A transient thermal analysis method for spatial thin-walled structures based on Lagrangian expansion

Abstract

The present application provides a transient thermal analysis method for a spatial thin-walled structure based on a Lagrangian expansion, comprising: S1: using a one-dimensional beam unit shape function to describe the temperature distribution in the longitudinal direction of the thin-walled structure; S2: using the Lagrangian expansion to expand the single-valued temperature at each node of the one-dimensional beam unit into a two-dimensional temperature field distributed along the interface of the thin-walled structure, and obtaining the three-dimensional temperature field distribution characteristics of the thin-walled structure; S3: integrating within the thin-walled structure and within the boundary surface to obtain a thermal equilibrium equation that satisfies the energy conservation in the domain; S4: replacing the three-dimensional temperature field distribution characteristics using the one-dimensional beam unit and the Lagrangian expansion into the thermal equilibrium equation to obtain a heat conduction control equation for the thin-walled structure; S5: solving the heat conduction control equation to obtain a three-dimensional time-domain temperature field of the thin-walled structure during on-orbit operation.

Description

Technical Field

[0001] The invention relates to a transient thermal analysis method of a space thin-wall structure based on Lagrangian expansion. Background Art

[0002] When a spacecraft is in orbit, it is directly exposed to the sun's radiation heating. The air in space is very thin, so it cannot form effective convection heat exchange. Its temperature will rise sharply when heated for a long time. When the spacecraft is in the shadow area, the thermal radiation load disappears, the spacecraft is in a radiation heat dissipation state, and the background temperature in space can be as low as 4K (minus 269.15℃), so the temperature of the spacecraft will drop sharply. The above extreme high and low temperature phenomena will have unpredictable effects on the structural performance of the spacecraft.

[0003] The structural characteristics of spacecraft are different from those of conventional engineering structural components. Limited by the space volume and carrying weight of the vehicle, aerospace structures usually use lightweight, deployable thin-walled structural components. The mechanical behavior of thin-walled structures is particularly affected by extreme high and low temperatures. Therefore, the mechanical behavior analysis of thin-walled structures in extreme high and low temperature environments has very important engineering significance for the design of their initial structural parameters. The transient heat conduction analysis of space thin-walled structures is the basis for mechanical behavior analysis.

[0004] The thermal environment of a space structure is different from that of a surface structure. The scarce air causes the convective heat transfer on the surface of the structure to be negligible. The heat exchange pathways between the surface of the structure and the outside world are mainly solar radiation absorption and radiation heat dissipation. Solar radiation can be regarded as a surface heat source, and radiation heat dissipation is a channel for the loss of internal energy in the structure. When establishing a mathematical model for a space structure, the radiation heat dissipation term is a fourth-order term of the temperature, which is a strong nonlinear condition. Therefore, it becomes very difficult to solve the nonlinear ordinary differential equation about the temperature field. Since it is impossible to obtain a theoretical analytical solution to the temperature field results, commercial finite element software is currently used in structural heat transfer analysis.

[0005] The principle of finite element software is the finite element method that discretizes three-dimensional shape function units. This method has the advantages of wide application range and simple and easy operation. However, due to the unique geometric form of spatial thin-walled structures, especially the extremely small wall thickness and large longitudinal scale, it is very easy to have mismatched mesh dimensions when dividing units, resulting in poor mesh quality, which greatly affects the accuracy of the finite element model results. When using the three-dimensional finite element method, in order to ensure a high mesh quality, it is necessary to ensure that the mesh size along the longitudinal direction of the thin wall is close to the mesh size within the thin wall surface, which will cause the model's calculation degree of freedom to increase sharply, significantly affecting the efficiency of calculation and analysis. Summary of the invention

[0006] In order to solve the problems of large mesh size, low computational efficiency, and poor result accuracy existing in the three-dimensional finite element method, this application proposes an analysis model based on the Carrera Unified Formulation principle. One-dimensional beam elements are used for discretization along the longitudinal direction of the thin-walled beam, and Lagrangian expressions of different orders are used at the nodes of the beam elements to expand the node single-valued variables into two-dimensional field quantities. This model can be used to calculate the transient heat conduction problem of spatial thin-walled structures during on-orbit operation, which can effectively reduce the amount of calculation of the calculation model and improve the calculation and analysis efficiency of the problem.

[0007] The present application provides a transient thermal analysis method for a spatial thin-walled structure based on Lagrangian expansion, comprising:

[0008] S1: Along the longitudinal direction of the thin-walled structure, the temperature distribution in the longitudinal direction of the thin-walled structure is described by using the one-dimensional beam element shape function;

[0009] S2: Using the Lagrangian expansion formula, the single-valued temperature at each node of the one-dimensional beam unit is expanded into a two-dimensional temperature field distributed along the interface of the thin-walled structure, and the three-dimensional temperature field distribution characteristics of the thin-walled structure are obtained;

[0010] S3: Integrate within the thin-walled structure and the boundary surface to obtain the thermal equilibrium equation that satisfies the energy conservation in the domain;

[0011] S4: Substitute the three-dimensional temperature field distribution characteristics using one-dimensional beam elements and Lagrangian expansion into the thermal equilibrium equation to obtain the heat conduction control equation of the thin-walled structure;

[0012] S5: Solve the heat conduction control equation to obtain the three-dimensional time-domain temperature field of the thin-walled structure during on-orbit operation.

[0013] According to at least one embodiment of the present application, in step S1, the shape function adopts a beam element in the form of a linear, quadratic, or cubic function.

[0014] According to at least one embodiment of the present application, in step S2, a linear Lagrangian expansion is used.

[0015] According to at least one embodiment of the present application, in step S2, a Lagrangian expansion of quadratic terms is used.

[0016] According to at least one embodiment of the present application, in step S2, a Lagrangian expansion of a cubic term is used.

[0017] According to at least one embodiment of the present application, in step S3, the weighted residual method and the Galerkin method are used to perform integration within the thin-walled structure and within the boundary surface based on the internal energy balance equation of the thin-walled structure and the thermal radiation boundary conditions and the radiation heat dissipation boundary conditions.

[0018] According to at least one embodiment of the present application, in step S4, the heat conduction control equation of the thin-walled structure is a heat conduction control equation of the thin-walled structure based on the CUF principle.

[0019] According to at least one embodiment of the present application, step S4 further includes: calculating a basic kernel related to the heat conduction control equation by using a Gaussian integral method.

[0020] According to at least one embodiment of the present application, in step S5, the heat conduction control equation is a nonlinear ordinary differential equation, which is solved using the Adams method.

[0021] The present application also provides a computer-readable storage medium having software instructions stored thereon, wherein the software instructions implement the above method when executed.

[0022] The present invention abandons the three-dimensional solid units in traditional commercial finite element software and adopts one-dimensional beam units combined with Lagrange expansion to describe the three-dimensional temperature field. While ensuring the calculation accuracy, it can effectively reduce the calculation freedom of the calculation model and greatly improve the calculation efficiency of transient thermal analysis problems of spatial structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The following will further explain the above characteristics, technical features, advantages and implementation methods of the present application in a clear and understandable manner through the description of the preferred embodiments and in combination with the accompanying drawings. The following drawings are only intended to illustrate and explain the present application, and do not limit the scope of the present application. Among them:

[0024] Figure 1 This is the idea diagram of transient heat conduction analysis model based on Lagrangian expansion;

[0025] Figure 2a-2c Different types of Lagrangian expansions at the nodes of a beam element. DETAILED DESCRIPTION

[0026] In order to have a clearer understanding of the technical features, purposes and effects of the present application, the specific implementation methods of the present application are now described with reference to the accompanying drawings.

[0027] This application proposes a method for analyzing transient heat conduction problems in spatial thin-walled structures. This method uses a new model that is different from the 3D solid unit of existing commercial finite element software. In this model, one-dimensional beam units are used to discretize the spatial thin-walled structure longitudinally, and the Lagrangian expansion is used to expand the single-valued state quantity at the node of the beam unit into a field quantity in the two-dimensional domain, realizing the function of using one-dimensional units to describe the three-dimensional characteristic field quantity of the thin-walled structure.

[0028] like Figure 1As shown in FIG2 , a transient thermal analysis method for a spatial thin-walled structure based on Lagrangian expansion according to an embodiment of the present invention includes:

[0029] S1: Along the longitudinal direction of the thin-walled structure, a one-dimensional beam element shape function is used to describe the temperature distribution in the longitudinal direction of the thin-walled structure. The shape function can be in the form of a B2, B3 or B4 beam element in the form of a first-order, second-order, or third-order function.

[0030] S2: In order to obtain the three-dimensional temperature field distribution characteristics of the thin-walled structure, the single-valued temperature at each node of the one-dimensional beam unit is expanded into a two-dimensional temperature field distributed along the interface of the thin-walled structure. The specific form can be the Lagrangian expansion of linear, quadratic, and cubic terms, such as Figures 2a to 2c As shown, they are the Lagrangian expansion units of L4, L9 and L16 respectively;

[0031] S3: Based on the internal energy balance equation of the thin-walled structure and the thermal radiation boundary conditions and radiation heat dissipation boundary conditions, the weighted residual method and the Galerkin method are used to integrate within the thin-walled structure and within the boundary surface to obtain the thermal balance equation that satisfies the energy conservation in the domain;

[0032] S4: Substitute the three-dimensional temperature field distribution characteristics using one-dimensional beam elements and Lagrangian expansion into the heat balance equation to obtain the heat conduction control equation of the thin-walled structure based on the CUF (Carrera Unified Formulation) principle. The basic kernel related to the heat conduction control equation is calculated by the Gaussian integral method.

[0033] S5: The Adams method is used to solve the nonlinear ordinary differential equation (heat conduction control equation) to obtain the three-dimensional time-domain temperature field of the thin-walled structure during on-orbit operation.

[0034] The above description is only an illustrative embodiment of the present application and is not intended to limit the scope of the present application. Any equivalent changes, modifications and combinations made by any technician in the field without departing from the concept and principle of the present application shall fall within the scope of protection of the present application.

Claims

1. A transient thermal analysis method for a space thin-walled structure based on Lagrangian expansion, comprising: S1: Along the longitudinal direction of the thin-walled structure, the temperature distribution in the longitudinal direction of the thin-walled structure is described by using the one-dimensional beam element shape function; S2: Using the Lagrangian expansion formula, the single-valued temperature at each node of the one-dimensional beam unit is expanded into a two-dimensional temperature field distributed along the interface of the thin-walled structure, and the three-dimensional temperature field distribution characteristics of the thin-walled structure are obtained; S3: Integrate within the thin-walled structure and the boundary surface to obtain the thermal equilibrium equation that satisfies the energy conservation in the domain; S4: Substitute the three-dimensional temperature field distribution characteristics using one-dimensional beam elements and Lagrangian expansion into the thermal equilibrium equation to obtain the heat conduction control equation of the thin-walled structure; S5: Solve the heat conduction control equation to obtain the three-dimensional time-domain temperature field of the thin-walled structure during on-orbit operation.

2. The method according to claim 1, wherein: In step S1, the shape function adopts a beam element in the form of a linear, quadratic, or cubic function.

3. The method according to claim 1, wherein: In step S2, a linear Lagrangian expansion is used.

4. The method according to claim 1, wherein: In step S2, the Lagrange expansion of the quadratic term is used.

5. The method according to claim 1, wherein: In step S2, the Lagrange expansion of the cubic term is used.

6. The method according to claim 1, wherein: In step S3, according to the internal energy balance equation of the thin-walled structure and the thermal radiation boundary conditions and the radiation heat dissipation boundary conditions, the weighted residual method and the Galerkin method are used to perform integration within the thin-walled structure and within the boundary surface.

7. The method according to claim 1, wherein: In step S4, the heat conduction control equation of the thin-walled structure is a heat conduction control equation of the thin-walled structure based on the CUF principle.

8. The method according to claim 1, wherein: Step S4 also includes: calculating the basic kernel related to the heat conduction control equation by Gaussian integral method.

9. The method according to claim 1, wherein: In step S5, the heat conduction control equation is a nonlinear ordinary differential equation, which is solved using the Adams method.

10. A computer-readable storage medium having stored thereon software instructions which, when executed, implement the method of any one of claims 1-9.

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