the vector is zero, terminating the iteration. The final point of compaction is a node 278,
Figure BDA0003041535040000104
the zero vector, and therefore the position of node 278 is the optimum position of the pinch point, with coordinates (350, 900), where the first order natural frequency of the sun wing is 27.7 Hz. The compaction point position optimization path is shown in fig. 5, and an iteration curve of the first-order natural frequency of the solar wing finite element model along with the change of the compaction point position is shown in fig. 6.
Through the implementation of the embodiment, the optimal hinge installation position and the optimal pressing point installation position of the solar wing are found, and the natural frequency (the first-order natural frequency of the original model is 24Hz) of the solar wing is improved relative to the original hinge installation position and the pressing point installation position which are only selected according to experience. The embodiment is automatically completed by writing a matlab program, so that the efficiency of solar wing structure design is improved, and the workload of designers is reduced.
Example 4
A computer device comprising a memory storing a computer program and a processor implementing the steps of the solar wing structure optimization method combining the finite element method and the gradient method according to any one of embodiments 1-3 when the computer program is executed by the processor.
Example 5
A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the solar wing structure optimization method of any one of embodiments 1 to 3 in combination with the finite element method and the gradient method.
The embodiments of the present invention have been described above, but the scope of the present invention is not limited to the disclosure of the embodiments and the accompanying drawings.

Claims (9)

1. A solar wing structure optimization method combining a finite element method and a gradient method is characterized by comprising the following specific steps:
step 1: according to the external dimension and the material property of the solar wing structure, a solar wing finite element model is established by utilizing commercial finite element software to generate a modal analysis working condition, wherein a finite element grid is a two-dimensional rectangular grid, and a file with an extension name of. bdf, namely a bdf file, required by the computation of the nartran software is generated;
step 2: parameterizing a finite element model of the solar wing: setting the installation position of the hinge and the position of the compaction point as variable variables, and setting the density of the finite element grid, namely setting the sizes of two directions of the finite element grid unit as delta x and delta y respectively; given that the length and width dimensions of the solar wing are l and h respectively, defining m as l/Δ x, and n as h/Δ y, the number of elements of the finite element grid is m · n, the number of nodes in the finite element grid is (m +1) (n +1), defining the coordinate origin to be located at the first node position at the lower left corner of the finite element grid, the x axis points from left to right, the y axis points from bottom to top, and the z axis is determined according to the right-hand rule;
generating finite element mesh information by utilizing matlab software, wherein the finite element mesh information comprises coordinate information of nodes and node composition information of finite element mesh units; replacing the finite element mesh information in the bdf file generated in the step 1, wherein the finite element mesh information comprises the coordinate information of nodes and the node composition information of units;
and step 3: optimizing the installation position of the solar wing hinge;
and 4, step 4: and optimizing the position of the solar wing pressing point.
2. The method for optimizing the solar wing structure by combining the finite element method and the gradient method according to claim 1, wherein in the step 3, the installation position of the solar wing hinge is optimized by the following specific steps:
step 3.1: setting initial hinge installation positions, wherein the two hinges comprise a first hinge and a second hinge, the first hinge and the second hinge are both positioned on the lower bottom edge of the solar wing, the first hinge installation position selects any node N1 on the lower bottom edge of the solar wing, the second hinge installation positions N2 and N1 are symmetrically distributed along the midpoint of the lower bottom edge, and the two nodes both restrict six degrees of freedom, wherein the six degrees of freedom comprise translation along the x axis, translation along the y axis, translation along the z axis, rotation around the x axis, rotation around the y axis and rotation around the z axis;
modifying the constraint condition in the bdf file by using matlab software, calling the nanostran software to perform modal analysis to obtain a result file with the extension name of f06, namely an f06 file, and extracting a first-order natural frequency f in the f06 file by using the matlab software;
step 3.2: changing the constraint working condition, wherein the constraint point selects a first node N1L1 on the left side of N1 and a node N2R1 which is symmetrically distributed with N1L1 along the midpoint of the lower bottom edge; modifying the constraint condition in the bdf file by using matlab software, calling the nanostran software to perform modal analysis to obtain an f06 file, and extracting the first-order natural frequency f in the f06 file by using the matlab softwareL；
Step 3.3: changing the constraint condition, selecting a first node N1R1 on the right side of the N1 and a node N2L1 symmetrically distributed with the N1R1 along the midpoint of the lower bottom edge as constraint points; modifying the constraint condition in the bdf file by using matlab software, calling the nanostran software to perform modal analysis to obtain an f06 file, and extracting the first-order natural frequency f in the f06 file by using the matlab softwareR；
Step 3.4: comparing f with fLAnd fRWhen f is large or small<fLWhen the installation position of the first hinge is updated to be the node N1L1, the installation position of the second hinge is updated to be the node N2R1, and the steps 3.1 to 3.3 are repeated; when f is<fRWhen the installation position of the first hinge is updated to be the node N1R1, the installation position of the second hinge is updated to be the node N2L1, and the steps 3.1 to 3.3 are repeated; when f is>＝fLAnd f>＝fRStopping iteration, and setting the first hinge mounting position and the second hinge mounting position as optimal positions。
3. The solar wing structure optimization method combining the finite element method and the gradient method according to claim 1, wherein the solar wing compaction point position is optimized by the following specific steps:
step 4.1: setting an initial position of a compaction point, selecting an arbitrary node N3 on the finite element model of the solar wing at the initial position of the compaction point, wherein the coordinate of N3 is (x, y), and constraining six degrees of freedom;
modifying the constraint condition in the bdf file by using matlab software, calling the nanostran software to perform modal analysis to obtain an f06 file, and extracting a first-order natural frequency f' in the f06 file by using the matlab software;
step 4.2: changing constraint conditions, respectively selecting left, right, upper and lower adjacent nodes N3L1, N3R1, N3U1 and N3D1 of N3 for constraint points, respectively modifying the constraint conditions in bdf files under the four constraint points by using matlab software, calling nastran software to perform modal analysis on finite element models under the four constraint points to obtain f06 files, and respectively extracting first-order natural frequency f in the f06 files by using the matlab softwareL’、fR’、fU' and fD’；
Step 4.3: calculating the gradient of the first order natural frequency
Figure FDA0003041535030000021
Step 4.4: calculating the optimized direction of the compaction point according to the formula (1), wherein the coordinates (x ', y') of the new compaction point are shown in the formula (1):
Figure FDA0003041535030000022
in the formula (1), alpha is a step length;
step 4.5: when in use
Figure FDA0003041535030000023
When the vector is not zero, the compaction point is updated to the section closest to the coordinate (x', yCounting, and repeating the steps 4.1 to 4.4; when in use
Figure FDA0003041535030000024
And when the vector is zero, terminating the iteration, and setting the compaction point as the optimal position.
4. A method for solar wing structural optimization combining finite element and gradient methods according to claim 1, wherein the dimensions in both directions are less than 100 mm.
5. The solar wing structure optimization method combining the finite element method and the gradient method according to claim 1, wherein the coordinate information of the ith node is defined as follows:
GRID i xi yi 0.00
GRID is a coordinate identification symbol of a node, xi ═ mod (i-1, m +1) ×, yi ═ floor ((i-1)/(m +1)) × Δ y, a function mod (i-1, m +1) represents that i-1 is divided by m +1 to obtain a remainder, and a function floor ((i-1)/(m +1)) represents that a maximum integer smaller than (i-1)/(m +1) is obtained;
the node composition information of the jth finite element mesh unit is defined as follows:
CQUAD4 j 1 j+1 j+2 j+m+2 j+m+1
wherein CQUAD4 is a type of finite element mesh element.
6. The method for optimizing the solar wing structure by combining the finite element method and the gradient method as claimed in claim 3, wherein the step length value range is (max (Δ x, Δ y))2～5(max(Δx,Δy))2And (max (Δ x, Δ y)) represents the maximum value of Δ x and Δ y.
7. The method for optimizing a solar wing structure by combining a finite element method and a gradient method according to claim 3, wherein the gradient of the first-order natural frequency is calculated according to the formula (2)
Figure FDA0003041535030000031
Figure FDA0003041535030000032
In the formula (2), the reaction mixture is,
Figure FDA0003041535030000033
8. a computer arrangement comprising a memory and a processor, the memory storing a computer program, characterized in that the processor, when executing the computer program, performs the steps of the method for solar wing structure optimization combining the finite element method and the gradient method according to any one of claims 1 to 7.
9. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method for solar wing structure optimization combining the finite element method and the gradient method according to any one of claims 1 to 7.
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