Topological optimization method and device considering volume constraint, boundary condition and design domain based on deep learning
By replacing the traditional iterative process with a fully convolutional neural network model, the problem of long computation time in topology optimization is solved, achieving efficient end-to-end topology optimization, which is suitable for complex structure design.
Patent Information
- Application Number
- CN202511820068.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-04
- Publication Date
- 2026-02-17
AI Technical Summary
Traditional topology optimization methods are time-consuming and computationally expensive during iterations, making them unsuitable for real-time optimization scenarios. Furthermore, the fixed dimensionality of neural network input data makes them unsuitable for topology optimization problems in different design domains.
A fully convolutional neural network model is constructed, a dataset is generated through finite element analysis, and the network is trained to achieve end-to-end topology optimization. Combining the SIMP interpolation method and the OC optimization criterion, the optimization results are directly output, replacing the traditional iterative process.
It achieves efficient topology optimization without iteration, significantly shortens computation time, adapts to different design domains and boundary conditions, and improves computational efficiency and accuracy.
Smart Images
Figure CN121543438A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of topology optimization design technology, specifically relating to a topology optimization method and apparatus based on deep learning that considers volume constraints, boundary conditions and design domain. Background Technology
[0002] Topology optimization is an advanced engineering design method that aims to optimize the distribution and layout of materials within a given design space through mathematical modeling and optimization algorithms to achieve specific performance goals, such as maximizing structural stiffness, minimizing weight, or improving durability, while meeting requirements such as load, boundary conditions, and manufacturing constraints. The core idea of topology optimization is to allow materials to distribute freely within the design space, even forming voids or altering connection methods, thereby breaking through the limitations of traditional parameter optimization and generating innovative and efficient structural forms.
[0003] Topology optimization is widely used in aerospace, automotive manufacturing, and civil engineering. In the aerospace industry, designers use topology optimization to design lightweight fuselage components to reduce fuel consumption and improve flight efficiency. In automotive manufacturing, it helps optimize suspension or body structures to enhance safety and reduce costs. In civil engineering, topology optimization can design aesthetically pleasing and earthquake-resistant bridges or long-span roofs. Typical topology optimization methods include SIMP (Solid Isotropic Material Penalty Model) and asymptotic structure methods. The SIMP method gradually approximates the optimal solution by introducing a continuous change in material density, while the asymptotic structure method evolves the structure by gradually removing material from low-stress regions.
[0004] Most modern large-scale industrial numerical simulation software has integrated topology optimization modules, greatly lowering the barrier to entry. However, topology optimization also faces challenges, such as the difficulty in directly manufacturing complex geometries. This has spurred the rapid development of additive manufacturing technologies (such as 3D printing), making optimized design possible.
[0005] Currently, research on traditional gradient-based topology optimization methods has made some progress. However, each iteration of the traditional gradient method requires finite element analysis, which consumes a significant amount of computational resources and time. Therefore, accelerating the traditional topology optimization process is an urgent problem to be solved.
[0006] Based on the variable density method, the mathematical model for topology optimization with the objective of minimizing structural flexibility and the constraint of total volume is as follows:
[0007] ;
[0008] in, This indicates solving for design variables. It is the relative density of the unit cell. For the 1st to the 1st The relative density of each unit For transpose operation, For the real number field, To find the minimum value, The number of finite element elements. Objective function. This represents the sum of the structural compliance under various operating conditions. It is a displacement vector. The overall stiffness matrix, For external load vector, It indicates compliance with constraints. This represents the volume after topology optimization. It is the first The relative density of a finite element, Indicates the first Volume of each unit Represents volume fraction. The initial volume fraction of the structure. This represents the minimum relative density of the element. The purpose of setting a minimum limit value is to prevent singularities in the element stiffness matrix.
[0009] Solving the above mathematical model using traditional topology optimization methods requires repeated iterations and is time-consuming, making it unsuitable for engineering scenarios that require real-time optimization.
[0010] Traditional neural networks have certain limitations on the dimensionality of input data, which is often immutable. The design domains of different topology optimization problems are often different. Therefore, it is necessary to develop a neural network with variable input to realize the change of geometric design domain.
[0011] In topology optimization problems, displacement boundary conditions and load boundary conditions are often expressed in vector form, lacking a unified data structure, and need to be quantized into data that can be input for deep learning.
[0012] In topology optimization problems, volume fractions are often expressed as scalars and need to be quantized into data that can be input for deep learning. Summary of the Invention
[0013] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:
[0014] A topology optimization method based on deep learning that considers volume constraints, boundary conditions, and design domain includes:
[0015] Step 1: To achieve structural weight reduction and material distribution optimization, a topology optimization mathematical model is constructed with the goal of minimizing structural flexibility and the constraint of total volume.
[0016] Step 2 involves continuously changing the displacement boundary conditions, volume fraction constraints, load boundary conditions, and the original design domain. Under each set of parameters, finite element analysis is performed on the design domain to obtain the corresponding strain energy distribution cloud map and stress distribution cloud map. Based on this, using the topology optimization mathematical model established in Step 1, iterative calculations are performed using the SIMP interpolation method combined with the OC optimization criterion to obtain optimized topologies that satisfy different displacement boundary conditions, volume fraction constraints, load boundary conditions, and the original design domain. By iteratively inputting and calculating different sets of parameters, topology optimization samples covering various working conditions and different design domains are formed, thereby constructing a dataset for training a fully convolutional neural network.
[0017] Step 3: Based on the dataset constructed in Step 2 for training the fully convolutional neural network, different volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shape, stress cloud map, and strain energy cloud map are used as input features, and the corresponding optimized topology is used as the output label to perform supervised offline training on the fully convolutional neural network. By continuously adjusting the network parameters, the difference between the prediction results and the actual optimization results is minimized, and finally a fully convolutional neural network model that can characterize the topology optimization law is obtained.
[0018] Step 4: In the practical application stage, the different volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shape, stress cloud map, and strain energy cloud map information of the structure to be optimized are input into the fully convolutional neural network model obtained in Step 3, and the corresponding topology optimization results are directly output, realizing the end-to-end replacement of the traditional iterative optimization process.
[0019] A topology optimization device based on deep learning that considers volume constraints, boundary conditions, and design domain includes:
[0020] The topology optimization mathematical model construction module constructs a topology optimization mathematical model with the goal of minimizing structural flexibility and the constraint of total volume in order to achieve structural weight reduction and material distribution optimization.
[0021] The dataset construction module continuously changes the displacement boundary conditions, volume fraction constraints, load boundary conditions, and the original design domain. Under each set of parameter conditions, it performs finite element analysis on the design domain to obtain the corresponding strain energy distribution contour maps and stress distribution contour maps. Based on this, the topology optimization mathematical model established by the topology optimization mathematical model construction module is used to perform iterative calculations using the SIMP interpolation method combined with the OC optimization criterion to obtain optimized topologies that satisfy different displacement boundary conditions, volume fraction constraints, load boundary conditions, and the original design domain. By iteratively inputting and calculating different sets of parameter sets, topology optimization samples covering various working conditions and different design domains are formed, thereby constructing a dataset for training a fully convolutional neural network.
[0022] The fully convolutional neural network model acquisition module, based on the dataset construction module, uses a dataset for training the fully convolutional neural network. Different volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shape, stress contour maps, and strain energy contour maps are used as input features, and the corresponding optimized topology is used as the output label. Supervised offline training is performed on the fully convolutional neural network. By continuously adjusting the network parameters, the difference between the prediction results and the actual optimization results is minimized, and finally a fully convolutional neural network model that can represent the topology optimization law is obtained.
[0023] In the practical application stage, the output module inputs the information of different volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shape, stress cloud map and strain energy cloud map of the structure to be optimized into the fully convolutional neural network model obtained by the fully convolutional neural network model acquisition module, and directly outputs the corresponding topology optimization results, realizing an end-to-end replacement of the traditional iterative optimization process.
[0024] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the topology optimization method based on deep learning that considers volume constraints, boundary conditions, and design domain.
[0025] A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the aforementioned topology optimization method based on deep learning that considers volume constraints, boundary conditions, and design domain.
[0026] The present invention has the following beneficial effects:
[0027] This invention achieves a non-iterative solution to the end-to-end minimum compliance topology optimization problem with volume constraints by constructing and training a fully convolutional neural network for end-to-end topology optimization.
[0028] This invention achieves geometric domain generalization of deep learning non-iterative topology optimization methods by constructing a fully convolutional neural network with variable input in the geometric domain.
[0029] This invention achieves boundary condition generalization of the deep learning non-iterative topology optimization method by constructing displacement boundary condition and load boundary condition matrices.
[0030] This invention achieves the generalization of volume fraction constraints in deep learning-based non-iterative topology optimization methods by constructing a volume fraction matrix. Attached Figure Description
[0031] Figure 1This is a flowchart of the topology optimization method based on deep learning that considers volume constraints, boundary conditions and design domain according to the present invention; wherein, (a) is a schematic diagram of online training and (b) is a schematic diagram of offline use;
[0032] Figure 2 The diagram shows the input parameters of the topology-optimized fully convolutional neural network structure; where (a) is a schematic diagram of the case working condition, (b) is the volume fraction matrix, (c) is the load condition matrix in the Y direction, (d) is the load condition matrix in the X direction, (e) is the displacement boundary condition matrix in the X direction, (f) is the displacement boundary condition matrix in the Y direction, (g) is the stress contour matrix, and (h) is the strain energy contour matrix.
[0033] Figure 3 Optimize the fully convolutional neural network architecture diagram for topology;
[0034] Figure 4 This diagram illustrates the comparison between the optimization results of the traditional gradient algorithm and the prediction results of the fully convolutional neural network under different volume fractions. Detailed Implementation
[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.
[0036] like Figure 1 As shown, this invention proposes a topology optimization method based on deep learning that considers volume constraints, boundary conditions, and the design domain. Figure 1 (a) is a schematic diagram of online training. Figure 1 (b) is a schematic diagram of offline use. By inputting information such as volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shape, stress cloud map and strain energy cloud map into the trained fully convolutional neural network model, end-to-end optimization without iteration is achieved, and the topology optimization density distribution result is directly output.
[0037] The method includes an offline training phase, in which a neural network is trained by generating a dataset containing various constraints to establish an accurate mapping model from input parameters to optimization results; and an online application phase, in which efficient topology optimization schemes are quickly obtained by inputting volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shape, stress contour map and strain energy contour map parameters.
[0038] Compared with traditional iterative optimization, this invention significantly improves computational efficiency, accuracy, and engineering applicability, and is suitable for complex scenarios such as aerospace, automobile manufacturing, and construction engineering.
[0039] This invention simultaneously considers the influence of volume constraints, displacement boundary conditions, load boundary conditions, and design domain shape parameters. It introduces deep learning technology into the traditional topology optimization process, constructing a training dataset containing various boundary conditions and design domains, and offline training a fully convolutional neural network (LCN) to obtain a LCN model capable of representing the topology optimization rules. In practical applications, the trained LCN model replaces the iterative calculation process of traditional topology optimization algorithms, achieving rapid end-to-end prediction of topology optimization results, thereby significantly reducing computation time while maintaining optimization accuracy. This invention includes the following steps:
[0040] Step 1: For applications in aerospace, automotive, shipbuilding, and construction, a topology optimization mathematical model is constructed with the goal of minimizing structural flexibility and constrained by total volume, aiming to achieve structural weight reduction and material distribution optimization. Based on the finite element method, the variable density method is used to discretize the continuous design domain into N elements, and the state of each element is described as a discrete variable, where 0 represents a hole and 1 represents a solid. This establishes a topology optimization mathematical model with the goal of minimizing structural flexibility and constrained by total volume.
[0041] Step 2 involves continuously changing the displacement boundary conditions, volume fraction constraints, load boundary conditions, and the original design domain. Finite element analysis is performed on the design domain under each set of parameters to obtain the corresponding strain energy distribution and stress distribution contour maps. Based on this, using the topology optimization mathematical model established in Step 1, iterative calculations are performed using the SIMP interpolation method combined with the OC (Optimality Criteria) optimization criteria to obtain optimized topologies that satisfy different displacement boundary conditions, volume fraction constraints, load boundary conditions, and the original design domain. By iteratively inputting and calculating different sets of parameters, topology optimization samples covering various working conditions and different design domains are formed, thereby constructing a dataset for training a fully convolutional neural network.
[0042] Step 3: Based on the dataset constructed in Step 2 for training the fully convolutional neural network, different volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shape, stress contour maps, and strain energy contour maps are used as input features, and the corresponding optimized topology is used as the output label. Supervised offline training is then performed on the fully convolutional neural network. By continuously adjusting the network parameters and minimizing the difference between the predicted results and the actual optimization results, a fully convolutional neural network model capable of representing the topology optimization rules is finally obtained.
[0043] Step 4: In the practical application stage, the different volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shape, stress cloud map, and strain energy cloud map information of the structure to be optimized are input into the fully convolutional neural network model obtained in Step 3, and the corresponding topology optimization results can be directly output, thereby realizing the end-to-end replacement of the traditional iterative optimization process.
[0044] The method of this invention can significantly shorten the computation time while ensuring the accuracy of topology optimization, and realize rapid prediction and efficient application of topology optimization.
[0045] Specifically, in step 1, a topology optimization mathematical model is established with discrete variables of holes (0) and solids (1), aiming to minimize structural flexibility and constrained by total volume:
[0046] ;
[0047] Specifically, in step 2:
[0048] As attached Figure 2 As shown, the dataset used for training the fully convolutional neural network contains seven input channels: volume fraction matrix and volume fraction matrix. The form is shown in the following formula. It represents the structural grid dimension, and also the geometry of the structural design domain. This represents the volume fraction required for topology optimization. Figure 2 (a) is a schematic diagram of the case working conditions. Figure 2 (b) is the volume fraction matrix. Figure 2 (c) is the load condition matrix in the Y direction. Figure 2 (d) is the load condition matrix in the X direction. Figure 2 (e) is the boundary condition matrix for displacement in the X direction. Figure 2 f is the boundary condition matrix for displacement in the Y direction. Figure 2 (g) is the stress contour matrix. Figure 2 (h) is the strain energy cloud map matrix.
[0049] ;
[0050] X-direction displacement boundary conditions: The X-direction displacement boundary conditions are expressed in matrix form, as shown in the following equation, where "0" indicates that the X-direction degree of freedom is 0, and "1" indicates that the X-direction degree of freedom is 1. Indicates the structural grid dimension. Let X be the boundary condition matrix for displacement in the X direction.
[0051] ;
[0052] Y-direction displacement boundary conditions: The Y-direction displacement boundary conditions are expressed in matrix form, as shown in the following equation, where "0" indicates that the Y-direction degree of freedom is 0, and "1" indicates that the Y-direction degree of freedom is 1. Indicates the structural grid dimension. This is the boundary condition matrix for displacement in the Y direction.
[0053] ;
[0054] X-direction load boundary conditions: The X-direction load boundary conditions are expressed in matrix form, as shown in the following equation, where... This indicates the magnitude of the force in the X direction at this location; "0" indicates that the force in the X direction at this location is zero. Indicates the structural grid dimension. Let X be the boundary condition matrix for the load in the X direction.
[0055] ;
[0056] Y-direction load boundary conditions: The Y-direction load boundary conditions are expressed in matrix form, as shown in the following equation, where... This indicates the magnitude of the force in the Y direction at this location; "0" indicates that the force in the Y direction at this location is zero. Indicates the structural grid dimension; This is the boundary condition matrix for the load in the Y direction.
[0057] ;
[0058] Stress distribution cloud diagram: The von Mises stress calculation formula for a two-dimensional plane stress problem is shown below. Wherein, Von Mises equivalent stress represents the equivalent uniaxial tensile stress of a material under complex stress states. This is the normal stress in the direction of the first principal stress. This is the normal stress in the direction of the second principal stress. The shear stress component describes the shear stress between the X-plane (first orthogonal plane) and the Y-plane (second orthogonal plane).
[0059] ;
[0060] As a dataset, ignoring coefficients, we obtain the following formula:
[0061] ;
[0062] Strain energy distribution contour plot: The formula for calculating the strain energy in a two-dimensional plane stress problem is shown below. For strain energy, This represents the normal strain in the direction of the first principal stress. This represents the normal strain in the direction of the second principal stress. This represents shear strain.
[0063] .
[0064] Specifically, in step 3: as shown in the appendix Figure 3 As shown in the fully convolutional neural network architecture diagram, based on the dataset constructed in step 2 for training the fully convolutional neural network, different volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shape, stress contour maps, and strain energy contour maps are used as input features, and the corresponding optimized topology is used as the output label. Supervised offline training is then performed on the fully convolutional neural network. By continuously adjusting the network parameters and minimizing the difference between the predicted results and the actual optimization results, a fully convolutional neural network model capable of representing the topology optimization law is finally obtained.
[0065] In this invention, a fully convolutional neural network (WCNN) model serves as the core model, directly mapping input structural parameters (such as volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shape, stress contour maps, and strain energy contour maps) to the topology-optimized density distribution result. The WCNN consists of an encoder (downsampling path) and a decoder (upsampling path). The encoder extracts high-dimensional features through multiple convolutions and pooling, while the decoder restores spatial resolution through transposed convolutions and skip connections, ensuring the refinement and accuracy of the output density map. This design allows for end-to-end pixel-level prediction, avoiding the computational overhead of traditional iterative optimization. During training, the loss function is crucial for optimizing network performance. This invention employs a composite loss function, including Mean Squared Error (MSE) loss primarily based on pixel-level errors, to quantify the predicted density distribution. Compared with the true density distribution Differences between :
[0066] ;
[0067] in, This represents the number of training samples.
[0068] Fully convolutional neural networks (LCNs) use convolutional neural networks to transform image pixels into pixel categories. Unlike convolutional neural networks used for image classification or object detection, LCNs transform the height and width of intermediate layer feature maps back to the dimensions of the input image, achieved through transposed convolution. Therefore, the category prediction output by an LCN has a one-to-one correspondence with the input image at the pixel level: the output value in the channel dimension is the category prediction result for the pixel at that spatial location.
[0069] Transposed convolution: For an input of size ... The image has a convolution kernel size of [size missing]. As shown in the following formula:
[0070] ;
[0071] ;
[0072] in, For the input matrix, - for Each element, For convolution kernel, , , , for The elements.
[0073] The specific implementation method for calculating the output is matrix multiplication. The convolution kernel... Represented as a sparse matrix :
[0074] ;
[0075] Among them, sparse matrix Each row vector represents a convolution operation at a location, and the zero-padded locations represent regions not covered by the convolution kernel.
[0076] Expand the input X into a column vector:
[0077] ;
[0078] in, These are the elements of the column vector of input X.
[0079] The convolution operation can then be represented as:
[0080] ;
[0081] Output vector The size is The column vectors, rewritten as matrices, are: .in, The input vector.
[0082] Transposed convolution is... Input / output swapping in the middle:
[0083] ;
[0084] in, Representing a sparse matrix Transpose, and the size is now That is, by Input After transposing the convolution, the output size is obtained as follows: column vectors At this time and The numerical values are different from the original, only the shape remains the same.
[0085] Specifically, in step 4, the required volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shape, stress cloud map and strain energy cloud map parameters are input online to the trained fully convolutional neural network model, which can achieve near real-time topology optimization and obtain the topology optimization density distribution result.
[0086] Essentially, the original topology optimization problem is a complex nonlinear mathematical programming problem, requiring the separate calculation of the objective function and its sensitivity, as well as the constraint functions and their sensitivities, and then solving it through iterative computation using the Objective-C algorithm. This process is extremely complex and consumes significant online computation time. However, the introduction of fully convolutional neural networks (WCNNs) effectively solves this problem. WCNN models, trained on large offline datasets, establish mathematical mappings between various input and output data, enabling real-time topology optimization.
[0087] The topology optimization method of this invention achieves efficient end-to-end optimization through the following four key steps: First, steps 1 to 2 constitute the offline training stage, generating a topology optimization dataset containing parameters such as volume fraction constraints, load boundary conditions, displacement boundary conditions, and design domain shape, providing high-quality input and output samples for subsequent model training; Second, step 3 utilizes a fully convolutional neural network (FCN) to construct a mapping model, extracting features and training through an encoder-decoder structure, and combining mean square error loss to optimize the network, enhancing accuracy and physical consistency; Next, step 4, based on the trained model, inputs volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shape, stress contour map, and strain energy contour map parameters to achieve near real-time topology optimization density distribution output, replacing the traditional iterative process; The overall process significantly improves computational efficiency, accuracy, and engineering applicability, and is suitable for complex structural optimization needs.
[0088] Steps 1 and 2 together constitute the topology optimization dataset generation process in the offline training phase. This process takes into account the volume constraints of the structure during data preparation, thereby providing input and output samples that meet the design requirements for training the fully convolutional neural network model.
[0089] Step 3 establishes a mapping model using a fully convolutional neural network. This model takes parameters such as fractional constraints, load boundary conditions, displacement boundary conditions, design domain geometry, stress cloud map, and strain energy cloud map as inputs, and the topology optimization density distribution result as output. Based on the dataset constructed in step 2 for training the fully convolutional neural network, training and testing sets are built to train and validate the fully convolutional neural network, ensuring the accuracy and generalization ability of the network model.
[0090] Step 4, based on the trained fully convolutional neural network model, allows for online input of the required material property parameters, displacement stress constraint parameters, and frequency constraint parameters, enabling near real-time topology optimization calculations to obtain the desired topology optimization density distribution results. This method is also applicable to practical engineering applications, achieving rapid and efficient design optimization.
[0091] Example:
[0092] To better understand the features of this invention and its applicability to practical engineering, the following points are made regarding... Figure 4 The square plate structure shown has been optimized. For example... Figure 2 As shown in (a), the left side of the square plate has a fixed X-direction degree of freedom, the right lower corner of the square plate has a fixed Y-direction degree of freedom, and the upper left corner is subjected to a force in the Y-direction. , The optimization results of traditional gradient algorithms and the prediction results of fully convolutional neural networks under different volume fractions are compared, for example... Figure 4 As shown, the prediction results of the fully convolutional neural network are similar to those of the gradient optimization algorithm, with a small error. This indicates that the fully convolutional neural network has a good prediction effect and can greatly shorten the topology optimization time.
[0093] In summary, this invention proposes a deep learning-based topology optimization method, aiming to address the challenges of computational time and complexity in traditional iterative optimization through an efficient end-to-end optimization process. The invention comprises four key steps: First, in the offline training phase, a topology optimization dataset containing parameters such as volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shape, stress contour maps, and strain energy contour maps is generated, laying a solid foundation for subsequent model training. Second, a fully convolutional neural network (FCN) is used to construct a mapping model, extracting features through an encoder and restoring spatial resolution through a decoder, with mean squared error loss as the core to ensure prediction accuracy and physical consistency. Third, in the online application phase, by inputting the volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shape, stress contour maps, and strain energy contour map parameters, the trained model is used to achieve near real-time topology optimization density distribution output. This method improves computational efficiency, accuracy, and engineering practicality while being compatible with modern additive manufacturing technologies, making it suitable for complex scenarios such as aerospace, automotive manufacturing, and construction engineering. Compared with existing technologies, this invention has significant advantages in terms of efficiency, accuracy, generalization ability, flexibility, and practicality, providing intelligent and efficient solutions for complex structure design and demonstrating broad application prospects.
[0094] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The embodiments of the present invention can be implemented using various computer languages.
[0095] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0096] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0097] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0098] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.
[0099] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.
[0100] The above description is merely an embodiment of the present invention and does not limit the scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention specification and drawings, or direct or indirect applications in other related system fields, are similarly included within the protection scope of the present invention.
[0101] The contents not described in detail in this specification are existing technologies known to those skilled in the art.
Claims
1. A topology optimization method considering volume constraints, boundary conditions and topology of design domain based on deep learning, characterized in that, Comprise: Step 1, in order to realize structural weight reduction and material distribution optimization, a topology optimization mathematical model is constructed, which takes the minimization of structural flexibility as the objective and the total volume as the constraint; Step 2, by continuously changing the displacement boundary condition, volume fraction constraint, load boundary condition and original design domain, finite element analysis is carried out on the design domain under each set of parameter conditions to obtain the corresponding strain energy distribution cloud picture and stress distribution cloud picture; On this basis, based on the topology optimization mathematical model established in step 1, SIMP interpolation method combined with OC optimization criterion is used for iterative calculation to obtain the optimized topology structure meeting different displacement boundary conditions, volume fraction constraints, load boundary conditions and original design domain; Through the cyclic input and calculation of different groups of parameters, the topology optimization samples covering multiple working conditions and different design domains are formed, thereby constructing the data set for training the full convolutional neural network; Step 3, based on the data set for training the full convolutional neural network constructed in step 2, different volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shapes, stress cloud pictures and strain energy cloud pictures are taken as input features, and the corresponding optimized topology structure is taken as output label, and the full convolutional neural network is supervised offline training; By continuously adjusting the network parameters, the difference between the prediction result and the real optimization result is minimized, and finally the full convolutional neural network model capable of representing the topology optimization rule is obtained; Step 4, in the actual application stage, the different volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shapes, stress cloud pictures and strain energy cloud picture information of the structure to be optimized are input into the full convolutional neural network model obtained in step 3, and the corresponding topology optimization result is directly output, realizing the end-to-end replacement of the traditional iterative optimization process. 2.The topology optimization method based on deep learning considering volume constraint, boundary condition and design domain according to claim 1, wherein, Step 1 includes: based on the finite element method, the idea of variable density method is adopted to discretize the continuous design domain into N units, and the unit state is described in the form of discrete variables, wherein 0 represents a hole and 1 represents a solid, thereby establishing a topology optimization mathematical model taking the minimization of structural flexibility as the objective and the total volume as the constraint. 3.The topology optimization method based on deep learning considering volume constraint, boundary condition and design domain according to claim 2, wherein, In step 1, the topology optimization mathematical model is: ； wherein, denotes solving the design variables, the design variables is the relative density of the element, is the relative density of the first to the element, is the transpose operation, is the real number field, is the minimum value, is the number of finite element units; objective function denotes the sum of the compliances of the structure in each working condition, is the displacement vector, is the total stiffness matrix, is the external load vector, denotes subject to the constraint condition; denotes the volume after topology optimization, is the relative density of the first finite element unit, denotes the volume of the first element, denotes the volume fraction, is the initial volume fraction of the structure, denotes the minimum value of the relative density of the element. 4.The topology optimization method based on deep learning considering volume constraint, boundary condition and design domain according to claim 1, wherein, In step 2, the dataset used for training the fully convolutional neural network contains seven input channels: the volume fraction matrix: the volume fraction matrix is in the following form: ； wherein, represents the structure grid dimension, also represents the geometry shape of the structure design domain, represents the volume fraction required by the topology optimization; X-direction displacement boundary condition: the X-direction displacement boundary condition is expressed in the form of a matrix: ； wherein "0" indicates that the X-direction degree of freedom is 0 at this point, and "1" indicates that the X-direction degree of freedom is 1 at this point, represents the structure grid dimension, is the X-direction displacement boundary condition matrix; Y-direction displacement boundary condition: the Y-direction displacement boundary condition is expressed in the form of a matrix: ； Wherein, "0" represents the Y direction freedom degree is 0 here, "1" represents the Y direction freedom degree is 1 here, represents the structure grid dimension, is the Y direction displacement boundary condition matrix; X-direction load boundary condition: the X-direction load boundary condition is expressed in the form of a matrix: ； wherein, represents the magnitude of the force in the X direction at this point, and "0" represents that the force in the X direction at this point is 0, represents the dimension of the structure grid, is the X direction load boundary condition matrix; Y-direction load boundary condition: the Y-direction load boundary condition is expressed in the form of a matrix: ； wherein, represents the magnitude of the force in the Y direction at this point, and "0" represents that the force in the Y direction at this point is 0, represents the dimension of the structure grid; is the Y direction load boundary condition matrix; Stress distribution cloud picture: the von Mises stress calculation formula of the two-dimensional plane stress problem is: ； wherein is the von Mises equivalent stress, representing the equivalent uniaxial tensile stress of the material under complex stress state, is the normal stress in the direction of the first principal stress, is the normal stress in the direction of the second principal stress, is the shear stress component; Strain energy distribution cloud picture: the strain energy calculation formula of the two-dimensional plane stress problem is: ； wherein is the strain energy, denotes the normal strain in the direction of the first principal stress, denotes the normal strain in the direction of the second principal stress, denotes the shear strain. 5.The topology optimization method based on deep learning considering volume constraint, boundary condition and design domain according to claim 1, wherein, In step 3, the full convolutional neural network model is used to directly map from the input structure parameters to the topology optimization density distribution result; the full convolutional neural network is composed of an encoder and a decoder, the encoder extracts high-dimensional features through multiple layers of convolution and pooling, and the decoder restores the spatial resolution through transposed convolution and skip connection to ensure the fineness and accuracy of the output density map. 6.The topology optimization method based on deep learning considering volume constraint, boundary condition and design domain according to claim 1, wherein, In step 3, during the training of the fully convolutional neural network model, a compound loss function is used, including a mean squared error loss based on pixel-level error, quantifying the difference between the predicted density distribution and the true density distribution : ； wherein, is the number of training samples. 7.The topology optimization method based on deep learning considering volume constraint, boundary condition and design domain according to claim 5, wherein, The input structural parameters include volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shapes, stress contour maps, and strain energy contour maps.
8. A device for topology optimization considering volume constraint, boundary condition and topology of design domain based on deep learning, characterized by, The method comprises the following steps: A topology optimization mathematical model construction module is configured to construct a topology optimization mathematical model with the minimum structural flexibility as the target and the total volume as the constraint to achieve structural weight reduction and material distribution optimization; A dataset construction module is configured to perform finite element analysis on the design domain under each set of parameter conditions by continuously changing the displacement boundary conditions, volume fraction constraints, load boundary conditions, and original design domain, and obtain the corresponding strain energy distribution contour map and stress distribution contour map; on this basis, the SIMP interpolation method is combined with the OC optimization criterion to perform iterative calculation based on the topology optimization mathematical model constructed by the topology optimization mathematical model construction module, to obtain an optimized topology structure that meets different displacement boundary conditions, volume fraction constraints, load boundary conditions, and original design domain; by cyclic input and calculation of different sets of parameters, a topology optimization sample covering multiple working conditions and different design domains is formed, thereby constructing a dataset for training of a full convolutional neural network; A full convolutional neural network model acquisition module is configured to, based on the dataset constructed by the dataset construction module for training of the full convolutional neural network, take different volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shapes, stress contour maps, and strain energy contour maps as input features, take the corresponding optimized topology structure as output labels, and perform supervised offline training on the full convolutional neural network; By continuously adjusting the network parameters, the difference between the prediction result and the real optimization result is minimized, and finally a full convolutional neural network model capable of representing the topology optimization rule is obtained; An output module is configured to, in the actual application stage, input the different volume fraction constraints, load boundary conditions, displacement boundary conditions, design domain shapes, stress contour maps, and strain energy contour maps of the structure to be optimized into the full convolutional neural network model obtained by the full convolutional neural network model acquisition module, directly output the corresponding topology optimization result, and realize end-to-end replacement of the traditional iterative optimization process.
9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to implement the steps of the topology optimization method based on deep learning considering volume constraints, boundary conditions, and design domains according to any one of claims 1 to 7. 10.A non-transitory computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the steps of the topology optimization method based on deep learning considering volume constraints, boundary conditions, and design domains according to any one of claims 1 to 7.