CN113378441A - Delay construction method of deformable surface bound conformal array unit - Google Patents
Delay construction method of deformable surface bound conformal array unit Download PDFInfo
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Abstract
The invention relates to a delay construction method of a deformable surface bound conformal array unit. And (3) establishing a one-to-one correspondence relationship between the grids before deformation and the grids after deformation by depending on force-heat simulation software, and constructing the whole process of deformation of the antenna array bottom plate (controlling the deformation of the antenna array). Thus, the force-heat simulation and the electromagnetic simulation can be completely decoupled. Therefore, the invention provides a calculation method which can input any conformal array on the surface before different deformations and output the position and the posture of the array unit after the deformation under the condition of the states before and after the deformation of the given surface. The method can perform structural mechanics calculation (single mechanical working condition) once, and can perform electromagnetic analysis on different initial layouts, thereby greatly improving the calculation efficiency of analyzing the simulation design of the problems and optimizing the conformal array layout.
Description
Technical Field
The invention relates to a delay construction method of a deformable surface bound conformal array unit, and belongs to the technical field of simulation modeling.
Background
The surface conformal array is a novel array antenna with low detectability (weak radar wave scattering), high performance and multiple functions. However, since the background platform is not protected by a large external radome, and the unit is usually anchored on the surface, if the curved surface structure deforms due to external force or the like, the performance of the antenna array will change along with the deformation of the surface, and in some cases, the change has a great influence on the application. Therefore, the influence of the deformation of the background surface is often considered when electromagnetically simulating the radiation characteristics of a surface conformal array antenna. In general, people use structural mechanics and electromagnetic simulation to perform combined multi-physical field analysis, and calculate the deformation of the whole structure first, and then calculate the electromagnetic radiation characteristic of the deformed array antenna.
As mentioned above, conformal antennas often work under a force deformation, so there is some uncertainty about the real working state, which presents a great challenge to the initial laying design and optimization of the array. If the traditional combined simulation of force heat and electromagnetism shown in fig. 1 is carried out, firstly, the antenna array needs to be laid when no deformation exists (for example, a local orthogonal coordinate system is established by means of a certain determination rule, the normal direction of a unit is the local normal direction of a curved surface, a certain distance is taken in the local orthogonal coordinate system, a unit is placed in the local orthogonal coordinate system), then the mechanical/thermal simulation is carried out to obtain the deformed antenna array, and then the performance simulation of the deformed antenna array is carried out. However, if the electromagnetic performance in the deformation state does not reach the standard, the original state needs to be returned to for re-laying (still within the range allowed by the original rule), then the force-heat simulation is carried out to obtain the deformation, and finally the electromagnetic simulation is carried out to see whether the electromagnetic performance can reach the standard …, so that repeated iteration is carried out, and the efficiency is extremely low. Since it is difficult to directly predict the final operating state from the initial installation state of the antenna array (due to the influence of the stress heat), it can only be approached step by step. This is not only inefficient, but is prone to various operational problems and data conversion problems. If the "after deformation" surface is laid down directly (still according to the original "certain rules") with the array antenna, although the repeated iterative force-heat simulation process is avoided, the laid array is very different from the actual deformed array (the direction, the spacing and the relative posture of the units on the surface may be different). Because the actual deformed array layout does not actually satisfy the previous laying rules (e.g., the cells are no longer along the local normal direction). Moreover, such differences cannot be expressed by simple mathematical expressions. Therefore, the method of directly laying on the deformed curved surface is not operable, and even if the method is forcibly operated, the error will be large.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the conformal antenna usually works under stress deformation, so the real working state of the conformal antenna has uncertainty, and therefore, when the initial laying design and optimization of the conformal array are carried out by utilizing the traditional force-heat-electromagnetism combined simulation method, repeated iteration needs to be carried out, and the efficiency is extremely low.
In order to solve the above technical problem, an embodiment of the present invention provides a delay structure method for a deformable surface constrained conformal array unit, including the following steps:
step 1, obtaining a topological data structure of a finite element model before deformation, wherein the topological data structure comprises node coordinates of all nodes related to all elements contained in the finite element model;
step 2, obtaining displacement data of each anchor point after performing structural mechanics simulation on the finite element model;
step 3, obtaining a 3x3 transformation matrix and a 3-dimensional displacement vector of each anchor point, comprising the following steps:
step 301, judging whether the current anchor point is outside or inside all the units according to the displacement data of the current anchor point, if the current anchor point is outside all the units, entering step 302, and if the current anchor point is inside a certain unit, entering step 303;
step 302, selecting one unit from all units according to the principle of proximity, calculating the distance between the current anchor point and the surface of the current unit, if the distance is greater than a preset distance threshold value, a surface adsorption unit cannot be obtained, exiting the method, otherwise, taking the current unit as the surface adsorption unit, determining a point on a limited unit closest to the current anchor point according to an interpolation function, obtaining the local coordinate representation of the point, wherein the node has at least one local coordinate component in the surface adsorption unit, and the rest are outside the surface adsorption unit, and entering step 304;
step 303, if the current anchor point is in the current unit, taking the current unit as a surface adsorption unit, calculating the local coordinate representation of the current anchor point in the surface adsorption unit, and entering step 304;
step 304, representing the displacement data of the current anchor point, the surface adsorption unit and the local coordinate obtained in the previous step to form a deformation calculation object, and calculating to obtain a 3x3 transformation matrix and a 3-dimensional displacement vector of the current anchor point;
step 4, if the array unit to be designed is rigidly fixed, performing matrix decomposition calculation on the 3x3 matrix calculated in the step 3, calculating and extracting an optimal rotation transformation matrix, combining the optimal rotation transformation matrix and the displacement vector calculated in the step 3 to obtain a complete transformation matrix capable of describing translation and rotation changes of the local coordinate system of the unit, and entering the step 5;
if the array unit to be designed is flexible, the 3x3 matrix calculated in the step 3 is reserved, the 3x3 matrix is combined with the displacement vector calculated in the step 3, a complete transformation matrix capable of describing the translation and rotation change of the unit local coordinate system is obtained, and the step 5 is carried out;
step 5, designing an array unit before deformation;
step 6, transforming the coordinate system of the array unit and key points in the coordinate system according to the complete transformation matrix obtained by calculation in the step 4 to obtain the position and the local coordinate system of the deformed array unit, and entering the step 7;
and 7, performing electromagnetic simulation on the deformed array unit, if the displacement and the posture of the array unit meet the requirements and the distance threshold value in the step 302 is not exceeded, quitting the method, and if the displacement and the posture of the array unit do not meet the requirements, redesigning the array unit before deformation by a user or moderately correcting the distance threshold value and returning to the step 6 until the electromagnetic simulation result meets the requirements.
Preferably, in step 1, the finite element model is directly established or imported, or after a parametric scan volume which is a non-finite element model is input, the parametric scan volume is converted into the finite element model through finite sampling.
Preferably, in step 1, the topology data structure further includes unit information.
Preferably, in step 1, the cell information includes cell type information or interpolated shape function about its node and node numbers of all the nodes with which the cell is associated.
Preferably, after the step 1 and before the step 2, the method further comprises the following steps:
and (2) converting the topological data structure of the finite element model obtained in the step (1) into a quick lookup table, inputting any three-dimensional coordinate into the quick lookup table, quickly judging whether the three-dimensional coordinate has the surface adsorption unit, and if so, outputting the surface adsorption unit and the corresponding local coordinate representation.
The deformation of the antenna array caused by force and heat is determined by a thick and strong structure of an antenna array bottom plate and a connecting bottom plate, and the antenna array is generally composed of a thin metal structure and a fine structure, so that the influence on the deformation is weak. Although the deformation caused by force and heat has no simple mathematical expression form, the one-to-one correspondence relationship between the grids before deformation and the grids after deformation can be established by relying on force and heat simulation software, and the whole process of the deformation of the base plate of the antenna array (the deformation of the antenna array is controlled) is established. Therefore, the force-heat simulation and the electromagnetic simulation can be completely decoupled: the force-heat simulation informs the space corresponding relation between the deformed state and the deformed state, and then the electromagnetic simulation can be directly carried out by using each state after the deformation. Finally, if the up-to-standard deformed antenna array is found, the original laying method before deformation can be found immediately through the corresponding relation.
Based on the knowledge, the invention provides a calculation method which can input any conformal array on the surface before different deformations and output the position and the posture of the array unit after the deformation under the condition of the state before and after the deformation of the given surface. The method can perform structural mechanics calculation (single mechanical working condition) once, and can perform electromagnetic analysis on different initial layouts, thereby greatly improving the calculation efficiency of analyzing the simulation design of the problems and optimizing the conformal array layout.
Drawings
FIG. 1 is a simulation process of "force thermal-electromagnetic coupling" of a conventional surface conformal array with surface deformation;
FIG. 2 is a structural-electromagnetic coupling simulation process for deformation of a conformal array of surfaces with a surface provided by the present invention;
FIG. 3 is a distribution of a conformal array prior to deformation of a base;
FIG. 4 is a diagram of the deformed conformal array of the base after position and attitude adjustments occur with deformation of the base.
Detailed Description
The invention will be further illustrated with reference to the following specific examples. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes and modifications of the present invention may be made by those skilled in the art after reading the teachings of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.
The following terms are used in the present invention:
1) local coordinate system: the system is composed of a global representation of the origin of a local coordinate system and a representation of three base vectors of the local coordinate system under global coordinates.
2) A finite element: a physical entity is divided into a finite number of discrete blocks, each of which is represented approximately with a known particular geometry. These particular geometries have respective interpolation functions, and a continuous function defined on a solid can be approximated by values on a finite element mesh node (after the concept). An object having the geometry of the interpolation function described above is referred to as a finite element object (simply referred to herein as a finite element or element). Herein, "cell" other than "array cell" (see term 3) denotes a concept of cell in "finite cell".
3) Array unit: the array unit refers specifically to a unit structure in an antenna array or a periodic structure. The unit structures with the same geometrical structure are repeatedly placed at different places (postures can be different) according to a certain rule (called as array layout) in the array structure or the periodic structure.
4) And (3) node: the "node" or "unit node" herein refers to a "finite unit node". A key point on the interpolated shape function of finite elements.
5) Anchor point: definition "anchor point" means the coordinates of the location where the antenna element is anchored on a deformed surface or within the body, and is referred to herein as an "array element anchor point" for short. "anchored" means that the antenna element is attached to the deformation surface by a rigid connection (e.g., rivet attachment, surface embedding, etc.).
6) Parameter scanning volume: a geometry is represented by a set of ternary sets of real functions:
x＝fx(u，v，n)
y＝fy(u，v，n)
z＝fz(u，v，n)
in the formula, the values u e [ u ] of three real number parameters are respectively selected in a limited cuboid interval1，u2]，v∈[v1，v2]，n∈[n1，n2]. The parametric swept volume may be a finite element lattice consisting of a regular hexahedral mesh by appropriate discretization in the defined interval of (u, v, n).
Based on the above definition of terms, as shown in fig. 2, the method for constructing a deformable surface-constrained conformal array element provided by the present invention comprises the following steps:
step 1, directly establishing or importing a topological data structure of the finite element model before deformation, wherein the topological data structure comprises two parts, one part is node coordinates of all associated nodes, and the other part is element information. The unit information further includes unit type information and a node number associated with each unit.
If the parameter scanning body is input as a non-finite element model, the parameter scanning body is converted into a finite element model through finite sampling and then the same subsequent operation is carried out.
And 2, converting the topological data structure of the finite element model obtained in the step 1 into a quick look-up table. After any three-dimensional coordinate is input into the quick lookup table, whether a surface adsorption unit exists in the three-dimensional coordinate can be quickly judged, if yes, the surface adsorption unit and local coordinate representation are output, and the method specifically comprises the following steps:
step 201, judging whether the currently input three-dimensional coordinate is outside all cells in the fast lookup table or in a certain cell. If the currently input three-dimensional coordinates are outside all the cells, the process proceeds to step 202, and if the currently input three-dimensional coordinates are in a certain cell, the process proceeds to step 203.
Step 202, finding a most possible unit as a surface adsorption unit according to the principle of proximity, calculating the distance between the three-dimensional coordinates and the surface adsorption unit, if the distance exceeds a preset distance threshold, determining that the position corresponding to the input three-dimensional coordinates is not adsorbed on the surface of the finite unit model, and outputting or not processing the position as a warning or additional error information according to needs. If the distance does not exceed the predetermined distance threshold, a point (which may be a numerically sufficiently similar value) closest to the location of the three-dimensional coordinate is determined according to the unit surface interpolation function, and the point should have at least 1 local coordinate component in the surface adsorption unit and the rest outside the surface adsorption unit, and the process proceeds to step 204.
Step 203, calculating the local coordinate representation of the position corresponding to the input three-dimensional coordinate in the current unit, taking the current unit as a surface adsorption unit, and entering step 204.
And step 204, outputting the surface adsorption unit and the local coordinate representation.
And 3, performing structural mechanics simulation on the finite element model to obtain displacement data of each anchor point, wherein the displacement data are component values of each node in X, Y, Z three directions.
And 4, acquiring a surface adsorption unit and a local coordinate representation corresponding to each anchor point by using the quick lookup table obtained in the step 2. And expressing the displacement data of each anchor point, the obtained surface adsorption unit and the local coordinates as a deformation calculation object, and calculating to obtain a 3x3 transformation matrix and a 3-dimensional displacement vector of the current anchor point.
Step 5, if the array unit to be designed is rigidly fixed, performing matrix decomposition calculation on the 3x3 matrix calculated in the step 4, calculating and extracting an optimal rotation transformation matrix, combining the optimal rotation transformation matrix and the displacement vector calculated in the step 4 to obtain a complete transformation matrix capable of describing translation and rotation changes of the local coordinate system of the unit, and entering the step 6;
if the array unit to be designed is flexible, the 3x3 matrix calculated in step 4 is retained, the 3x3 matrix is combined with the displacement vector calculated in step 4 to obtain a complete transformation matrix which can describe the translation and rotation changes of the unit local coordinate system, and the process proceeds to step 6.
And 6, designing an array unit before deformation.
And 7, transforming the coordinate system of the array unit and key points in the coordinate system according to the complete transformation matrix obtained by calculation in the step 5 (for the array unit with a plurality of constraint points, all the constraint points need to be transformed), obtaining the position and the local coordinate system of the deformed array unit, and entering a step 8.
And 8, performing electromagnetic simulation on the deformed array unit, exiting the method if the displacement and the posture of the array unit meet the requirements and the distance threshold value exceeding the step 202 does not occur, redesigning the array unit before deformation or moderately correcting the distance threshold value if the displacement and the posture of the array unit do not meet the requirements or the distance threshold value exceeding the conditions occurs, and returning to the step 7 until the electromagnetic simulation result meets the requirements.
Because the influence of the surface conformal array on the whole deformation is generally smaller than the response of the whole structure, the simulation process of the invention can accelerate the design efficiency of the surface conformal array, realize the rapid iterative design of the surface conformal array and lay a technical foundation for optimizing the layout and control under the complex deformation working condition on the premise of greatly reducing the simulation calculation amount.
Claims (5)
1. A method for delayed structuring of a deformable surface constrained conformal array element, comprising the steps of:
step 1, obtaining a topological data structure of a finite element model before deformation, wherein the topological data structure comprises node coordinates of all nodes related to all elements contained in the finite element model;
step 2, obtaining displacement data of each anchor point after performing structural mechanics simulation on the finite element model;
step 3, obtaining a 3x3 transformation matrix and a 3-dimensional displacement vector of each array unit anchor point, comprising the following steps:
step 301, judging whether the current anchor point is outside or inside all the units according to the displacement data of the current anchor point, if the current anchor point is outside all the units, entering step 302, and if the current anchor point is inside a certain unit, entering step 303;
step 302, selecting one unit from all units according to the principle of proximity, calculating the distance between the current anchor point and the surface of the current unit, if the distance is greater than a preset distance threshold value, a surface adsorption unit cannot be obtained, exiting the method, otherwise, taking the current unit as the surface adsorption unit, determining a point on a limited unit closest to the current anchor point according to an interpolation function, obtaining the local coordinate representation of the point, wherein the node has at least one local coordinate component in the surface adsorption unit, and the rest are outside the surface adsorption unit, and entering step 304;
step 303, if the current anchor point is in the current unit, taking the current unit as a surface adsorption unit, calculating the local coordinate representation of the current anchor point in the surface adsorption unit, and entering step 304;
step 304, representing the displacement data of the current anchor point, the surface adsorption unit and the local coordinate obtained in the previous step to form a deformation calculation object, and calculating to obtain a 3x3 transformation matrix and a 3-dimensional displacement vector of the current anchor point;
step 4, if the array unit to be designed is rigidly fixed, performing matrix decomposition calculation on the 3x3 matrix calculated in the step 3, calculating and extracting an optimal rotation transformation matrix, combining the optimal rotation transformation matrix and the displacement vector calculated in the step 3 to obtain a complete transformation matrix capable of describing translation and rotation changes of the local coordinate system of the unit, and entering the step 5;
if the array unit to be designed is flexible, the 3x3 matrix calculated in the step 3 is reserved, the 3x3 matrix is combined with the displacement vector calculated in the step 3, a complete transformation matrix capable of describing the translation and rotation change of the unit local coordinate system is obtained, and the step 5 is carried out;
step 5, designing an array unit before deformation;
step 6, transforming the coordinate system of the array unit and key points in the coordinate system according to the complete transformation matrix obtained by calculation in the step 4 to obtain the position and the local coordinate system of the deformed array unit, and entering the step 7;
and 7, performing electromagnetic simulation on the deformed array unit, if the displacement and the posture of the array unit meet the requirements and the distance threshold value in the step 302 is not exceeded, quitting the method, and if the displacement and the posture of the array unit do not meet the requirements, redesigning the array unit before deformation or moderately correcting the distance threshold value and returning to the step 6 until the electromagnetic simulation result meets the requirements.
2. The method as claimed in claim 1, wherein in step 1, the finite element model is directly created or imported, or after inputting the parametric scan volume as a non-finite element model, the parametric scan volume is converted into the finite element model by finite sampling.
3. The method for delayed structuring of deformable surface constrained conformal array elements as claimed in claim 1, wherein in step 1, said topological data structure further comprises element information.
4. The method for delayed construction of deformable surface constrained conformal array elements as claimed in claim 3, wherein in step 1, said element information comprises element type information or interpolated shape function about its nodes and node numbers of all said nodes with which the element is associated.
5. The method for delayed structuring of a deformable surface constrained conformal array element according to claim 1, further comprising, after said step 1 and before said step 2, the steps of:
and (2) converting the topological data structure of the finite element model obtained in the step (1) into a quick lookup table, inputting any three-dimensional coordinate into the quick lookup table, quickly judging whether the three-dimensional coordinate has the surface adsorption unit, and if so, outputting the surface adsorption unit and the corresponding local coordinate representation.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN120012187A (en) * | 2025-04-22 | 2025-05-16 | 江苏赛博空间科学技术有限公司 | TDFIT-based antenna housing thermoelectric integrated simulation analysis method |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5347287A (en) * | 1991-04-19 | 1994-09-13 | Hughes Missile Systems Company | Conformal phased array antenna |
| CN107622148A (en) * | 2017-08-29 | 2018-01-23 | 西安电子科技大学 | Determination Method of Optimum Elastic Modulus of Cylindrical Conformal Array Antenna Structure Based on Electromechanical Coupling |
| CN110110458A (en) * | 2019-05-14 | 2019-08-09 | 西安电子科技大学 | The conformal array antenna modeling method of deformation based on high order MoM |
-
2021
- 2021-06-28 CN CN202110716879.XA patent/CN113378441B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5347287A (en) * | 1991-04-19 | 1994-09-13 | Hughes Missile Systems Company | Conformal phased array antenna |
| CN107622148A (en) * | 2017-08-29 | 2018-01-23 | 西安电子科技大学 | Determination Method of Optimum Elastic Modulus of Cylindrical Conformal Array Antenna Structure Based on Electromechanical Coupling |
| CN110110458A (en) * | 2019-05-14 | 2019-08-09 | 西安电子科技大学 | The conformal array antenna modeling method of deformation based on high order MoM |
Non-Patent Citations (3)
| Title |
|---|
| 徐延林;李振;黄贤俊;: "曲面共形阵列结构快速数值分析方法", 电波科学学报, no. 04, pages 76 - 83 * |
| 齐子森;郭英;王布宏;侯文林;: "共形阵列天线单元极化形式的优化设计", 航空学报, no. 04, pages 129 - 137 * |
| 齐子森;郭英;王布宏;霍文俊;: "基于ESPRIT算法的柱面共形阵列天线DOA估计", 系统工程与电子技术, no. 08, pages 49 - 53 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN120012187A (en) * | 2025-04-22 | 2025-05-16 | 江苏赛博空间科学技术有限公司 | TDFIT-based antenna housing thermoelectric integrated simulation analysis method |
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