Method for establishing data-driven finite volume for predicting thermal stress of heterogeneous material

Abstract

The invention discloses a data-driven finite volume method for predicting thermal stress of a heterogeneous material. The method comprises the following steps of: firstly, establishing a numerical model part comprising a stress field module, a temperature field module and a thermal stress module based on a data driving algorithm and a lattice point type finite volume method (CV-FVM) by considering the heterogeneity and thermal deformation characteristics of a material, and solving and calculating data meeting the law of conservation; secondly, introducing the temperature, strain and stress data of the material into a material data part to form a material database to replace the thermodynamic response of the material; and finally, searching data closest to the data meeting the conservation law in the material database through iterative search of a data driving part, and taking the data as an optimal solution. The calculation efficiency and precision are further improved through a k-d tree optimization solving module in the accelerated search part and a data clustering analysis module in the result optimization part.

Description

Technical Field

[0001] The present invention relates to a data-driven calculation algorithm for multi-physical field coupling, specifically a calculation method that uses material data drive instead of constitutive models to solve thermal stress problems. Background Art

[0002] Thermal stress is widely present in thermal engine components such as engine pistons and rocket nozzles. The increasingly harsh working environment has brought challenges to thermal stress prediction. The mechanical properties of a single material can no longer meet actual needs. Due to the designability of the thermodynamic properties of composite materials and the integration of the superior properties of multiphase materials, they have been widely used and received attention. Therefore, it is imperative to conduct research on the thermodynamic properties of composite materials. The microstructure of composite materials is complex and has developed rapidly. The resulting problems such as difficulty in constitutive modeling and high costs have seriously hindered the application of new composite materials in engineering. To this end, data-driven computational mechanics aims to solve thermodynamic problems by replacing constitutive models with material data, and establish a data-driven grid-type volume method that combines material data with numerical calculation methods. It has strong engineering application value for shortening the R&D cycle of new materials and predicting the thermodynamic behavior of composite materials. Summary of the Invention

[0003] The purpose of the present invention is to shorten the research and development and application cycle of new materials and to predict and simulate the thermodynamic behavior of composite materials.

[0004] In order to achieve the purpose of the above invention, the technical solution provided by the present invention is as follows:

[0005] A data-driven finite volume method for thermal stress prediction of heterogeneous materials includes: a stress field module, a temperature field module, a thermal stress module, a kd tree optimization solution module, and a data clustering analysis module.

[0006] The steps of constructing a data-driven finite volume method for thermal stress prediction of heterogeneous materials are as follows: first, considering the heterogeneity and thermal deformation characteristics of the material, based on the data-driven algorithm and the grid-type finite volume method (CV-FVM), a numerical model part including a stress field module, a temperature field module, and a thermal stress module is established, and the data that satisfies the conservation law is solved and calculated. Secondly, the temperature, strain and stress data of the material are introduced into the material data part to form a material database instead of the material thermodynamic response. Finally, through the iterative search of the data-driven part, the data closest to the data that satisfies the conservation law in the material database is found as the optimal solution. The purpose of optimizing the solution efficiency and improving the accuracy of the results is achieved through the kd tree optimization solution module in the accelerated search part and the data clustering analysis module in the result optimization part.

[0007] Stress field module: Based on the data-driven algorithm for the stress field problem of heterogeneous materials, it is introduced into the data-driven CV-FVM numerical model of the stress field problem, and the data-driven finite volume method is used to solve the stress field problem of heterogeneous materials.

[0008] Temperature field module: Based on the data-driven algorithm for the temperature field problem of heterogeneous materials, a temperature field numerical model and data-driven calculation framework are established, and the data-driven finite volume method is used to solve the heat conduction problem of heterogeneous materials.

[0009] Thermal stress module: Based on the stress field module and temperature field module, a calculation method for thermal stress problems of heterogeneous materials is constructed and introduced into the thermal stress CV-FVM numerical calculation model, a data-driven solution framework for thermal stress problems is established, and a data-driven grid finite volume method numerical solution method for thermal stress problems is constructed.

[0010] KD tree optimization solution module: To address the low efficiency of traversal data search methods, the KD tree optimization solution module is introduced to build and read the database, then use the KD tree structure to store data, and finally use the (approximate) nearest neighbor search algorithm to optimize the solution efficiency.

[0011] Data clustering analysis module: To address the problem of low convergence accuracy of calculation results, the data clustering analysis module is introduced to study the factors affecting algorithm accuracy, then perform data cluster analysis, and finally use the entropy maximization algorithm to improve the accuracy of the results.

[0012] After the results are optimized by the kd-tree optimization solution module and the data clustering analysis module, a data-driven finite volume method for thermal stress prediction of heterogeneous materials is finally established.

[0013] The construction process of the above-mentioned data-driven finite volume method for thermal stress prediction of heterogeneous materials includes a numerical model part, a material data part, a data-driven part, an accelerated search part, and a result optimization part.

[0014] Numerical model part: CV-FVM is used to establish the control equations for the thermal stress problem of heterogeneous materials. The penalty function is formulated through the law of conservation of energy to define the distance between data points in the phase space. The constraint conditions of the thermal stress problem are constructed based on the geometric equations and thermodynamic equilibrium equations. The control equations of the data-driven thermal stress problem are derived by combining the Lagrange multiplier method. The control equations are discretized using CV-FVM to obtain the numerical model of the data-driven grid-type finite volume method.

[0015] The process of establishing the CV-FVM control equation in the numerical model part is as follows: based on the relevant theories of heat transfer and linear elasticity, the control equation of the temperature field is established by the thermal balance equation, and the control equation of the stress field is formulated by the force balance equation and the geometric equation. On this basis, the control equation of the thermal stress problem is derived through the thermodynamic balance equation.

[0016] Material data section: Material data is obtained through experiments or simulation calculations, and the temperature and the thermal deformation and thermal stress caused by the temperature are introduced into the calculation framework in the form of a database to avoid errors caused by the establishment of the thermal constitutive model and data fitting.

[0017] The method for establishing a heterogeneous material database for thermal stress problems in the material data section is as follows: the thermal constitutive relationship of the heterogeneous material is expressed by discrete data points in the material database, and no fitting is performed on the stress-strain data, thereby avoiding errors caused by the constitutive modeling step.

[0018] Data-driven part: The data-driven algorithm combines material data with CV-FVM, uses staggered grid technology, defines the variables to be solved at the nodes, and defines the stress and strain data within the unit. It iteratively calculates and searches for matching data for each grid unit to solve the minimum distance between the point that satisfies the conservation law and the point in the material database, that is, the optimal solution to the problem, and uses C++ language to develop the data-driven finite volume method numerical solution program.

[0019] The data-driven method under the CV-FVM numerical format in the data-driven part is: based on the CV-FVM, the matching material data is calculated and searched for each grid cell according to the spatial variation characteristics of heterogeneous materials. The constructed staggered grid method defines the variables to be solved at the grid nodes, and defines the parameters in the data-driven algorithm at the grid center and varies with space.

[0020] Accelerated Search: The material database is stored in a kd-tree data structure, arranged by stress and strain magnitude. The database is divided into several subtrees based on the amount of data. Based on tree-based search technology, the data point closest to the target data is quickly found by traversing the subtrees during each data search step.

[0021] Result optimization part: When the material database contains noise, the result accuracy will be reduced. Therefore, based on cluster analysis theory, an entropy maximization algorithm is formed through data clustering, fixed-point iteration and simulated annealing of material data. This algorithm reduces the calculation error caused by noise points in the database by assigning a reasonable weight to each point in the material database.

[0022] This application demonstrates a data-driven finite volume method for predicting thermal stress in heterogeneous materials. A discrete material database drives the simulation throughout the entire process, avoiding errors caused by data fitting and the difficulties associated with constitutive modeling. The solver, written in C++, presents the results as cloud maps, providing a reference for structural design optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Data-driven finite volume method numerical framework

[0024] Figure 2 Program calculation flow chart

[0025] Figure 3 Schematic diagram of functionally graded material tension and compression plate

[0026] Figure 4 Schematic diagram of the CV-FVM control volume (the thick solid line is the mesh boundary, the solid circles are the mesh nodes, and the hollow circles are the mesh centers)

[0027] Figure 5 Schematic diagram of database phase space projection

[0028] Figure 6 Calculation result line graph

[0029] Figure 7 Displacement result cloud chart (the left picture is the reference solution result, the right picture is the data-driven grid finite volume method result) DETAILED DESCRIPTION

[0030] The data-driven finite volume method for predicting thermal stress in heterogeneous materials is suitable for predicting and simulating the structural mechanical behavior of new composite materials, including solving solid structural mechanics problems and solving thermal stress problems. The following example illustrates this using a two-dimensional functionally graded material (FGM) tension-compression plate:

[0031] Consider a FGM tension-compression plate composed of a uniform composite of aluminum (Al) and silicon carbide (SiC). The rectangular plate has a length of L and a width of h. Under the plane stress assumption, a quadrilateral mesh is used to divide the computational domain. The Young's modulus E of the plate varies with the spatial coordinates, while the Poisson's ratio μ is a constant. The plate is simply supported at both ends, with the upper surface free. The lower surface is subjected to a spatially varying distributed load p.

[0032] The stress and strain data of the material can be obtained through a reasonably designed experiment. Due to the limitations of experimental conditions, numerical simulation calculations are used here instead of experiments to obtain material data.

[0033] The specific procedure flow is as follows:

[0034] i) Input: material database D, mesh model, boundary conditions and parameters C;

[0035] ii) Set the number of iterations k and assign an initial data point (ε*,σ*) to each grid cell k ;

[0036] iii) Solve the governing equation to obtain the displacement u k and the Lagrange multiplier η k :

[0037]

[0038] Calculate strains and stresses (ε,σ) that satisfy geometric and equilibrium constraints k :

[0039]

[0040] iv) Search the material database for stress-strain data pairs (ε*,σ*) k+1 , so that (ε*,σ*) k+1 and (ε,σ) k The distance is the smallest;

[0041] F(ε-ε*,σ-σ*)≤F(ε-ε',σ-σ') (5)

[0042] v) Convergence criterion: k+1th search data (ε*,σ*) k+1 Is it consistent with the last searched data (ε*,σ*) k equal,

[0043] If not, let k=k+1, (ε*,σ*) k =(ε*,σ*) k+1 , repeat step ii),

[0044] If they are equal, the displacement result u calculated at the kth iteration is k and stress-strain results (ε,σ) k Output and end the program.

[0045] During the overall program calculation:

[0046] In step i), the material database is stored by constructing a kd-tree and reading the grid model information in the form of a CGNS file. According to the spatial variation characteristics of the non-uniform material, a spatially varying parameter C is assigned to each grid cell. By combining the staggered grid technique, the parameter C is evenly distributed within the cell and unevenly distributed within the control volume, thereby introducing the spatially varying parameter C into the discrete equation.

[0047] In step ii), the initial data for the first iteration are randomly assigned from the material database;

[0048] In step iii), the variables to be solved at each node and the stress and strain data of each grid element are calculated;

[0049] In step iv), the (approximate) nearest neighbor search technique is used. First, the kd-tree is recursively traversed to find the data point with the smallest distance in the sub-database and update the current closest distance. Then, the current kd-tree node is backtracked to check whether other sub-databases of the current kd-tree node contain closer points. If so, the search continues in that sub-database until the data point closest to the target data point is found. Through these steps, the (approximate) nearest neighbor search technique can quickly find the nearest neighbor of the target point in high-dimensional space, improving search efficiency.

[0050] In step v), the convergence criterion is to search for the data point in the material database for each element that matches the closest distance conservation constraint.

[0051] A data-driven finite volume method for thermal stress prediction of heterogeneous materials is applied to two-dimensional functionally graded material (FGM) tension and compression plates. The steps are as follows: first, considering the heterogeneity and thermal deformation characteristics of the material, based on the data-driven algorithm and the grid-type finite volume method (CV-FVM), a numerical model part including a stress field module, a temperature field module, and a thermal stress module is established, and the data that satisfies the conservation law is solved and calculated. Secondly, the temperature, strain, and stress data of the material are introduced into the material data part to form a material database instead of the material thermodynamic response. Finally, through the iterative search of the data-driven part, the data closest to the data that satisfies the conservation law in the material database is found as the optimal solution. The efficiency and accuracy of the calculation are further improved by the kd tree optimization solution module in the accelerated search part and the data clustering analysis module in the result optimization part. The solution program is written in C++ language, and the calculation results are presented in the form of a cloud map.

Claims

1. A data-driven finite volume method for thermal stress prediction of heterogeneous materials, characterized by: include: Stress field module, temperature field module, thermal stress module, kd tree optimization solution module, data clustering analysis module; The steps to construct a data-driven finite volume method for thermal stress prediction in heterogeneous materials are: Firstly, considering the material heterogeneity and thermal deformation characteristics, a numerical model including stress field module, temperature field module and thermal stress module is established based on data-driven algorithm and lattice finite volume method (CV-FVM), and the data satisfying the conservation law is calculated. Secondly, the temperature, strain and stress data of the material are introduced into the material data part to form a material database to replace the material thermodynamic response; Finally, the data-driven part is iterated to find the data closest to the data that satisfies the conservation law in the material database as the optimal solution. After further improving the efficiency and accuracy of the calculation through the kd tree optimization solution module in the accelerated search part and the data clustering analysis module in the result optimization part, a data-driven finite volume method for thermal stress prediction of heterogeneous materials is finally established.

2. A data-driven finite volume method for thermal stress prediction of heterogeneous materials according to claim 1, characterized in that: Stress field module: Based on the data-driven algorithm for the stress field problem of heterogeneous materials, it is introduced into the data-driven CV-FVM numerical model of the stress field problem, and the data-driven finite volume method is used to solve the stress field problem of heterogeneous materials; Temperature field module: Based on the data-driven algorithm for the temperature field problem of heterogeneous materials, a temperature field numerical model and a data-driven calculation framework are established, and the data-driven finite volume method is used to solve the heat conduction problem of heterogeneous materials.

3. The data-driven finite volume method for thermal stress prediction of heterogeneous materials according to claim 1, characterized in that: Thermal stress module: Based on the stress field module and temperature field module, a calculation method for thermal stress problems of heterogeneous materials is constructed and introduced into the thermal stress CV-FVM numerical calculation model, a data-driven solution framework for thermal stress problems is established, and a data-driven grid-type finite volume method numerical solution method for thermal stress problems is constructed.

4. The data-driven finite volume method for thermal stress prediction of heterogeneous materials according to claim 1, characterized in that: KD tree optimization solution module: To address the low efficiency of traversal data search, the KD tree optimization solution module is introduced to build and read the database, and then the KD tree structure is used to store data. Finally, the (approximate) nearest neighbor search algorithm is used to optimize the solution efficiency.

5. The data-driven finite volume method for thermal stress prediction of heterogeneous materials according to claim 1, characterized in that: Data clustering analysis module: To address the problem of low convergence accuracy of calculation results, the data clustering analysis module is introduced to study the factors affecting algorithm accuracy, then perform data clustering analysis, and finally use the entropy maximization algorithm to improve the accuracy of the results.

6. The data-driven finite volume method for thermal stress prediction of heterogeneous materials according to claim 1, characterized in that: Numerical model part: CV-FVM is used to establish the control equation for the thermal stress problem of heterogeneous materials. The penalty function is formulated through the law of conservation of energy to define the distance between data points in the phase space. The constraint conditions of the thermal stress problem are constructed based on the geometric equation and the thermodynamic equilibrium equation. The control equation of the data-driven thermal stress problem is derived by combining the Lagrange multiplier method. CV-FVM is used to discretize the control equation to obtain the numerical model of the data-driven grid finite volume method. The process of establishing the CV-FVM control equation in the numerical model part is as follows: based on the relevant theories of heat transfer and linear elasticity, the control equation of the temperature field is established by the thermal balance equation, and the control equation of the stress field is formulated by the force balance equation and the geometric equation. On this basis, the control equation of the thermal stress problem is derived through the thermodynamic balance equation.

7. The data-driven finite volume method for thermal stress prediction of heterogeneous materials according to claim 1, characterized in that: Material data section: Obtain material data through experiments or simulation calculations, introduce temperature and the thermal deformation and thermal stress caused by temperature into the calculation framework in the form of a database, and avoid errors caused by the establishment of thermal constitutive models and data fitting; The database method in the material data part is as follows: the thermal constitutive relationship of the heterogeneous material is expressed by discrete data points in the material database, and no fitting is performed on the stress-strain data, so as to avoid the error caused by the constitutive modeling step.

8. The data-driven finite volume method for thermal stress prediction of heterogeneous materials according to claim 1, characterized in that: Data-driven part: The data-driven algorithm combines material data with CV-FVM, uses staggered grid technology, defines the variables to be solved at the nodes, defines the stress-strain data in the unit, and iteratively calculates and searches for matching data for each grid unit to solve the minimum distance between the point that satisfies the conservation law and the point in the material database, that is, the optimal solution to the problem, and uses C++ language to develop the data-driven finite volume method numerical solution program; The data-driven method in the CV-FVM numerical format in the data-driven part is as follows: in view of the spatial variation characteristics of heterogeneous materials, matching material data is calculated and searched for for each grid unit based on CV-FVM. The constructed staggered grid method defines the variables to be solved at the grid nodes, and defines the parameters in the data-driven algorithm at the grid center and varies with space.

9. The data-driven finite volume method for thermal stress prediction of heterogeneous materials according to claim 1, characterized in that: Accelerated search part: The material database is stored in the data structure of kd tree, arranged according to the stress and strain, and divided into several subtrees according to the amount of data. Based on tree search technology, in each data search step, the data point closest to the target data is quickly found by traversing the subtree.

10. The data-driven finite volume method for thermal stress prediction of heterogeneous materials according to claim 1, characterized in that: Result optimization part: When the material database contains noise, the result accuracy will be reduced. Therefore, based on the cluster analysis theory, an entropy maximization algorithm is formed through steps such as data clustering, fixed-point iteration and simulated annealing of the material data. This algorithm assigns a reasonable weight to each point in the material database to reduce the calculation error caused by the noise points in the database.

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