A topology optimization method for functionally graded material structures based on a layered approach
By adopting the hierarchical method and secondary development of the subroutine interface in ABAQUS software, the characteristics of functionally gradient materials are approximately simulated, the problem that topology optimization cannot be performed in ABAQUS is solved, and the effective analysis and design of functionally gradient materials under thermal loads are achieved.
Patent Information
- Application Number
- CN202210060082.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-01-19
- Publication Date
- 2025-09-12
- Estimated Expiration
- 2042-01-19
AI Technical Summary
Existing functionally gradient materials cannot be topologically optimized in ABAQUS software, especially in the temperature-displacement coupling analysis step and optimization module, resulting in the inability to effectively analyze functionally gradient materials in ABAQUS.
The functional gradient material structure is divided into several layers using the layered method. The material parameters of each layer vary in the form of a function. Secondary development is carried out through the subroutine interface of ABAQUS. The UMAT and UMATHT subroutines are written in FORTRAN language to approximately simulate the material properties of the functional gradient material and perform topology optimization.
The topology optimization of functionally gradient material structures was realized in ABAQUS software, which enables effective analysis under thermal load conditions and improves the accuracy and efficiency of material design.
Smart Images
Figure CN114492123B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of functional gradient material structures, and specifically to a research method for approximately simulating the characteristics of functional gradient materials by a layered method in simulation software to realize a topology optimization function in the software. Background Art
[0002] Functionally graded materials (FGMs) are a new type of composite material composed of two or more materials with a continuous gradient of composition and structure. They were developed to meet the needs of high-tech fields such as the modern aerospace industry, specifically to ensure repeated normal operation under extreme conditions. Their design requirements for function and performance vary with the position within a component, and these requirements are met by optimizing the overall performance of the component.
[0003] From the perspective of material structure, functionally gradient materials (FGMs) differ from homogeneous materials and composite materials. They are formed by continuously changing the composition and structure of two (or more) materials with different properties, eliminating their interface. This results in the material's properties slowly changing with the composition and structure of the materials, creating a functionally gradient material.
[0004] Existing software implementations of functionally graded materials typically utilize ABAQUS's secondary development interfaces, such as the UMAT and UMATHT subroutines. These interfaces calculate element material parameters, element strain increments, element stress increments, and other parameters within an incremental step, then are written in FORTRAN to enable functionally graded materials to be implemented within the software. However, many ABAQUS modules, such as the topology optimization module, do not have subroutine interfaces, making it impossible to implement the required analysis using subroutine secondary development. Furthermore, the ABAQUS optimization module cannot utilize temperature-displacement coupling analysis steps or temperature-displacement coupling elements, so the temperature finite element simulation and optimization steps are separated into two models.
[0005] In order to apply the functionally gradient material model to parts of ABAQUS that do not have a secondary development interface reserved, such as the optimization module in ABAQUS, this project divides the model into layers in the software, calculates the material parameters of each layer according to the power method of functionally gradient materials, assigns the material parameters of the corresponding number of layers to each layer, and approximately simulates the theoretical distribution of functionally gradient materials, so that the structural topology optimization using functionally gradient materials can be implemented in the software. Summary of the Invention
[0006] The purpose of the present invention is to provide a method for simulating the characteristics of functionally gradient materials through a layered method in simulation software, so as to achieve topological optimization of functionally gradient material structures under thermal load conditions in the software, so as to solve the problems raised in the above background technology.
[0007] To achieve the above-mentioned objectives, the present invention provides the following technical solutions: a research method for approximately simulating functional gradient materials in software, specifically using a composition distribution function to describe the spatial variation of the components of the functional gradient material, solving the elastic modulus and Poisson's ratio, thermal conductivity and specific heat at each position inside the material through the composition distribution function of the functional gradient material, performing secondary development of the functional gradient material through the subroutine interface of the software, obtaining the temperature field of the structure at different times when it is only subjected to thermal loads, importing the obtained temperature field into a new model, and using the layered composite material function provided by the software to approximately simulate the material properties of the functional gradient material using the layered method to perform topological optimization.
[0008] The above-mentioned composition distribution function is used to describe the change of the components of the functional gradient material with space. Taking the composite material composed of linear elastic materials A and B as an example, as the thickness direction coordinate gradually increases, the volume fraction of material A gradually decreases, and the volume fraction of material B gradually increases. The mechanical parameters of the two materials are different, and the mechanical parameters at different positions must be different. The fundamental reason why the mechanical parameters of the functional gradient material change with the change of the position of the research point is that the mechanical parameters of the material are a function of the position.
[0009] The above-mentioned composition distribution function of the functionally gradient material is used to solve the elastic modulus and Poisson's ratio, thermal conductivity and specific heat at each position inside the material. In the idealized functionally gradient material, materials A and B are represented centrally. When the interaction between A and B is not considered, the mechanical parameters and thermal parameters of the functionally gradient material in the thickness direction are the combination of materials A and B. At this time, the mechanical parameters and thermal parameters of the functionally gradient material along the thickness direction can be expressed by the mechanical parameters and thermal parameters of materials A and B and the composition distribution function of the functionally gradient material.
[0010] The aforementioned secondary development of functionally graded materials (FGMs) is carried out through the software's subroutine interface. ABAQUS provides a user-defined subroutine interface, including the UMAT subroutine for defining material properties and the UMATHT subroutine for defining material thermodynamic properties. Through the software's subroutine interface, users can write subroutines in FORTRAN to customize constitutive models for specific problems. FGMs can be developed based on the program's subroutines, enabling the customization of unified elastic-plastic constitutive models.
[0011] The temperature field of the structure at different times when it is subjected only to thermal loads is obtained through secondary development, and the obtained temperature field is imported into the new model. In the first model, the temperature field of the entire structure at different times when it is subjected only to thermal-related loads is obtained through secondary development. The temperature field obtained from the first model is imported into the second model and topology optimization or mechanical simulation is performed.
[0012] The above-mentioned topological optimization is performed by approximately simulating the material properties of functionally gradient materials using the layered method. The functionally gradient material structure is divided into several layers. The material parameters of each layer change in the form of a function. The material parameters between adjacent layers have good continuity. Each layer is meshed according to the conventional finite element method, and a finite element model is established to solve the mechanical problems of functionally gradient materials. The functionally gradient material structure is topologically optimized based on different needs. BRIEF DESCRIPTION OF THE DRAWINGS
[0013] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:
[0014] Figure 1 Schematic diagram of the research method of the present invention.
[0015] Figure 2 Schematic diagram of material distribution of functionally graded materials.
[0016] Figure 3 This is the wing-rudder structure selected for the specific embodiment.
[0017] Figure 4 This is a schematic diagram of the rudder body layering.
[0018] Figure 5 This is the result of rudder body topology optimization. DETAILED DESCRIPTION
[0019] In order to make it easier to understand and appreciate the application scenarios and objectives of the invention, a specific embodiment is described in detail below for further elaboration.
[0020] Take the wing-rudder structure under study, which is composed of two isotropic linear elastic materials A and B. The interaction between materials A and B is not considered. Assume that the volume fraction of material A c(y)∈[0,1] satisfies:
[0021] c(y)=c0[1-(k / b) n ]
[0022] Where c0, k, and n are material parameters.
[0023] According to the Mori-Tanaka method, it can be assumed that the material mechanical parameters expressed in terms of volume fraction, elastic modulus and Poisson's ratio vary according to the following rules:
[0024] E(y)=c(y)E1+[1-c(y)]E2
[0025] v(y)=c(y)v1+[1-c(y)]v2
[0026] At the same time, the thermodynamic material parameters, thermal conductivity and specific heat change according to the following rules:
[0027]
[0028] C(y)=c(y)C1+[1-c(y)]C2
[0029] According to the changing rules of thermodynamic material parameters of functionally graded materials, the UMAT and UMATHT subroutines were written in FORTRAN language for secondary development.
[0030] Create the following 3D model in ABAQUS. It consists of a leading edge strip, skin, rudder, and outer shell. The rudder is constructed using a Ti / Al2O3 gradient material. Create a subroutine with material properties and assign this material to the rudder. Create a temperature-displacement coupling analysis step, apply the corresponding constraints and thermal loads to the structure, mesh the structure, and specify the element type. Submit the job. Select the UMATHT subroutine you created in the job module. Submit the job to generate the simulation result file, which shows the temperature field of the structure at different times under the current thermal load.
[0031] Create a general analysis step, apply the corresponding constraints and mechanical loads to the structure, import the temperature field from the result file, and select the increment required for topology optimization. Create a mesh and specify the element type. In the job module, select the UMAT subroutine you wrote and submit the job to obtain the simulation results of the structure after applying UMAT secondary development without topology optimization.
[0032] Create the same three-dimensional model, and divide the rudder body into several layers along the thickness direction in the material module. Using the above calculation method, calculate the elastic modulus, Poisson's ratio, thermal conductivity, and specific heat of each layer according to the material parameters at different temperatures recorded in the material manual, create the corresponding material and assign the corresponding layer. After the material of each layer is assigned, create a general analysis step, apply the corresponding constraints and mechanical loads to the structure, import the temperature field in the above result file for the structure, and select the incremental step required for topology optimization. Divide the mesh and specify the unit type, submit the job, and obtain the simulation results of the layered method when the structure is not topologically optimized. According to the comparison between the results of the layered method and the secondary development results when different numbers of layers are selected, select the appropriate number of layers according to the required accuracy.
[0033] In the same model from the previous step, create a topology optimization task, select the rudder body as the design domain, create an objective function, and select minimizing the strain energy of the entire model. Create constraints, and select the rudder body's retained volume percentage to be less than or equal to 50%. Based on the simulation results obtained in the previous step without topology optimization, select the appropriate maximum deformation displacement as the constraint. Create a topology optimization job, select a maximum number of optimization cycles of 50, and submit the job to obtain the structural topology optimization results corresponding to the temperature field.
Claims
1. A method for topological optimization of a functionally graded material wing-rudder structure based on a layered approach, characterized by: This involves dividing thermal simulation and topology optimization into two models and performing them sequentially, using a layered approach to simulate the material properties of functionally graded materials for topology optimization: The composition distribution function is used to describe the spatial variation of the functionally gradient material components. The elastic modulus, Poisson's ratio, thermal conductivity, and specific heat at various locations within the material are calculated using the composition distribution function. The functionally gradient material is then secondary developed through the software's subroutine interface. The temperature field of the rudder structure at different times when subjected only to thermal loads is obtained. This temperature field is then imported into a new model. Using the software's built-in layered composite material function, the material properties of the functionally gradient material are approximately simulated using the layered approach for topological optimization. The composition distribution function is used to describe the spatial variation of the components of functionally gradient materials. A composite material composed of linear elastic materials A and B is used as a functionally gradient material. As the thickness coordinate gradually increases, the volume fraction of material A gradually decreases, while the volume fraction of material B gradually increases. The mechanical parameters of the two materials are different, and the mechanical parameters at different positions must be different. The fundamental reason why the mechanical parameters of functionally gradient materials change with the position of the research point is that the mechanical parameters of the material are functions of the position. The elastic modulus, Poisson's ratio, thermal conductivity and specific heat at each position inside the material are solved through the composition distribution function of the functionally gradient material. In the idealized functionally gradient material, materials A and B are represented centrally. When the interaction between A and B is not considered, the mechanical parameters and thermal parameters of the functionally gradient material in the thickness direction are the combination of materials A and B. At this time, the mechanical parameters and thermal parameters of the functionally gradient material along the thickness direction are expressed by the mechanical parameters and thermal parameters of materials A and B and the composition distribution function of the functionally gradient material. Functionally graded materials can be developed through the software's subroutine interface. ABAQUS provides a user-defined subroutine interface, including the UMAT subroutine for defining material properties and the UMATHT subroutine for defining material thermodynamic properties. Through the software's subroutine interface, users can write subroutines in FORTRAN to customize constitutive models for specific problems. Functionally graded materials can be developed through the program's subroutine secondary development, enabling customization of a unified elastoplastic constitutive model. Through secondary development, the temperature field of the wing-rudder structure at different times when it is subjected only to thermal loads is obtained. The obtained temperature field is imported into the new model. In the first model, secondary development is used to obtain the temperature field of the entire wing-rudder structure at different times when it is subjected only to thermal-related loads. The temperature field obtained from the first model is imported into the second model and topology optimization is performed.
2. The method for topological optimization of a functionally gradient material wing-rudder structure based on a layered approach according to claim 1, characterized in that: The topology optimization is performed by approximately simulating the material properties of functionally gradient materials using the layered method. The functionally gradient material wing-rudder structure is divided into several layers. The material parameters of each layer change in a functional form, and the material parameters between adjacent layers have good continuity. Each layer is meshed according to the conventional finite element method, and a finite element model is established to solve the mechanical problems of functionally gradient materials. Based on different requirements, the topology optimization design of the functionally gradient material wing-rudder structure is performed.