Method and system suitable for thermal deformation analysis of anisotropic composite material structure

Abstract

The invention provides a method and a system suitable for thermal deformation analysis of an anisotropic composite material structure. The method comprises the following steps: establishing a structural finite element analysis model; applying boundary constraint and load conditions; setting a thermal expansion coefficient attribute and a material mechanical attribute of a model material; initializing setting of model material thermal expansion coefficient properties and material mechanical property polarities; simulating, analyzing and calculating the internal strain of the structure; checking and correcting the thermal constitutive attribute polarity of each unit according to the temperature and load calculation result of each unit of the finite element model; checking and correcting the force constitutive attribute polarity of each unit according to the temperature and load calculation result of each unit of the finite element model; judging whether the current strain calculation result meets the tolerance requirement or not according to the convergence criterion, and if yes, entering the next step of analysis and calculation; and according to the previous unit strain analysis result, modifying the expansion coefficient of the finite element model unit and the material mechanical parameter polarity, carrying out analysis and calculation, and outputting a final calculation result.

Description

Technical Field

[0001] This invention relates to the field of spacecraft structure technology, and more specifically, to a method and system applicable to thermal deformation analysis of anisotropic composite material structures. Background Technology

[0002] As spacecraft functions and missions become more diversified, the proportion of payload weight carried by spacecraft is increasing, making the need for lightweight spacecraft structures increasingly urgent. Composite materials, due to their high specific strength and designability, facilitate lightweight design and are increasingly widely used in spacecraft structures. On the other hand, the high precision and non-maintainable nature of on-orbit spacecraft operations necessitates addressing the simulation problems of thermal deformation caused by orthotropic composite material structures in the complex thermo-mechanical coupling environment of space.

[0003] Anisotropy in composite material structures is not only manifested in the different moduli in different directions, but also in the different tensile and compressive moduli, thermal expansion and contraction coefficients in the same direction. In view of this, most analyses of the thermal deformation response of composite material structures in engineering are based on the assumption of isotropic elastic modulus and thermal expansion coefficient, while there is little research on the anisotropy of tensile and compressive modulus and thermal expansion coefficient of three-dimensional orthotropic composite material structures.

[0004] Currently, general-purpose finite element software has difficulty accurately analyzing the deformation behavior of anisotropic composite material structures. Solving engineering problems mainly relies on the isotropic assumption, and approximate solutions to thermal deformation are obtained through calculations using commercial finite element analysis software.

[0005] In their paper "A constitutive model for OSB and its application in finite element analysis", Zhu et al. artificially divided the tension and compression zones according to the stress conditions of anisotropic structures and used different material constitutive relations to analyze the stress conditions of the structures. However, this division requires prior human judgment and is not applicable to complex stress conditions.

[0006] In their paper "Adaptive Algorithm for Three-Dimensional Orthotropic Composite Material Structures," Cao Yuhao et al. proposed an iterative mechanical algorithm applicable to three-dimensional orthotropic composite material structures. Targeting composite material structures widely used in spacecraft, they proposed an adaptive iterative algorithm that overcomes the limitation of assuming isotropic elastic modulus for orthotropic composite materials in engineering, greatly improving the accuracy of mechanical calculations for orthotropic composite material structures. However, the problem of deformation analysis under complex thermo-mechanical coupling environments remains unsolved.

[0007] In their paper "Finite Element Method for Elastic Mechanics with Different Tension and Compression Moduli," Zou Xianwei et al. proposed an adaptive iterative method for mechanical analysis, addressing the anisotropy of elastic moduli in the tensile and compressive properties of many organs in plant stems and stalks during growth. This method overcomes the limitations of previous methods that required artificial assumptions about stress conditions and allows for analysis of more complex stress scenarios. However, it still fails to solve the problem of deformation analysis under complex thermo-mechanical coupling environments.

[0008] Patent application CN105631122A discloses a method for thermal deformation simulation analysis and modeling of large machine tool components. It uses the general-purpose finite element analysis software Ansys for thermo-structural coupling analysis. After the finite element analysis, based on the extracted thermal deformation results, a mathematical model of thermal deformation at a specific location on the large machine tool component is established using polynomial fitting and multiple linear regression. This method fully utilizes the efficiency and reliability of commercial software for simulation analysis and is a commonly used method in engineering. However, this method does not provide further detailed explanations for the thermo-structural coupling analysis of thermal deformation in anisotropic structures. Applications to anisotropic composite material structures require the assumption of isotropy of the structural materials, which limits the calculation accuracy.

[0009] Patent application CN104537182A discloses an analytical method for the impact of lens thermal deformation on the imaging results of an optical system. This method analyzes lens deformation caused by changes in the thermal environment using finite element analysis software, obtaining deformation data for each node of the lens. After data processing, the deformation amount in the lens's sagittal direction is obtained. The deformation amount is then fitted with a Zernike polynomial to obtain Zernike coefficients, which are input into optical simulation software to view the imaging results after deformation. This method can provide guidance for the design of optical systems under complex thermal environments. However, this method does not incorporate the mechanical properties of the composite structure formed by the mirror structure into the calculation, and there is still room for improvement in the calculation accuracy.

[0010] Patent application document CN102364489A discloses a numerical simulation method for a complex anisotropic constitutive relation model of wood, which overcomes the shortcomings of existing constitutive models that fail to identify different mechanical properties under tension, shear and compression. However, it still fails to solve the problems of inconsistent tensile and compressive moduli and inconsistent thermal expansion coefficients under high temperature expansion and low temperature contraction.

[0011] Patent application CN108345741A discloses a two-dimensional thermal deformation and thermal stress analysis method for anisotropic material structures based on meshless methods. This method avoids the requirement of numerical simulation calculations in finite element analysis, simplifies the model processing, and eliminates the need for commercial analysis software. However, this method relies on relatively complex formula derivations and requires custom programming, which limits its application in engineering problems.

[0012] Patent application CN108573081A discloses a method for analyzing the thermal deformation of automotive headlight reflectors using thermo-mechanical coupling simulation. This method includes data processing and extraction during thermal simulation; data processing and extraction during mechanical simulation; thermo-mechanical coupling and solving of the extracted data; and post-processing of the results to calculate the thermal deformation of the headlight. This method utilizes commercial finite element analysis software, resulting in high efficiency and reliable analysis results. However, it lacks further analysis for anisotropic materials, and there is still room for improvement in the accuracy of calculations for structures composed of anisotropic materials.

[0013] Therefore, there is an urgent need for an adaptive method and system suitable for thermal deformation analysis of anisotropic composite material structures, which can comprehensively reflect the thermal and mechanical constitutive properties of anisotropic composite materials in thermal deformation analysis, adaptively analyze the thermal deformation of anisotropic composite material structures under thermo-mechanical coupled load conditions, and solve the problem of thermal deformation analysis in aerospace engineering. Summary of the Invention

[0014] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system suitable for thermal deformation analysis of anisotropic composite material structures.

[0015] The method for thermal deformation analysis of anisotropic composite material structures provided by the present invention includes:

[0016] Step 1: Establish a finite element analysis model for the anisotropic composite material structure; Step 2: Apply boundary constraints and load conditions to the finite element analysis model; Step 3: Set the thermal expansion coefficient and mechanical properties of the materials in the finite element analysis model; Step 4: Initialize the polarity of the thermal expansion coefficient and the mechanical properties of all elements in the finite element analysis model; the initialization is set as follows: assume that all elements are in a tensile state and an expansion state, and assign initial mechanical properties and thermal expansion coefficient polarity to each element accordingly. Step 5: Based on the initial polarity of the material's mechanical properties and the polarity of its thermal expansion coefficient, perform the first simulation analysis to calculate the internal strain and temperature results of each element in the finite element analysis model. Step 6: Based on the temperature results of each unit obtained from the first simulation analysis, examine and correct the thermal constitutive property polarity of each unit. The correction includes: determining whether each unit is expanding or contracting according to its temperature state, and adjusting its thermal expansion coefficient accordingly. Step 7: Based on the strain results of each unit and the adjusted coefficient of thermal expansion obtained from the first simulation analysis, check and correct the polarity of the force constitutive property of each unit. The correction includes: determining whether each unit is under tension or compression according to the strain state of each unit in each material direction, and adjusting its elastic modulus in that direction accordingly. Step 8: According to the preset convergence criterion, determine whether the structural strain calculated at the moment meets the requirements; if it does, proceed to step 9; if it does not, update the material properties of the finite element analysis model based on the corrected thermal constitutive polarity and force constitutive polarity, and return to step 5 for a new round of simulation analysis and polarity correction iteration. Step 9: Based on the last attribute polarity correction result when the convergence criterion is met, update the material properties of the finite element analysis model, perform the final analysis calculation, and output the thermal deformation results of the anisotropic composite material structure.

[0017] Preferably, the anisotropic composite material structure is an orthotropic composite material structure, and its material properties are as follows: the elastic modulus is different in the three main directions of the material, and in the same direction, the tensile elastic modulus is different from the compressive elastic modulus; the coefficient of thermal expansion is different in each direction, and in the same direction, the coefficient of thermal expansion in the expanded state is different from the coefficient of thermal expansion in the contracted state.

[0018] Preferably, the anisotropic composite material undergoes thermal deformation in the free state. With temperature increment Related to the coefficient of thermal expansion, it is expressed as:

[0019] in, This is the expansion coefficient matrix;

[0020] in, , , These are elements in the expansion coefficient matrix; For orthogonal anisotropic composite materials, the expansion coefficient matrix... Some elements in Related to the polarity of unit expansion, that is:

[0021]

[0022]

[0023] When the actual temperature T of a certain finite element model element is higher than the reference temperature At that time, the coefficient of thermal expansion is expressed as When the actual temperature T is lower than the reference temperature At that time, the coefficient of thermal expansion is expressed as ; The stiffness and strength of orthotropic composite material structures are related to the load conditions. The constitutive equations of the structure are determined by the load and constraint conditions, and the constitutive relation is expressed as:

[0024] in, For strain tensor, For stress tensor, This is the compliance matrix;

[0025] in, , , , , , , , , , , , These are elements in the compliance matrix; For orthotropic composite materials, the compliance matrix Some elements in Related to the direction of element stress, i.e.:

[0026]

[0027] in, Poisson's ratio, , These are the tensile and compressive elastic moduli, respectively. For orthotropic composite materials with tension-compression anisotropy, when any point in the material is in the local coordinate system When in tension , Then in The modulus in the direction of tension is the tensile modulus. ,at this time The material strength in the direction of tensile strength is the tensile strength; when in When under directional compression Then in The modulus in the directional direction is the compressive modulus. ,at this time The material strength in the direction of compression is the compressive strength.

[0028] Preferably, for each element in the extracted finite element model, the free thermal strain of the finite element in the temperature field environment is obtained by combining the temperature with the coefficient of thermal expansion under the boundary constraint free state. for:

[0029] If the relative temperature of a certain unit is obtained from the analysis That is, the thermal deformation polarity of this unit in the free state is expansion, then in the next iterative calculation... If the relative temperature of a certain unit is obtained from the analysis If the thermal deformation polarity of this unit in the free state is contraction, then in the next iterative calculation, the corresponding thermal expansion coefficient matrix will be modified as follows: ; For the total strain in each direction of each element in the extracted finite element model and the free thermal strain of each element calculated Analyze whether the element is under tension or compression, i.e.:

[0030] Based on the stress polarity in each direction of each element, determine whether the assumptions made in the previous step are consistent with the actual situation. If they are consistent, then maintain the corresponding compliance matrix for that element in that stress direction. If an element remains unchanged, then that element is modified. If the analysis yields a certain unit's... direction That is, the unit's If the direction is under tension, then in the next iterative calculation... If the analysis yields the results of a certain unit direction That is, the unit's If the direction is under pressure, then in the next iteration calculation, the corresponding... Modified to .

[0031] Preferably, the convergence criterion includes: When the proportion n of the total number of constitutive relations to be modified does not exceed a preset value. When, i.e., when n≤ Stop iteration when; if If the value is 0, it indicates that there are no constitutive equations that can be modified. Or the deviation between the calculation result and the previous iteration step Not exceeding the preset error limit At that time, that is ≤ Stop iteration when; if =0 indicates that the result has fully converged and the calculation result will no longer change with the increase of iterations.

[0032] The system for thermal deformation analysis of anisotropic composite material structures provided by the present invention includes: Module M1: Establish the finite element analysis model of the anisotropic composite material structure; Module M2: Apply boundary constraints and load conditions to the finite element analysis model; Module M3: Sets the thermal expansion coefficient and mechanical properties of the materials in the finite element analysis model; Module M4: Initializes the polarity of the thermal expansion coefficient and the mechanical properties of all elements in the finite element analysis model; the initialization is set as follows: assume that all elements are in a tensile state and an expansion state, and assign initial mechanical properties and thermal expansion coefficient polarity to each element accordingly. Module M5: Based on the polarity of the material's mechanical properties and thermal expansion coefficient after initialization, the first simulation analysis is performed to calculate the internal strain and temperature results of each element in the finite element analysis model. Module M6: Based on the temperature results of each unit obtained from the first simulation analysis, examine and correct the thermal constitutive polarity of each unit. The correction includes: determining whether each unit is expanding or contracting according to its temperature state, and adjusting its thermal expansion coefficient accordingly. Module M7: Based on the strain results of each unit obtained from the first simulation analysis and the adjusted coefficient of thermal expansion, the force constitutive property polarity of each unit is checked and corrected. The correction includes: determining whether each unit is under tension or compression according to the strain state of each material direction, and adjusting its elastic modulus in that direction accordingly. Module M8: Based on the preset convergence criterion, determine whether the currently calculated internal strain of the structure meets the requirements; if it does, trigger module M9; if it does not, update the material properties of the finite element analysis model based on the corrected thermal constitutive property polarity and force constitutive property polarity, and call module M5 to perform a new round of simulation analysis and polarity correction iteration. Module M9: Based on the last attribute polarity correction result when the convergence criterion is met, update the material properties of the finite element analysis model, perform the final analysis calculation, and output the thermal deformation results of the anisotropic composite material structure.

[0033] Preferably, the anisotropic composite material structure is an orthotropic composite material structure, and its material properties are as follows: the elastic modulus is different in the three main directions of the material, and in the same direction, the tensile elastic modulus is different from the compressive elastic modulus; the coefficient of thermal expansion is different in each direction, and in the same direction, the coefficient of thermal expansion in the expanded state is different from the coefficient of thermal expansion in the contracted state.

[0034] Preferably, the anisotropic composite material undergoes thermal deformation in the free state. With temperature increment Related to the coefficient of thermal expansion, it is expressed as:

[0035] in, This is the expansion coefficient matrix;

[0036] in, , , These are elements in the expansion coefficient matrix; For orthogonal anisotropic composite materials, the expansion coefficient matrix... Some elements in Related to the polarity of unit expansion, that is:

[0037]

[0038]

[0039] When the actual temperature T of a certain finite element model element is higher than the reference temperature At that time, the coefficient of thermal expansion is expressed as When the actual temperature T is lower than the reference temperature At that time, the coefficient of thermal expansion is expressed as ; The stiffness and strength of orthotropic composite material structures are related to the load conditions. The constitutive equations of the structure are determined by the load and constraint conditions, and the constitutive relation is expressed as:

[0040] in, For strain tensor, For stress tensor, This is the compliance matrix;

[0041] in, , , , , , , , , , , , These are elements in the compliance matrix; For orthotropic composite materials, the compliance matrix Some elements in Related to the direction of element stress, i.e.:

[0042]

[0043] in, Poisson's ratio, , These are the tensile and compressive elastic moduli, respectively. For orthotropic composite materials with tension-compression anisotropy, when any point in the material is in the local coordinate system When in tension , Then in The modulus in the direction of tension is the tensile modulus. ,at this time The material strength in the direction of tensile strength is the tensile strength; when in When under directional compression Then in The modulus in the directional direction is the compressive modulus. ,at this time The material strength in the direction of compression is the compressive strength.

[0044] Preferably, for each element in the extracted finite element model, the free thermal strain of the finite element in the temperature field environment is obtained by combining the temperature with the coefficient of thermal expansion under the boundary constraint free state. for:

[0045] If the relative temperature of a certain unit is obtained from the analysis That is, the thermal deformation polarity of this unit in the free state is expansion, then in the next iterative calculation... If the relative temperature of a certain unit is obtained from the analysis If the thermal deformation polarity of this unit in the free state is contraction, then in the next iterative calculation, the corresponding thermal expansion coefficient matrix will be modified as follows: ; For the total strain in each direction of each element in the extracted finite element model and the free thermal strain of each element calculated Analyze whether the element is under tension or compression, i.e.:

[0046] Based on the stress polarity in each direction of each element, determine whether the assumptions made in the previous step are consistent with the actual situation. If they are consistent, then maintain the corresponding compliance matrix for that element in that stress direction. If an element remains unchanged, then that element is modified. If the analysis yields a certain unit's... direction That is, the unit's If the direction is under tension, then in the next iterative calculation... If the analysis yields the results of a certain unit direction That is, the unit's If the direction is under pressure, then in the next iteration calculation, the corresponding... Modified to .

[0047] Preferably, the convergence criterion includes: When the proportion n of the total number of constitutive relations to be modified does not exceed a preset value. When, i.e., when n≤ Stop iteration when; if If the value is 0, it indicates that there are no constitutive equations that can be modified. Or the deviation between the calculation result and the previous iteration step Not exceeding the preset error limit At that time, that is ≤ Stop iteration when; if =0 indicates that the result has fully converged and the calculation result will no longer change with the increase of iterations.

[0048] Compared with the prior art, the present invention has the following beneficial effects: (1) This invention overcomes the shortcomings of the existing simulation analysis of thermo-coupling engineering problems, which adopts the assumption of single polarity of mechanical and thermal properties and fails to consider the different mechanical and thermal properties of anisotropic composite material structures under tension / compression and expansion / contraction during the analysis of thermo-coupling problems. It realizes that in the calculation and solution process, the constitutive relationship of the material is corrected according to the unit expansion / contraction and stress of the finite element analysis model, thereby improving the calculation accuracy.

[0049] (2) The present invention solves the problem that it is generally difficult for general finite element software to accurately analyze the thermo-mechanical coupling behavior of anisotropic composite material structures. Functional modules can be embedded through programming the external interface of general finite element software. It has the advantages of wide applicability and easy implementation with commercial finite element simulation analysis software. Attached Figure Description

[0050] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart of an adaptive method for thermal deformation analysis of anisotropic composite material structures provided by the present invention. Figure 2 It is the computational object of an embodiment of the present invention; Figure 3 This is an iterative evolution diagram of an embodiment of the present invention. Detailed Implementation

[0051] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0052] Example 1 like Figure 2 As shown, the orthotropic composite material structure is made of a needle-punched composite material. The structure is subjected to thermo-mechanical coupling loads. The temperature load is distributed on the outer surface of the structure, the tensile and compressive loads are distributed at one end of the structure, and the other end and part of the outer surface are constrained by displacement boundary conditions.

[0053] like Figure 1 This invention provides an adaptive method for thermal deformation analysis of anisotropic composite material structures, comprising the following steps: 1) Establish a finite element analysis model for orthogonal anisotropic composite material structures; 2) Apply boundary constraints and load conditions; 3) Set the thermal expansion coefficient and mechanical properties of the model materials; 4) Initialize and set the thermal expansion coefficient and material mechanical property polarity of the model materials; 5) Perform simulation analysis to calculate the strain within the structure; 6) Verify and correct the polarity of the thermal constitutive properties of each element based on the temperature and load calculation results of each element in the finite element model; 7) Verify and correct the polarity of the force constitutive properties of each element based on the temperature and load calculation results of each element in the finite element model; 8) Based on the convergence criterion, determine whether the current strain calculation result meets the tolerance requirements. If the tolerance meets the requirements, proceed to the next step of analysis and calculation; otherwise, return to step 6. 9) Based on the results of the previous round of element strain analysis, modify the expansion coefficient and material mechanical parameter polarity of the finite element model elements, perform analysis and calculation, and output the final calculation results.

[0054] Specifically, the structure in step 1) is composed of orthotropic composite materials, that is, the mechanical properties of anisotropic composite materials are characterized by different moduli in different directions, and different tensile and compressive moduli and strengths in the same direction, as shown in Table 1; the thermal expansion coefficient properties of three-dimensional orthotropic braided composite materials are shown in Table 2. Table 1 Mechanical properties of three-dimensional orthogonal braided composite materials

[0055] Table 2 Thermal expansion coefficient properties of three-dimensional orthogonal braided composite materials

[0056] Based on the linear assumption, the thermal deformation of anisotropic composite materials in the free state With temperature increment Related to the coefficient of thermal expansion, it can be expressed as follows:

[0057] Here is the expansion coefficient matrix:

[0058] in, , , These are elements in the expansion coefficient matrix; For orthogonal anisotropic composite materials, the expansion coefficient matrix... Some elements in the equation are related to the polarity of the unit expansion, namely:

[0059]

[0060]

[0061] That is, when the actual temperature T of a certain finite element model element is higher than the reference temperature At a typical temperature of 25°C, the coefficient of thermal expansion is as follows: However, when the actual temperature T is lower than the reference temperature At a typical temperature of 25°C, the coefficient of thermal expansion is as follows: .

[0062] From the perspective of material mechanics properties, anisotropic composite materials have different elastic moduli in different directions, and their tensile and compressive moduli and strengths are different in the same direction.

[0063] According to the linear elastic theory of composite materials, the stiffness and strength of orthotropic composite material structures are related to the load conditions. The constitutive equation of the structure is determined by the load and constraint conditions, and the constitutive relation can be expressed as follows:

[0064] in, For strain tensor, For stress tensor, This is the compliance matrix;

[0065] in, , , , , , , , , , , , These are elements in the compliance matrix; For orthotropic composite materials, the compliance matrix Some elements in the equation are related to the direction of the element stress, that is:

[0066]

[0067] It is Poisson's ratio, and , , These are the tensile and compressive elastic moduli, respectively.

[0068]

[0069] For orthotropic composite materials with tension-compression anisotropy, when any point in the material is in the local coordinate system When in tension , Then in The modulus in the direction of tension is the tensile modulus. ,at this time The material strength in the direction of tensile strength is the tensile strength; when in When under directional compression Then in The modulus in the directional direction is the compressive modulus. ,at this time The material strength in the direction of compression is the compressive strength.

[0070] Step 4) refers to the initial setting of the thermal expansion coefficient and mechanical property polarity of the model material. This means that at the start of the calculation, it is uncertain whether each element in the finite element model is under tension or compression, expansion or contraction in each direction; that is, at the beginning of the calculation, in step 3)... , The sign of the variable is uncertain and needs to be assigned an initial value.

[0071] Preferably, it is initially assumed that all elements in the finite element model are in a state of tension and expansion, i.e. , .at this time , If the undetermined elements in the model have definite values, the structural strain results under this assumption can be simulated and analyzed.

[0072] Step 5) refers to the process of extracting the total strain of each element in the finite element model after completing the simulation analysis using commercial finite element analysis software in step 4). Temperature conditions Step 6) refers to, based on the temperature of each element in the finite element model extracted in step 5), and combined with the coefficient of thermal expansion, determining the free thermal strain of that finite element in the temperature field environment under boundary constraint free state. .

[0073]

[0074] The thermal expansion coefficient matrix A can be precisely determined based on the temperature of each element. This allows for precise determination.

[0075] Specifically, if the relative temperature of a certain unit obtained from step 6) analysis... That is, the thermal deformation polarity of this unit in the free state is expansion, and correspondingly, in the next iterative calculation... If the relative temperature of a certain unit obtained from step 6) analysis If the thermal deformation polarity of this unit in the free state is contraction, then the corresponding thermal expansion coefficient matrix should be modified in the next iterative calculation. .

[0076] Step 7) refers to the total strain in each direction of each element in the finite element model extracted in step 5). Step 6) Calculate the free thermal strain of each element. Analyze whether the element is under tension or compression. That is:

[0077] Then, based on the stress direction polarity in each direction of each element, determine whether the assumptions made in the previous step are consistent with the actual situation. If they are consistent, maintain the corresponding compliance matrix for that element in that stress direction. If an element remains unchanged, then that element is modified.

[0078] Specifically, if the j-direction of a certain element obtained from step 7) analysis... That is, the element is under tension in the j-direction, and correspondingly, in the next iterative calculation... If the j-direction of a certain unit is obtained from step 7); If the element is compressed in the j-direction, then in the next iterative calculation, the corresponding... Modified to .

[0079] Step 8) refers to setting a termination condition, i.e. a convergence criterion, for the iterative calculation process. When the convergence criterion is met, the calculation result can be considered to have met the accuracy requirements.

[0080] To balance computational accuracy and efficiency, two convergence criteria are selected for use in the calculation: Convergence criterion A: When the proportion n of the total number of constitutive relations of elements that should be modified does not exceed a preset value. When, i.e., when n≤ Stop iteration when the time is right. If =0 indicates that there are no element constitutive equations that can be modified.

[0081] Convergence criterion B: The deviation between the calculation result and the previous iteration step. Not exceeding the preset error limit At that time, that is ≤ Stop iteration when the time is right. If =0 indicates that the result has fully converged and the calculation result will no longer change with the increase of iterations.

[0082] In this example, convergence criterion B is used, which is the deviation of the calculation result from the previous iteration step. Not exceeding the preset error limit At that time, that is ≤ The iteration stops when the time is right. In this example... =1%.

[0083] Step 9) refers to assigning material force and thermal properties to the finite element model based on the last correction of the expansion coefficient and material mechanical parameter polarity of the finite element model elements during the iterative process, and calculating the results. At this point, the material constitutive relationship of the elements in the finite element analysis model is closest to the actual situation, and the analysis results can characterize the deformation inside the structure, meeting the accuracy requirements for use.

[0084] Figure 3 This section shows the iterative convergence of the maximum deformation within the structure in this example. It can be seen that the maximum deviation between two adjacent displacement response calculations in the first iteration is 18.5%, the maximum deviation between two adjacent displacement response calculations in the second iteration is 1.71%, and after the third iteration, the deviation between two adjacent displacement response calculations is less than 1.0%. Therefore, for this structure with inconsistent tensile and compressive properties, three iterations are sufficient to ensure that the displacement deviation is controlled within 1%. Compared to before iterations, the displacement increases by 19% compared to when only the tensile modulus parameter is used in the constitutive equation. The thermo-mechanical coupling results also demonstrate similar convergence, indicating computational convergence.

[0085] Example 2 This invention also provides a system for analyzing the thermal deformation of anisotropic composite material structures, comprising: Module M1: Establish the finite element analysis model of the anisotropic composite material structure; Module M2: Apply boundary constraints and load conditions to the finite element analysis model; Module M3: Sets the thermal expansion coefficient and mechanical properties of the materials in the finite element analysis model; Module M4: Initializes the polarity of the thermal expansion coefficient and the mechanical properties of all elements in the finite element analysis model; the initialization is set as follows: assume that all elements are in a tensile state and an expansion state, and assign initial mechanical properties and thermal expansion coefficient polarity to each element accordingly. Module M5: Based on the polarity of the material's mechanical properties and thermal expansion coefficient after initialization, the first simulation analysis is performed to calculate the internal strain and temperature results of each element in the finite element analysis model. Module M6: Based on the temperature results of each unit obtained from the first simulation analysis, examine and correct the thermal constitutive polarity of each unit. The correction includes: determining whether each unit is expanding or contracting according to its temperature state, and adjusting its thermal expansion coefficient accordingly. Module M7: Based on the strain results of each unit obtained from the first simulation analysis and the adjusted coefficient of thermal expansion, the force constitutive property polarity of each unit is checked and corrected. The correction includes: determining whether each unit is under tension or compression according to the strain state of each material direction, and adjusting its elastic modulus in that direction accordingly. Module M8: Based on the preset convergence criterion, determine whether the currently calculated internal strain of the structure meets the requirements; if it does, trigger module M9; if it does not, update the material properties of the finite element analysis model based on the corrected thermal constitutive property polarity and force constitutive property polarity, and call module M5 to perform a new round of simulation analysis and polarity correction iteration. Module M9: Based on the last attribute polarity correction result when the convergence criterion is met, update the material properties of the finite element analysis model, perform the final analysis calculation, and output the thermal deformation results of the anisotropic composite material structure.

[0086] The anisotropic composite material structure is an orthotropic composite material structure, and its material properties are as follows: the elastic modulus is different in the three main directions of the material, and the tensile elastic modulus is different from the compressive elastic modulus in the same direction; the coefficient of thermal expansion is different in each direction, and the coefficient of thermal expansion in the expanded state is different from the coefficient of thermal expansion in the contracted state in the same direction.

[0087] Thermal deformation of anisotropic composite materials in the free state With temperature increment Related to the coefficient of thermal expansion, it is expressed as:

[0088] in, This is the expansion coefficient matrix;

[0089] in, , , These are elements in the expansion coefficient matrix; For orthogonal anisotropic composite materials, the expansion coefficient matrix... Some elements in Related to the polarity of unit expansion, that is:

[0090]

[0091]

[0092] When the actual temperature T of a certain finite element model element is higher than the reference temperature At that time, the coefficient of thermal expansion is expressed as When the actual temperature T is lower than the reference temperature At that time, the coefficient of thermal expansion is expressed as ; The stiffness and strength of orthotropic composite material structures are related to the load conditions. The constitutive equations of the structure are determined by the load and constraint conditions, and the constitutive relation is expressed as:

[0093] in, For strain tensor, For stress tensor, This is the compliance matrix;

[0094] in, , , , , , , , , , , , These are elements in the compliance matrix; For orthotropic composite materials, the compliance matrix Some elements in Related to the direction of element stress, i.e.:

[0095]

[0096] in, Poisson's ratio, , These are the tensile and compressive elastic moduli, respectively. For orthotropic composite materials with tension-compression anisotropy, when any point in the material is in the local coordinate system When in tension , Then in The modulus in the direction of tension is the tensile modulus. ,at this time The material strength in the direction of tensile strength is the tensile strength; when in When under directional compression Then in The modulus in the directional direction is the compressive modulus. ,at this time The material strength in the direction of compression is the compressive strength.

[0097] By considering the temperature of each element in the extracted finite element model and its expansion coefficient, the free thermal strain of the finite element in the temperature field environment under boundary constraints is obtained. for:

[0098] If the relative temperature of a certain unit is obtained from the analysis That is, the thermal deformation polarity of this unit in the free state is expansion, then in the next iterative calculation... If the relative temperature of a certain unit is obtained from the analysis If the thermal deformation polarity of this unit in the free state is contraction, then in the next iterative calculation, the corresponding thermal expansion coefficient matrix will be modified as follows: ; For the total strain in each direction of each element in the extracted finite element model and the free thermal strain of each element calculated Analyze whether the element is under tension or compression, i.e.:

[0099] Based on the stress polarity in each direction of each element, determine whether the assumptions made in the previous step are consistent with the actual situation. If they are consistent, then maintain the corresponding compliance matrix for that element in that stress direction. If an element remains unchanged, then that element is modified. If the analysis yields a certain unit's... direction That is, the unit's If the direction is under tension, then in the next iterative calculation... If the analysis yields the results of a certain unit direction That is, the unit's If the direction is under pressure, then in the next iteration calculation, the corresponding... Modified to .

[0100] Convergence criteria include: when the proportion n of the total number of constitutive relations of elements that should be modified does not exceed a preset value. When, i.e., when n≤ Stop iteration when; if =0 indicates that there are no more element constitutive equations that can be modified; or the deviation between the calculation result and the previous iteration step. Not exceeding the preset error limit At that time, that is ≤ Stop iteration when; if =0 indicates that the result has fully converged and the calculation result will no longer change with the increase of iterations.

[0101] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0102] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for analyzing the thermal deformation of anisotropic composite material structures, characterized in that, include: Step 1: Establish a finite element analysis model for the anisotropic composite material structure; Step 2: Apply boundary constraints and load conditions to the finite element analysis model; Step 3: Set the thermal expansion coefficient and mechanical properties of the materials in the finite element analysis model; Step 4: Initialize the polarity of the thermal expansion coefficient and the mechanical properties of all elements in the finite element analysis model; the initialization is set as follows: assume that all elements are in a tensile state and an expansion state, and assign initial mechanical properties and thermal expansion coefficient polarity to each element accordingly. Step 5: Based on the initial polarity of the material's mechanical properties and the polarity of its thermal expansion coefficient, perform the first simulation analysis to calculate the internal strain and temperature results of each element in the finite element analysis model. Step 6: Based on the temperature results of each unit obtained from the first simulation analysis, examine and correct the thermal constitutive property polarity of each unit. The correction includes: determining whether each unit is expanding or contracting according to its temperature state, and adjusting its thermal expansion coefficient accordingly. Step 7: Based on the strain results of each unit and the adjusted coefficient of thermal expansion obtained from the first simulation analysis, check and correct the polarity of the force constitutive property of each unit. The correction includes: determining whether each unit is under tension or compression according to the strain state of each unit in each material direction, and adjusting its elastic modulus in that direction accordingly. Step 8: According to the preset convergence criterion, determine whether the structural strain calculated at the moment meets the requirements; if it does, proceed to step 9; if it does not, update the material properties of the finite element analysis model based on the corrected thermal constitutive polarity and force constitutive polarity, and return to step 5 for a new round of simulation analysis and polarity correction iteration. Step 9: Based on the last attribute polarity correction result when the convergence criterion is met, update the material properties of the finite element analysis model, perform the final analysis calculation, and output the thermal deformation results of the anisotropic composite material structure.

2. The method for thermal deformation analysis of anisotropic composite material structures according to claim 1, characterized in that, The anisotropic composite material structure is an orthotropic composite material structure, and its material properties are as follows: the elastic modulus in the three principal directions of the material is different from each other, and in the same direction, the tensile elastic modulus and the compressive elastic modulus are different. The coefficient of thermal expansion is different in different directions, and in the same direction, the coefficient of thermal expansion in the expanded state is different from that in the contracted state.

3. The method for thermal deformation analysis of anisotropic composite material structures according to claim 1, characterized in that, Thermal deformation of anisotropic composite materials in the free state With temperature increment Related to the coefficient of thermal expansion, it is expressed as: in, This is the expansion coefficient matrix; in, , , These are elements in the expansion coefficient matrix; For orthogonal anisotropic composite materials, the expansion coefficient matrix... Some elements in Related to the polarity of unit expansion, that is: When the actual temperature T of a certain finite element model element is higher than the reference temperature At that time, the coefficient of thermal expansion is expressed as When the actual temperature T is lower than the reference temperature At that time, the coefficient of thermal expansion is expressed as ; The stiffness and strength of orthotropic composite material structures are related to the load conditions. The constitutive equations of the structure are determined by the load and constraint conditions, and the constitutive relation is expressed as: in, For strain tensor, For stress tensor, This is the compliance matrix; in, , , , , , , , , , , , These are elements in the compliance matrix; For orthotropic composite materials, the compliance matrix Some elements in Related to the direction of element stress, i.e.: in, Poisson's ratio, , These are the tensile and compressive elastic moduli, respectively. For orthotropic composite materials with tension-compression anisotropy, when any point in the material is in the local coordinate system When in tension , Then in The modulus in the direction of tension is the tensile modulus. ,at this time The material strength in the direction of tensile strength is the tensile strength; when in When under directional compression Then in The modulus in the directional direction is the compressive modulus. ,at this time The material strength in the direction of compression is the compressive strength.

4. The method for thermal deformation analysis of anisotropic composite material structures according to claim 3, characterized in that, By considering the temperature of each element in the extracted finite element model and its expansion coefficient, the free thermal strain of the finite element in the temperature field environment under boundary constraints is obtained. for: If the relative temperature of a certain unit is obtained from the analysis That is, the thermal deformation polarity of this unit in the free state is expansion, then in the next iterative calculation... ; If the relative temperature of a certain unit is obtained from the analysis If the thermal deformation polarity of this unit in the free state is contraction, then in the next iterative calculation, the corresponding thermal expansion coefficient matrix will be modified as follows: ; For the total strain in each direction of each element in the extracted finite element model and the free thermal strain of each element calculated Analyze whether the element is under tension or compression, i.e.: Based on the stress polarity in each direction of each element, determine whether the assumptions made in the previous step are consistent with the actual situation. If they are consistent, then maintain the corresponding compliance matrix for that element in that stress direction. If an element remains unchanged, then that element is modified. If the analysis yields a certain unit's... direction That is, the unit's If the direction is under tension, then in the next iterative calculation... ; If the analysis yields a certain unit's... direction That is, the unit's If the direction is under pressure, then in the next iteration calculation, the corresponding... Modified to .

5. The method for thermal deformation analysis of anisotropic composite material structures according to claim 1, characterized in that, Convergence criteria include: When the proportion n of the total number of constitutive relations to be modified does not exceed a preset value. When, i.e., when n≤ Stop iteration when; if If the value is 0, it indicates that there are no constitutive equations that can be modified. Or the deviation between the calculation result and the previous iteration step Not exceeding the preset error limit At that time, that is ≤ Stop iteration when; if =0 indicates that the result has fully converged and the calculation result will no longer change with the increase of iterations.

6. A system for analyzing the thermal deformation of anisotropic composite material structures, characterized in that, include: Module M1: Establish the finite element analysis model of the anisotropic composite material structure; Module M2: Apply boundary constraints and load conditions to the finite element analysis model; Module M3: Sets the thermal expansion coefficient and mechanical properties of the materials in the finite element analysis model; Module M4: Initializes the polarity of the thermal expansion coefficient and the mechanical properties of all elements in the finite element analysis model; the initialization is set as follows: assume that all elements are in a tensile state and an expansion state, and assign initial mechanical properties and thermal expansion coefficient polarity to each element accordingly. Module M5: Based on the polarity of the material's mechanical properties and thermal expansion coefficient after initialization, the first simulation analysis is performed to calculate the internal strain and temperature results of each element in the finite element analysis model. Module M6: Based on the temperature results of each unit obtained from the first simulation analysis, examine and correct the thermal constitutive polarity of each unit. The correction includes: determining whether each unit is expanding or contracting according to its temperature state, and adjusting its thermal expansion coefficient accordingly. Module M7: Based on the strain results of each unit obtained from the first simulation analysis and the adjusted coefficient of thermal expansion, the force constitutive property polarity of each unit is checked and corrected. The correction includes: determining whether each unit is under tension or compression according to the strain state of each material direction, and adjusting its elastic modulus in that direction accordingly. Module M8: Based on the preset convergence criterion, determine whether the currently calculated internal strain of the structure meets the requirements; if it does, trigger module M9; if it does not, update the material properties of the finite element analysis model based on the corrected thermal constitutive property polarity and force constitutive property polarity, and call module M5 to perform a new round of simulation analysis and polarity correction iteration. Module M9: Based on the last attribute polarity correction result when the convergence criterion is met, update the material properties of the finite element analysis model, perform the final analysis calculation, and output the thermal deformation results of the anisotropic composite material structure.

7. The system for thermal deformation analysis of anisotropic composite material structures according to claim 6, characterized in that, The anisotropic composite material structure is an orthotropic composite material structure, and its material properties are as follows: the elastic modulus in the three principal directions of the material is different from each other, and in the same direction, the tensile elastic modulus and the compressive elastic modulus are different. The coefficient of thermal expansion is different in different directions, and in the same direction, the coefficient of thermal expansion in the expanded state is different from that in the contracted state.

8. The system for thermal deformation analysis of anisotropic composite material structures according to claim 6, characterized in that, Thermal deformation of anisotropic composite materials in the free state With temperature increment Related to the coefficient of thermal expansion, it is expressed as: in, This is the expansion coefficient matrix; in, , , These are elements in the expansion coefficient matrix; For orthogonal anisotropic composite materials, the expansion coefficient matrix... Some elements in Related to the polarity of unit expansion, that is: When the actual temperature T of a certain finite element model element is higher than the reference temperature At that time, the coefficient of thermal expansion is expressed as When the actual temperature T is lower than the reference temperature At that time, the coefficient of thermal expansion is expressed as ; The stiffness and strength of orthotropic composite material structures are related to the load conditions. The constitutive equations of the structure are determined by the load and constraint conditions, and the constitutive relation is expressed as: in, For strain tensor, For stress tensor, This is the compliance matrix; in, , , , , , , , , , , , These are elements in the compliance matrix; For orthotropic composite materials, the compliance matrix Some elements in Related to the direction of element stress, i.e.: in, Poisson's ratio, , These are the tensile and compressive elastic moduli, respectively. For orthotropic composite materials with tension-compression anisotropy, when any point in the material is in the local coordinate system When in tension , Then in The modulus in the direction of tension is the tensile modulus. ,at this time The material strength in the direction of tensile strength is the tensile strength; when in When under directional compression Then in The modulus in the directional direction is the compressive modulus. ,at this time The material strength in the direction of compression is the compressive strength.

9. The system for thermal deformation analysis of anisotropic composite material structures according to claim 8, characterized in that, By considering the temperature of each element in the extracted finite element model and its expansion coefficient, the free thermal strain of the finite element in the temperature field environment under boundary constraints is obtained. for: If the relative temperature of a certain unit is obtained from the analysis That is, the thermal deformation polarity of this unit in the free state is expansion, then in the next iterative calculation... ; If the relative temperature of a certain unit is obtained from the analysis If the thermal deformation polarity of this unit in the free state is contraction, then in the next iterative calculation, the corresponding thermal expansion coefficient matrix will be modified as follows: ; For the total strain in each direction of each element in the extracted finite element model and the free thermal strain of each element calculated Analyze whether the element is under tension or compression, i.e.: Based on the stress polarity in each direction of each element, determine whether the assumptions made in the previous step are consistent with the actual situation. If they are consistent, then maintain the corresponding compliance matrix for that element in that stress direction. If an element remains unchanged, then that element is modified. If the analysis yields a certain unit's... direction That is, the unit's If the direction is under tension, then in the next iterative calculation... ; If the analysis yields a certain unit's... direction That is, the unit's If the direction is under pressure, then in the next iteration calculation, the corresponding... Modified to .

10. The system for thermal deformation analysis of anisotropic composite material structures according to claim 1, characterized in that, Convergence criteria include: When the proportion n of the total number of constitutive relations to be modified does not exceed a preset value. When, i.e., when n≤ Stop iteration when; if If the value is 0, it indicates that there are no constitutive equations that can be modified. Or the deviation between the calculation result and the previous iteration step Not exceeding the preset error limit At that time, that is ≤ Stop iteration when; if =0 indicates that the result has fully converged and the calculation result will no longer change with the increase of iterations.

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