Finite element modeling method for laying MFC solar wing sail
By using the finite element modeling method with absolute node coordinates, the modeling challenge of large flexible structures in microgravity environments was solved, enabling rapid simulation and active vibration suppression control, thereby improving the control accuracy and equipment lifespan of spacecraft.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-08-26
- Publication Date
- 2026-03-27
AI Technical Summary
Existing technologies make it difficult to accurately model large flexible structures such as solar panels in microgravity and low-damping environments, resulting in long vibration durations that affect spacecraft control accuracy and equipment lifespan.
A finite element modeling method based on absolute node coordinates is adopted, combined with the Matlab platform, to divide the element model and establish an electromechanical coupling model of the MFC solar panel. The kinematic differential equations are solved by Newton-Raphael implicit integrals to achieve rapid simulation.
It provides an accurate kinematic model, supports the design of active vibration suppression control algorithms, verifies the effectiveness of the algorithms, reduces the duration of vibration, and improves the control accuracy and equipment life of spacecraft.
Smart Images
Figure CN116050198B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of flexible body simulation analysis, in particular to a finite element modeling method for a solar wing sailboard coated with MFC. BACKGROUND
[0002] With the development of aerospace technology, the spacecrafts running in space now are all equipped with large flexible devices, such as solar sailboards of flexible structures. As the functions of such flexible structures become more and more important, their sizes become larger and larger, showing the characteristics of low damping, low stiffness and large deflection. The large flexible structures inevitably produce vibrations in operation, and the air damping in space is very small, so if not actively controlled, the vibrations will last for a long time. This will bring negative effects such as reduction of control accuracy of the spacecraft, fatigue damage of device parts, and interference to high-precision devices, so the spacecraft needs to have the ability to quickly suppress vibrations. In the process of designing an active control algorithm, the controlled object needs to be accurately modeled to obtain its kinematic differential equation. In order to solve the kinematic equation of the large displacement of the cantilevered laminated plate coated with MFC, a modeling method and programming implementation technology based on absolute node coordinates are proposed. SUMMARY
[0003] In view of the deficiencies of the prior art, the present application provides a finite element modeling method for a solar wing sailboard coated with MFC, which is used to establish an accurate and less computationally complex kinematic model of the solar wing sailboard coated with MFC, as a supplement to the solar wing sailboard experimental platform, to lay a foundation for the design of the active vibration suppression control algorithm of the solar wing sailboard, and to provide an important reference for verifying the effectiveness of the algorithm.
[0004] The technical scheme adopted by the present application to achieve the above-mentioned purpose is as follows:
[0005] A finite element modeling method for a solar wing sailboard coated with MFC, comprising the following steps:
[0006] Step 1: establishing an initial model of the base plate according to the "sunflower" solar wing sailboard, and setting the boundary conditions of the base plate;
[0007] Step 2: dividing the base plate units in Matlab, and defining the base plate unit model by applying an interpolation function and flexible plate theory;
[0008] Step 3: establishing a unit model of MFC according to the structure and piezoelectric properties of the piezoelectric laminated plate MFC, including a sensor model and an actuator model;
[0009] Step 4: setting the connection relationship of each base plate unit with its adjacent base plate units, and the bonding conditions of MFC and the base plate in the initial model of the solar wing sailboard;
[0010] Step 5: all unit models are integrated into integral finite element equations by using the connection matrix, inputting working condition parameters, and applying Newton-Raphson implicit integration for solving, so that simulation results of the model are calculated.
[0011] The boundary conditions of the cantilever plate are point constraint, rigid constraint and flexible component.
[0012] The substrate is an epoxy resin substrate and an isotropic material.
[0013] The substrate unit model is a four-node 12-degree-of-freedom one-dimensional quadrilateral element, and each vertex of the quadrilateral element has a degree of freedom in the x, y and z directions.
[0014] The structure of the MFC is a d33 type MFC piezoelectric structure, and the piezoelectric characteristic is a piezoelectric constitutive equation.
[0015] The substrate unit model includes two shapes: a long and narrow unit and a square unit; two rows of transverse long and narrow unit queues are arranged on the substrate, and square units are arranged at other positions; the length of the long and narrow unit is equal to the side length of the square unit, and the width of the long and narrow unit is less than the length.
[0016] The long and narrow unit setting comprises: setting the long and narrow unit queue according to the number of MFCs and the bonding position on the substrate, and the long and narrow units are arranged in sequence along the transverse central axis direction of the MFC to form the long and narrow unit queue.
[0017] The connection relationship is a force conduction relationship, which is used to represent the connection matrix of the force conduction of the unit node, and the force conduction relationship matrix between the local displacement of the substrate unit and the overall displacement of the model.
[0018] The working condition parameters include: a point constraint cantilever boundary condition, an initial displacement field and material properties.
[0019] The present application has the following beneficial effects and advantages:
[0020] 1. The present application provides a method for laying MFC solar wing sailboard electromechanical coupling finite element modeling, which lays the foundation for the active control algorithm design of the solar wing sailboard.
[0021] 2. The method provided by the present application can provide a rapid verification platform for the active vibration suppression algorithm.
[0022] 3. The present application is aimed at process simulation of flexible structures such as solar wing sailboards in microgravity and low damping environment, and can be expanded to vibration research on flexible space structures. BRIEF DESCRIPTION OF DRAWINGS
[0023] Figure 1 It is the method flow chart of the present application;
[0024] Figure 2 is a finite element model mesh diagram of a solar wing sailboard;
[0025] Figure 3 is a comparison diagram of free vibration experiment and simulation in time domain;
[0026] Figure 4 is a comparison diagram of free vibration experiment and simulation in frequency domain. DETAILED DESCRIPTION
[0027] The application will be described in further detail below with reference to the drawings and embodiments.
[0028] In order to make the above objectives, features and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application will be described in detail below with reference to the drawings. In the following description, a large number of specific details are set forth in order to provide a thorough understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the spirit of the present application, so the present application is not limited to the specific embodiments disclosed below.
[0029] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs. The terms used in the specification of the application herein are only for the purpose of describing specific embodiments and are not intended to limit the present application.
[0030] As Figure 1 is a flow chart of the method of the present application.
[0031] The method comprises the following steps:
[0032] 1) An initial model of the solar wing sailboard is established according to the "sunflower" solar wing sailboard, and the boundary conditions of the cantilever plate are considered as point constraints, and rigid constraints and flexible components are set;
[0033] Specifically, the initial physical parameters are input, including the size of the length, width and thickness of the cantilever plate, the elastic modulus, and the piezoelectric constant;
[0034] 2) In Matlab, the elements are divided, and an interpolation function and a flexible plate theory are applied to establish a substrate element model, and a one-dimensional four-node 12-degree-of-freedom one-dimensional four-edge element is adaptively applied;
[0035] Specifically, the element model is established based on the absolute node coordinate method, and the element mass, element stiffness and other matrices are obtained;
[0036] 3) A piezoelectric element model is established for the structure and piezoelectric characteristics of the MFC, including a sensor model and an actuator model; the second piezoelectric constitutive equation is applied to the piezoelectric characteristics, and the piezoelectric constant matrix therein is adjusted for the structure of the MFC;
[0037] Specifically, the piezoelectric constitutive equation is adjusted according to the MFC, and the piezoelectric braking matrix and the piezoelectric sensing matrix of the piezoelectric structure of the d33 type MFC are established;
[0038] 4) The connection relationship between the unit and the whole in the initial model of the solar wing sail is extracted, and a whole node connection relationship matrix is designed, which includes the bonding conditions of the MFC and the substrate (the lower surface of the MFC and the upper surface of the solar wing sail are ideally bonded, that is, seamless bonding: there is no relative displacement between the lower surface of the MFC and the upper surface of the solar wing sail);
[0039] Specifically, referring to the divided piezoelectric laminated plate unit, the unit node connection matrix is established, and the relationship Boolean matrix between the local displacement of the unit and the whole displacement of the model is established;
[0040] 5) The connection relationship matrix is used to integrate all the unit models into a whole finite element equation (second-order kinematic differential equation), and Newton-Raphson implicit integration is applied for solving, and the simulation results of the model are calculated.
[0041] Specifically, the connection relationship and the unit matrix are integrated to establish the whole kinematic differential equation; the Newton-Raphson method is used to solve the whole kinematic differential equation, and the modeling is realized in MATLAB.
[0042] As Figure 2 The grid chart of the solar wing sail finite element model is shown in the figure, and the substrate unit model includes two types: long and narrow unit and square unit (two physical sizes of units, that is, 10*30mm and 30*30mm); two rows of transverse long and narrow unit queues are arranged on the substrate, and square units are arranged at other positions; the length of the long and narrow unit is equal to the side length of the square unit, and the long and narrow unit is arranged to include: arranging the long and narrow unit queue according to the number of MFCs and the bonding position on the substrate, and the long and narrow units are arranged along the transverse central axis direction of the MFC to form the queue. The red frame unit is the piezoelectric laminated plate unit, and the front two points of the uppermost and lowermost two rows of piezoelectric units are the fixed point constraints of the solar wing sail.
[0043] Figure 3 The figure is a comparison chart of the free vibration experiment and simulation in the time domain, and it can be seen that the simulation model and the experimental data of the test bench are basically consistent in the adjustment time.
[0044] Figure 4 The figure is a comparison chart of the free vibration experiment and simulation in the frequency domain, and it can be seen that the simulation model and the experimental data of the test bench are basically consistent in the first-order free vibration frequency, which is about 2.7Hz, and the amplitude of other frequency components is basically consistent.
[0045] The above figures verify the effectiveness and accuracy of the present application.
[0046] The above merely illustrates the embodiments of the present application, but should not be used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, extension, etc. within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims
1. A method of finite element modeling of a deployed MFC solar wing sail, characterized in that , Step 1: setting boundary conditions of the substrate according to the initial model of the substrate of the solar wing sailboard; Step 2: dividing the substrate unit in Matlab, and applying an interpolation function and a flexible plate theory to define the substrate unit model; Step 3: establishing the unit model of the MFC according to the structure and piezoelectric characteristics of the piezoelectric laminated plate MFC, including a sensor model and an actuator model; Step 4: setting the connection relationship of each substrate unit with its adjacent substrate unit in the initial model of the solar wing sailboard, and the bonding conditions of the MFC and the substrate; the connection relationship is a force transmission relationship, a connection matrix for characterizing the force transmission of the unit node, and a relationship Boolean matrix between the local displacement of the substrate unit and the overall displacement of the model; Step 5: integrating all unit models into overall finite element equations using the connection relationship matrix, inputting working condition parameters, and applying Newton-Raphson implicit integration to solve and calculate the simulation results of the model.
2. The finite element modeling method of a deployed MFC solar wing sail according to claim 1, wherein The boundary conditions of the substrate are point constraints, rigid constraints and flexible components.
3. The finite element modeling method of deploying MFC solar wing sail according to claim 1, characterized in that The substrate is an epoxy resin substrate and an isotropic material.
4. The finite element modeling method of deploying MFC solar wing sail according to claim 1, characterized in that The substrate unit model is a four-node one-dimensional quadrilateral element with 12 degrees of freedom, and each vertex of the quadrilateral element has degrees of freedom in the x, y and z directions.
5. The finite element modeling method of deploying MFC solar wing sail according to claim 1, wherein The structure of the MFC is a d33 type MFC piezoelectric structure; and the piezoelectric characteristics are piezoelectric constitutive equations.
6. The finite element modeling method of deploying MFC solar wing sail according to claim 1, wherein The substrate unit model includes two shapes: a long and narrow unit and a square unit; two rows of transverse long and narrow unit queues are arranged on the substrate, and square units are arranged at other positions; the length of the long and narrow unit is equal to the side length of the square unit, and the width of the long and narrow unit is less than the length.
7. The finite element modeling method of deploying MFC solar wing sail according to claim 6, characterized in that The long and narrow unit setting includes: setting the long and narrow unit queue according to the number of MFCs and the bonding position on the substrate, and the long and narrow units are arranged along the transverse central axis of the MFC to form the long and narrow unit queue.
8. The finite element modeling method of deploying MFC solar wing sail according to claim 1, characterized in that The working condition parameters include: point constraint cantilever boundary conditions, initial displacement field, and material properties.