Isogeometric topology optimization method and device based on h-filtering, equipment and medium

Abstract

The application provides an equal geometry topology optimization method and device based on H-filtering, equipment and medium, and relates to the technical field of structural topology optimization. According to the model construction parameter information of a structure to be optimized, the relative density of the control points of the structure to be optimized is taken as a design variable, the minimum structural flexibility is taken as an optimization target, the volume fraction of the material is taken as a constraint, a preset equal geometry topology optimization model is constructed, the sensitivity of the preset equal geometry topology optimization model is calculated, the design variable is updated based on the sensitivity by using an optimization criterion method, until the preset convergence condition is met, and based on the obtained target equal geometry topology optimization model, a target unit density distribution and a target topology configuration are obtained. By introducing the constraint condition into the filtering process of the design variable, the problem of introducing a large number of constraints in topology optimization is solved, and the optimization result meeting the pull-out constraint can be obtained explicitly without increasing the complexity of the optimization problem and losing the performance of the structure.

Description

Technical Field

[0001] The present application relates to the technical field of structural topology optimization, and in particular to an isogeometric topology optimization method, apparatus, device and medium based on H-product filtering. Background Art

[0002] In traditional manufacturing processes, casting is one of the important processes in mechanical industry production, and it still plays an important role in engineering fields such as aerospace and automobile manufacturing.

[0003] During the casting process, the casting must possess certain geometric characteristics; otherwise, the casting cannot be removed from the mold smoothly, resulting in casting failure. As an efficient, versatile, and flexible structural optimization design method, topology optimization has gradually attracted widespread attention from scholars since the homogenization-based continuum structural topology optimization method was proposed. Topology optimization methods such as the density method, the level set method, and the evolutionary structure method have emerged. Furthermore, with the deepening of research, topology optimization is now able to handle the vast majority of structural optimization design problems and can provide good design results. However, the analysis model used by the traditional finite element method is an approximation of the original geometry, and the analysis accuracy is closely related to the fineness of the mesh.

[0004] The rise of geometric analysis has enabled people to directly use precise geometric models to perform structural analysis and optimization design on castings. The geometric conditions that castings need to meet are called draft constraints. Therefore, it is of great value to consider draft constraints in topology optimization design. The optimized structures obtained by topology optimization without considering manufacturing constraints are generally more complex and are often only applicable in theory. However, it is difficult to produce corresponding parts in actual processes, which brings huge challenges to traditional production and manufacturing.

[0005] Currently, the density method is commonly used for topology optimization design that considers casting constraints. Within the framework of the density method, the main methods for implementing casting constraints include adjacent density constraints, reparameterization, and auxiliary physical models. Adjacent density constraints introduce a large number of constraints, increasing computational costs. Reparameterization methods use different mapping strategies to reparameterize design variables based on castability requirements. The resulting results are reparameterized and require certain processing to obtain the material distribution of the structure. Auxiliary physical models require the introduction of additional physical fields, increasing the complexity of the problem.

[0006] However, there is currently no topology optimization design method that satisfies draft constraints without increasing the complexity of the optimization problem and losing structural performance. Summary of the Invention

[0007] The purpose of this application is to address the above problems and provide an isogeometric topology optimization method, device, equipment and medium based on H-product filtering to introduce constraints into the filtering process of design variables, solve the problem of introducing a large number of constraints in topology optimization, and explicitly obtain optimization results that meet the draft constraints without increasing the complexity of the optimization problem and losing structural performance.

[0008] In a first aspect, the present application provides an isogeometric topology optimization method based on H-product filtering, comprising: constructing parameter information according to a model of a structure to be optimized, using the relative density of control points of the structure to be optimized as a design variable, minimizing structural flexibility as an optimization goal, and using the volume fraction of the material as a constraint to construct a preset isogeometric topology optimization model of the structure to be optimized;

[0009] Calculating the sensitivity of the preset isogeometric topology optimization model;

[0010] Based on the sensitivity, the design variables of the preset isogeometric topology optimization model are updated using an optimization criterion method until a preset convergence condition is satisfied, thereby obtaining a target isogeometric topology optimization model;

[0011] Based on the target isogeometric topology optimization model, a target unit relative density distribution and a target topological configuration are obtained.

[0012] According to the technical solution provided in this application, the parameter information of the model of the structure to be optimized is constructed, the relative density of the control points of the structure to be optimized is used as the design variable, the minimum structural flexibility is used as the optimization goal, and the volume fraction of the material is used as the constraint to construct a preset geometric topology optimization model of the structure to be optimized, including:

[0013] Based on the isogeometric analysis model, obtaining a first unit relative density of the structure to be optimized according to the relative density of the control points;

[0014] Performing H-product filtering and threshold projection processing on the first unit relative density to obtain a second unit relative density of the structure to be optimized;

[0015] Based on the isogeometric analysis model, obtaining the Young's elastic modulus of the structure to be optimized according to the relative density of the second unit;

[0016] Based on the model construction parameter information, the relative density of the control points, the relative density of the second unit and the Young's elastic modulus, the relative density of the control points of the structure to be optimized is used as the design variable, the minimum structural flexibility is used as the optimization goal, and the volume fraction of the material is used as the constraint, a preset geometric topology optimization model of the structure to be optimized is constructed.

[0017] According to the technical solution provided in this application, the model construction parameter information includes the NURBS basis functions of the control points; accordingly, the first unit relative density of the structure to be optimized is obtained according to the relative density of the control points based on the isogeometric analysis model, including:

[0018] Based on the isogeometric analysis model, according to the formula:

[0019]

[0020] Represents the relationship between the relative density of the control point and the relative density of the corresponding first unit; where ρ i is the relative density of the first unit of unit i, x j represents the relative density of control point j, is the NURBS basis function corresponding to the control point j, r and l refer to the order of the basis function along the ξ and η directions respectively, and are the parameter coordinates along the ξ and η directions at the center of unit i, respectively.

[0021] According to the technical solution provided in this application, the model construction parameter information also includes an H-product kernel, a projection curvature control parameter, and a projection threshold; accordingly, performing H-product filtering and threshold projection processing on the first unit relative density to obtain the second unit relative density of the structure to be optimized includes:

[0022] According to the formula:

[0023]

[0024] Performing H-product filtering on the first unit relative density to obtain the intermediate unit relative density of the structure to be optimized; wherein, is the relative density of the intermediate units of the structure to be optimized, Θ is the H product core, P i is a unit relative density matrix with the same size as the H product kernel, and its central position is the first relative density ρ of unit i i , the values ​​at other positions are the first relative densities of the adjacent units of unit i in the structure to be optimized, and the operator (·) represents the H product (Hadamard product) of the matrix, that is, the multiplication of elements at the same position;

[0025] According to the formula:

[0026]

[0027] Performing threshold projection processing on the relative density of the intermediate unit to obtain the relative density of the second unit of the structure to be optimized; wherein, is the relative density of the second unit of the structure to be optimized, β is the projection curvature control parameter, δ is the projection threshold, is the relative density of the intermediate units of the structure to be optimized.

[0028] According to the technical solution provided in this application, the model construction parameter information also includes a penalty factor, a standard solid material Young's modulus, and a preset minimum Young's modulus; accordingly, the Young's modulus of the structure to be optimized is obtained based on the relative density of the second unit based on the isogeometric analysis model, including:

[0029] According to the formula:

[0030]

[0031] Obtain the Young's elastic modulus of the structure to be optimized; wherein, E i is the Young's modulus of the structure to be optimized, is the relative density of the second unit of the structure to be optimized, p is the penalty factor, E0 is the Young's modulus of elasticity of the standard solid material, E min is the preset minimum Young's modulus.

[0032] According to the technical solution provided in this application, the model construction parameter information also includes a global displacement vector, an overall stiffness matrix, a global force vector, a unit displacement vector, a unit stiffness matrix, a material volume, a design domain volume, a volume fraction, the number of units, and the number of control points. Accordingly, based on the model construction parameter information, the relative density of the control points, the relative density of the second unit, and the Young's elastic modulus, the relative density of the control points of the structure to be optimized is used as a design variable, the minimum structural flexibility is used as the optimization goal, and the volume fraction of the material is used as a constraint, a preset isogeometric topology optimization model of the structure to be optimized is constructed, including:

[0033] The preset isogeometric topology optimization model of the structure to be optimized is expressed as:

[0034]

[0035] Among them, c is the structural flexibility, U, K, and F represent the global displacement vector, the overall stiffness matrix, and the global force vector, respectively. is the relative density of the second unit of the structure to be optimized, E i is the Young's elastic modulus of the structure to be optimized, u i With k i are the unit displacement vector and the unit stiffness matrix respectively, V is the material volume, V0 is the design domain volume, VF represents the volume fraction, N and M are the number of units and the number of control points respectively.

[0036] According to the technical solution provided in this application, the calculation of the sensitivity of the preset isogeometric topology optimization model includes:

[0037] According to the formula:

[0038]

[0039] Sensitivity of the preset isogeometric topology optimization model is calculated; wherein, Sensitivity of the preset isogeometric topology optimization model is calculated; wherein, j Relative density of control point j is S j The set of control points j participating in the formation of the unit, Second unit relative density of the structure to be optimized is p, a penalty factor, E0 is the standard solid material Young's modulus, E min The preset minimum Young's modulus is u i Unit displacement vector is k0, unit stiffness matrix, B is the strain-displacement matrix, D0 is the elastic coefficient matrix, Jacobian matrix J1, J2 are the space variation relationship of NURBS basis function parameter domain to physical domain, integral domain to parameter domain, ω a The weight coefficient corresponding to the a-th Gauss integral point is N g The number of Gauss integral points is Intermediate unit relative density of the structure to be optimized is β, a projection curvature control parameter, δ is a projection threshold, θ i,t The value of unit t relative to unit i in the H kernel is, The NURBS basis function corresponding to control point j is And The parameter coordinates of unit i center along the ξ and η directions are respectively.

[0040] In the second aspect, the present application provides an isogeometric topology optimization device based on H integral filtering, comprising:

[0041] The construction module is configured to construct a preset isogeometric topology optimization model of a structure to be optimized according to model construction parameter information of the structure to be optimized, take the relative density of control points of the structure to be optimized as design variables, take the minimum structural flexibility as the optimization objective, and take the volume fraction of the material as the constraint.

[0042] The calculation module is configured to calculate the sensitivity of the preset isogeometric topology optimization model.

[0043] The update module is configured to update the design variables of the preset isogeometric topology optimization model based on the sensitivity using an optimization criterion method until a preset convergence condition is met, and obtain a target isogeometric topology optimization model.

[0044] The processing module is configured to obtain a target unit density distribution and a target topology configuration based on the target isogeometric topology optimization model.

[0045] In a third aspect, the present application provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method described above when executing the computer program.

[0046] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, and the computer program implements the method described above when executed by a processor.

[0047] Compared with the prior art, the beneficial effects of the present application are as follows: the embodiments of the present application provide an isogeometric topology optimization method, apparatus, equipment and medium based on H-product filtering. The method constructs parameter information according to the model of the structure to be optimized, takes the relative density of the control points of the structure to be optimized as the design variable, takes the minimum structural flexibility as the optimization target, takes the volume fraction of the material as the constraint, constructs a preset isogeometric topology optimization model of the structure to be optimized, and calculates the sensitivity of the preset isogeometric topology optimization model. Based on the sensitivity, the design variables of the preset isogeometric topology optimization model are updated using the optimization criterion method until the preset convergence conditions are met, and the target isogeometric topology optimization model is obtained. Then, based on the target isogeometric topology optimization model, the target unit density distribution and the target topological configuration are obtained. By introducing the constraint conditions into the filtering process of the design variables, the problem of introducing a large number of constraints in the topology optimization is solved. Without increasing the complexity of the optimization problem and losing the structural performance, the optimization result that meets the draft constraint can be explicitly obtained.

[0048] It should be understood that the description of technical features, technical solutions, beneficial effects or similar language in this application does not imply that all features and advantages can be realized in any single embodiment. On the contrary, it is understood that the description of a feature or beneficial effect means that a specific technical feature, technical solution or beneficial effect is included in at least one embodiment. Therefore, the description of a technical feature, technical solution or beneficial effect in this specification does not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions and beneficial effects described in the present embodiment can also be combined in any appropriate manner. Those skilled in the art will understand that the embodiment can be implemented without one or more specific technical features, technical solutions or beneficial effects of a specific embodiment. In other embodiments, additional technical features and beneficial effects can also be identified in specific embodiments that do not embody all embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solution in this embodiment, the following is a brief introduction to the drawings required for the description of the embodiment. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0050] Figure 1 Schematic diagram of a geometric structure that should be avoided in a casting;

[0051] Figure 2 A schematic diagram of another type of geometric structure that should be avoided in castings is shown below;

[0052] Figure 3 A flowchart of an isogeometric topology optimization method based on H-product filtering provided in an embodiment of the present application;

[0053] Figure 4 An example diagram of a 2D structural unit arrangement provided in an embodiment of the present application;

[0054] Figure 5 A schematic diagram of a control point participating unit in a 2D isogeometric model with a NURBS order of 2 provided in an embodiment of the present application;

[0055] Figure 6 A schematic diagram of the design domain, applied loads, and boundary conditions of a 2D simply supported beam provided in an embodiment of the present application;

[0056] Figure 7 A schematic diagram of the relative density distribution of target units of a 2D simply supported beam provided in an embodiment of the present application;

[0057] Figure 8 A schematic diagram of a target topological configuration of a 2D simply supported beam provided in an embodiment of the present application;

[0058] Figure 9 A schematic diagram showing how the structural flexibility changes with the number of iterations during the optimization of a 2D simply supported beam according to an embodiment of the present application;

[0059] Figure 10 Schematic diagram of relative density distribution of 2D simply supported beam element obtained based on traditional density method;

[0060] Figure 11 Schematic diagram of the 2D simply supported beam topology obtained based on the traditional density method;

[0061] Figure 12 Schematic diagram of the change of structural flexibility with the number of iterations in the process of optimizing a 2D simply supported beam based on the traditional density method;

[0062] Figure 13A schematic diagram of an equal geometry topology optimization device based on H-filtering is provided for an embodiment of the present application.

[0063] Figure 14 A schematic diagram of a computer system of an electronic device is provided for an embodiment of the present application. DETAILED DESCRIPTION

[0064] In order for those skilled in the art to better understand the technical solutions of the present application, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings, and the description in this part is only exemplary and explanatory, and should not have any limiting effect on the protection scope of the present application. Specifically, the described embodiments are only a part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should belong to the protection scope of the present application.

[0065] It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device including a series of steps or units does not have to be limited to only those steps or units clearly listed, but can include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0066] In order to facilitate the understanding of the present application, first, a brief introduction of related art is given:

[0067] In casting, the castings are required to have certain geometric characteristics, otherwise the castings cannot be smoothly taken out of the mold, resulting in casting failure, wherein the geometric conditions that the castings need to meet are called demolding constraints. The direction of taking out the castings is called the taking-out (parting) direction, and the opposite direction is the demolding (stripping) direction. As shown in Figure 1 and Figure 2 shown, which respectively show the geometric structures that the two castings should avoid, i.e. internal holes and recesses perpendicular to the demolding direction.

[0068] Under the framework of density method, the main methods to realize casting constraints include adjacent density constraints, re-parameterization, and auxiliary physical models. Adjacent density constraints will introduce a large number of constraints, increasing the calculation cost. The re-parameterization method uses different mapping strategies to re-parameterize the design variables according to the castability requirements, and the obtained results are the results after re-parameterization, which need to be processed to obtain the material distribution of the structure. And the above all forcibly require the following unit relative density distribution:

[0069] 1≥ρ1≥ρ2≥...≥ρ n ≥0;

[0070] Among them, ρ i (i=1,2,...n) is the relative density of the elements in the draft direction. The smaller i is, the closer the position is to the far end of the mold. Although this forced method is effective, in practice, we only need the relative density of the high-density elements to meet the following requirements:

[0071] |ρ i -ρ i-1 |≤ε;

[0072] Here, ε is an artificially small value. Therefore, the aforementioned forced approach inevitably results in a loss of structural performance. Furthermore, the auxiliary physics model requires the introduction of additional physical fields, increasing the complexity of the problem.

[0073] In view of this, the embodiments of the present application provide an isogeometric topology optimization method, apparatus, device, and medium based on H-product filtering. The method constructs parameter information based on the model of the structure to be optimized, uses the relative density of the control points of the structure to be optimized as the design variable, and takes minimizing the structural flexibility as the optimization goal; uses the volume fraction of the material as a constraint, constructs a preset isogeometric topology optimization model of the structure to be optimized, and calculates the sensitivity of the preset isogeometric topology optimization model. Based on the sensitivity, the design variables of the preset isogeometric topology optimization model are updated using an optimization criterion method until the preset convergence conditions are met, thereby obtaining a target isogeometric topology optimization model. Then, based on the target isogeometric topology optimization model, the target unit density distribution and the target topological configuration are obtained. By introducing constraints into the filtering process of the design variables, the problem of introducing a large number of constraints in topology optimization is solved. Without increasing the complexity of the optimization problem or losing structural performance, the optimization result that satisfies the draft constraints can be explicitly obtained.

[0074] In order to make the technical solution of this application clearer and easier to understand, the application scenarios corresponding to this application are introduced below.

[0075] In order to make the technical solution of the present application clearer and easier to understand, the isogeometric topology optimization method based on H-product filtering provided in the embodiment of the present application is introduced below.

[0076] like Figure 3 As shown in FIG, this figure is a flow chart of an isogeometric topology optimization method based on H-product filtering provided in this embodiment, the method comprising the following steps:

[0077] S101, constructing parameter information of a model of the structure to be optimized, using the relative density of control points of the structure to be optimized as a design variable, minimizing structural flexibility as an optimization goal, and using the volume fraction of the material as a constraint, to construct a preset isogeometric topology optimization model of the structure to be optimized;

[0078] Specifically, based on the isogeometric analysis model of the structure to be optimized, the finite element mesh discretized design domain is used, the relative density of the control points of the structure to be optimized is used as the design variable, the relationship between the design variable x and the corresponding unit relative density ρ and the Young's modulus E is established, the first unit relative density and Young's modulus of the structure to be optimized are obtained, the first unit relative density is subjected to H-product filtering and threshold projection processing to obtain the second unit relative density of the structure to be optimized, parameter information, the control point relative density, the second unit relative density and the Young's modulus are constructed based on the model, the control point relative density of the structure to be optimized is used as the design variable, the minimum structural flexibility is used as the optimization goal, and the volume fraction of the material is used as the constraint to construct a preset isogeometric topology optimization model of the structure to be optimized. Among them, the structure to be optimized is the design structure of the part to be cast, and the model construction parameter information may include the NURBS basis function of the control point, the H-product kernel, the projection curvature control parameter and the projection threshold, and may also include a penalty factor, the Young's modulus of the standard solid material, the preset minimum Young's modulus, and also include a global displacement vector, an overall stiffness matrix, a global force vector, a unit displacement vector, a unit stiffness matrix, a material volume, a design domain volume, a volume fraction, the number of units and the number of control points. The specific settings and adjustments are made according to the actual situation and are not specifically limited here.

[0079] S102, calculating the sensitivity of the preset isogeometric topology optimization model;

[0080] Specifically, the sensitivity of the objective function corresponding to the preset isogeometric topology optimization model is calculated based on the model construction parameter information. Since the embodiment of the present application takes the minimum structural flexibility as the optimization goal, the structural flexibility function is used as the objective function to calculate the sensitivity of the objective function.

[0081] S103, updating the design variables of the preset isogeometric topology optimization model using an optimization criterion method based on the sensitivity until a preset convergence condition is met, thereby obtaining a target isogeometric topology optimization model;

[0082] Specifically, based on the sensitivity, the optimization criterion method (OC method) is used to iteratively update the design variables of the preset isogeometric topology optimization model until a preset convergence condition is met, that is, the optimization design result of the preset isogeometric topology optimization model converges, and the preset isogeometric topology optimization model at this time is used as the target isogeometric topology optimization model. The preset convergence condition can be that the change in the design variable (i.e., the relative density of the control points) is less than a preset threshold or the number of iterations reaches a preset number. For example, the preset threshold can be set to 0.002, and the preset number can be set to 100 times. The specific values ​​can be set and adjusted according to actual conditions and are not specifically limited here.

[0083] S104: Based on the target isogeometric topology optimization model, obtain target unit relative density distribution and target topological configuration.

[0084] Specifically, based on the target isogeometric topology optimization model, the unit relative density corresponding to the obtained optimization result is obtained as the target unit relative density, and the topological configuration obtained after the result is cut with an isosurface having the same threshold as the projection threshold in the threshold projection processing process is the target topological configuration.

[0085] The isogeometric topology optimization method based on H-product filtering provided in the embodiment of the present application constructs parameter information based on the model of the structure to be optimized, takes the relative density of the control points of the structure to be optimized as the design variable, takes the minimum structural flexibility as the optimization goal, and takes the volume fraction of the material as the constraint. A preset isogeometric topology optimization model of the structure to be optimized is constructed, and the sensitivity of the preset isogeometric topology optimization model is calculated. Based on the sensitivity, the design variables of the preset isogeometric topology optimization model are updated using an optimization criterion method until the preset convergence conditions are met, thereby obtaining a target isogeometric topology optimization model. Then, based on the target isogeometric topology optimization model, the target unit density distribution and the target topological configuration are obtained. By introducing constraints into the filtering process of the design variables, the problem of introducing a large number of constraints in topology optimization is solved. Without increasing the complexity of the optimization problem or losing structural performance, an optimization result that satisfies the draft constraints can be explicitly obtained.

[0086] On the basis of the above embodiment, further, the parameter information of the model of the structure to be optimized is constructed, the relative density of the control points of the structure to be optimized is used as the design variable, the minimum structural flexibility is used as the optimization goal, and the volume fraction of the material is used as the constraint to construct a preset geometric topology optimization model of the structure to be optimized, including:

[0087] Based on the isogeometric analysis model, obtaining a first unit relative density of the structure to be optimized according to the relative density of the control points;

[0088] Specifically, the model construction parameter information includes the NURBS basis function of the control points, based on the isogeometric analysis model, according to the formula:

[0089]

[0090] Represents the relationship between the relative density of the control point and the relative density of the corresponding first unit; where ρ i is the relative density of the first unit of unit i, x j represents the relative density of control point j, is the NURBS basis function corresponding to the control point j, r and l refer to the order of the basis function along the ξ and η directions respectively, and are the parameter coordinates along the ξ and η directions at the center of unit i, respectively.

[0091] Performing H-product filtering and threshold projection processing on the first unit relative density to obtain a second unit relative density of the structure to be optimized;

[0092] Specifically, the model construction parameter information also includes the H-product kernel, the projection curvature control parameter and the projection threshold; according to the formula:

[0093]

[0094] Performing H-product filtering on the first unit relative density to obtain the intermediate unit relative density of the structure to be optimized; wherein, is the relative density of the intermediate units of the structure to be optimized, Θ is the H product core, P i is a unit relative density matrix with the same size as the H product kernel, and its central position is the first relative density ρ of unit i i , the values ​​at other positions are the first relative densities of the adjacent units of unit i in the structure to be optimized, and the operator (·) represents the H product (Hadamard product) of the matrix, that is, the multiplication of elements at the same position;

[0095] According to the formula:

[0096]

[0097] Performing threshold projection processing on the relative density of the intermediate unit to obtain the relative density of the second unit of the structure to be optimized; wherein, is the relative density of the second unit of the structure to be optimized, β is the projection curvature control parameter, δ is the projection threshold, is the relative density of the intermediate units of the structure to be optimized.

[0098] Based on the isogeometric analysis model, obtaining the Young's elastic modulus of the structure to be optimized according to the relative density of the second unit;

[0099] Specifically, the model construction parameter information also includes a penalty factor, a standard solid material Young's modulus, and a preset minimum Young's modulus; according to the formula:

[0100]

[0101] Obtain the Young's elastic modulus of the structure to be optimized; wherein, E i is the Young's modulus of the structure to be optimized, is the relative density of the second unit of the structure to be optimized, p is the penalty factor, E0 is the Young's modulus of elasticity of the standard solid material, E min is the preset minimum Young's modulus.

[0102] Based on the model construction parameter information, the relative density of the control points, the relative density of the second unit and the Young's elastic modulus, the relative density of the control points of the structure to be optimized is used as the design variable, the minimum structural flexibility is used as the optimization goal, and the volume fraction of the material is used as the constraint, a preset geometric topology optimization model of the structure to be optimized is constructed.

[0103] Specifically, the model construction parameter information also includes a global displacement vector, an overall stiffness matrix, a global force vector, a unit displacement vector, a unit stiffness matrix, a material volume, a design domain volume, a volume fraction, the number of units, and the number of control points; the preset geometric topology optimization model of the structure to be optimized is expressed as:

[0104]

[0105] Among them, c is the structural flexibility, U, K, and F represent the global displacement vector, the overall stiffness matrix, and the global force vector, respectively. is the relative density of the second unit of the structure to be optimized, E i is the Young's elastic modulus of the structure to be optimized, u i With k i are the unit displacement vector and the unit stiffness matrix respectively, V is the material volume, V0 is the design domain volume, VF represents the volume fraction, N and M are the number of units and the number of control points respectively.

[0106] Based on the above embodiment, further, the model construction parameter information includes NURBS basis functions of control points; accordingly, obtaining the first unit relative density of the structure to be optimized according to the relative density of the control points based on the isogeometric analysis model includes:

[0107] Based on the isogeometric analysis model, according to the formula:

[0108]

[0109] Represents the relationship between the relative density of the control point and the relative density of the corresponding first unit; where ρ i is the relative density of the first unit of unit i, x j represents the relative density of control point j, is the NURBS basis function corresponding to the control point j, r and l refer to the order of the basis function along the ξ and η directions respectively, and are the parameter coordinates along the ξ and η directions at the center of unit i, respectively.

[0110] Based on the above embodiment, the model construction parameter information further includes an H-product kernel, a projection curvature control parameter, and a projection threshold; accordingly, performing H-product filtering and threshold projection processing on the first unit relative density to obtain the second unit relative density of the structure to be optimized includes:

[0111] According to the formula:

[0112]

[0113] Performing H-product filtering on the first unit relative density to obtain the intermediate unit relative density of the structure to be optimized; wherein, is the relative density of the intermediate units of the structure to be optimized, Θ is the H product core, P i is a unit relative density matrix with the same size as the H product kernel, and its central position is the first relative density ρ of unit i i , the values ​​at other positions are the first relative densities of the adjacent units of unit i in the structure to be optimized, and the operator (·) represents the H product (Hadamard product) of the matrix, that is, the multiplication of elements at the same position;

[0114] Specifically, the size of the H-product kernel Θ for 3D structures is s×s×s, and the size of the 2D structure is s×s, where s is any odd number greater than 1. In the H-product kernel, except for the straight line units along the draft direction and passing through the center, the values ​​of other positions are 0. For example, Figure 4 In the 2D structure shown (where the index in the x and y directions corresponds to the index of the unit on the corresponding coordinate axis), the value is

[0115]

[0116] Where w is any constant greater than 0.

[0117] Similarly, for the positive 45° direction, we have:

[0118]

[0119] According to the formula:

[0120]

[0121] Performing threshold projection processing on the relative density of the intermediate unit to obtain the relative density of the second unit of the structure to be optimized; wherein, is the relative density of the second unit of the structure to be optimized, β is the projection curvature control parameter, δ is the projection threshold, is the relative density of the intermediate units of the structure to be optimized.

[0122] Specifically, the larger the value of the projection curvature control parameter β, the greater the curvature of the projection function curve. It is also an artificially set judgment standard for large-density units. Units with relative density greater than the projection threshold δ are large-density units. After projection, they approach 1, otherwise they approach 0. In this embodiment, the projection threshold δ is set to 0.5, and the projection curvature control parameter β is set to 2; of course, the projection threshold δ and the projection curvature control parameter β can also be set to other values, which can be set and adjusted according to actual conditions, and are not specifically limited here.

[0123] Based on the above embodiment, the model construction parameter information further includes a penalty factor, a standard solid material Young's modulus, and a preset minimum Young's modulus; accordingly, obtaining the Young's modulus of the structure to be optimized based on the relative density of the second unit based on the isogeometric analysis model includes:

[0124] According to the formula:

[0125]

[0126] Obtain the Young's elastic modulus of the structure to be optimized; wherein, E i is the Young's modulus of the structure to be optimized, is the relative density of the second unit of the structure to be optimized, p is the penalty factor, E0 is the Young's modulus of elasticity of the standard solid material, E min is the preset minimum Young's modulus.

[0127] Specifically, in the embodiment of the present application, the penalty factor p is set to 3; the preset minimum Young's modulus E min In order to avoid the occurrence of singularity in the stiffness matrix, the value of this embodiment is set to 10 -9 Of course, the penalty factor p and the preset minimum Young's modulus E min Both can be set and adjusted according to actual conditions.

[0128] On the basis of the above-mentioned embodiments, further, the model construction parameter information further comprises a global displacement vector, an overall stiffness matrix, a global force vector, an element displacement vector, an element stiffness matrix, a material volume, a design domain volume, a volume fraction, an element quantity and a control point quantity; correspondingly, based on the model construction parameter information, the control point relative density, the second element relative density and the Young's modulus, taking the control point relative density of a structure to be optimized as a design variable, taking the minimum structural flexibility as an optimization objective, taking the volume fraction of the material as a constraint, a preset equal geometric topology optimization model of the structure to be optimized is constructed, comprising:

[0129] The preset equal geometric topology optimization model of the structure to be optimized is expressed as:

[0130]

[0131] Wherein, c is the structural flexibility, U, K and F respectively represent the global displacement vector, the overall stiffness matrix and the global force vector, is the second element relative density of the structure to be optimized, E i is the Young's modulus of the structure to be optimized, u i and k i are respectively the element displacement vector and the element stiffness matrix, V is the material volume, V0 is the design domain volume, VF represents the volume fraction, N and M are respectively the element quantity and the control point quantity.

[0132] On the basis of the above-mentioned embodiments, further, the sensitivity of the preset equal geometric topology optimization model is calculated, comprising:

[0133] According to the formula:

[0134]

[0135] The sensitivity of the preset equal geometric topology optimization model is calculated; wherein, is the sensitivity of the preset equal geometric topology optimization model, c is the structural flexibility, x j is the relative density of the control point j, S j is the set of elements composed of the control point j, is the second element relative density of the structure to be optimized, p is a penalty factor, E0 is the standard solid material Young's modulus, E min is the preset minimum Young's modulus, u i is the element displacement vector, k0 is the element stiffness matrix, B is the strain-displacement matrix, D0 is the elastic coefficient matrix, the Jacobian matrices J1 and J2 are respectively the spatial variation relationship from the NURBS basis function parameter domain to the physical domain and from the integral domain to the parameter domain, ω a is the weight coefficient corresponding to the a-th Gauss integral point, Ng is the number of Gaussian integration points, is the relative density of the intermediate units of the structure to be optimized, β is the projection curvature control parameter, δ is the projection threshold, θ i,t is the value of the corresponding position of unit t relative to unit i in the H product core, is the NURBS basis function corresponding to the control point j, and are the parameter coordinates along the ξ and η directions at the center of unit i, respectively.

[0136] Specifically, if Figure 5 As shown, S i represents the set of cells with non-zero H-product cores near cell i. In addition, for 2D structures, D0 under plane stress is defined as follows:

[0137]

[0138] For 3D structures, D0 is defined as:

[0139]

[0140] Wherein, μ is the Poisson's ratio of the material, and in this embodiment, its value is set to 0.3, and can be specifically set and adjusted according to actual conditions.

[0141] In addition, for volume constraints, there are:

[0142]

[0143] Where c is the structural flexibility, is the relative density of the second unit of the structure to be optimized, and N is the number of units.

[0144] In order to prove the objective technical effect of the present invention, a specific example is used below to verify the technical effect of the present invention:

[0145] like Figure 6 The simply supported beam structure shown in FIG1 has its bottom ends completely fixed, a vertical downward unit load F is applied to the middle of the upper portion, and the draft direction is vertically downward. A two-dimensional second-order NURBS is used to construct an isogeometric model, and the design domain is discretized into 60×20. The value of w in the H product kernel Θ is 0.5. The structure is optimized according to the method and steps described in the above embodiment of the present invention. When the relative density change of the control point is less than 0.002 or the number of iterations reaches 100, the optimization is terminated. The unit relative density distribution of the optimization result is shown in FIG1. Figure 7 As shown, after the result is cut with the isosurface with the same threshold and δ as 0.5, the resulting topological configuration is as follows Figure 8 As shown, for example Figure 10 and Figure 11The density method is directly used to optimize the results shown in the figure. The structure obtained in this application can be easily manufactured by casting. During the optimization process, the iterative curve of the present invention is as follows Figure 9 As shown, the density method iteration curve is as follows Figure 12 As shown in the figure, the final structural flexibility values ​​are 129.2640 and 154.4342 respectively. Compared with the traditional density method, the structural flexibility of the isogeometric topology optimization method based on H-product filtering provided by the present invention is reduced by 16.30%. From the results of this specific example, it is not difficult to see that the isogeometric topology optimization method based on H-product filtering provided by this application solves the problem of introducing a large number of constraints in topology optimization by introducing constraints into the filtering process of design variables. Without increasing the complexity of the optimization problem or compromising structural performance, it can explicitly obtain optimization results that meet the draft constraints.

[0146] Combined with the above Figure 3-12 The isogeometric topology optimization method based on H-product filtering provided in the embodiment of the present application is introduced in detail. The isogeometric topology optimization device, electronic device and computer-readable storage medium provided in the embodiment of the present application will be introduced in conjunction with the accompanying drawings.

[0147] like Figure 13 As shown in FIG, this figure is a schematic diagram of an isogeometric topology optimization device based on H-product filtering provided by the present application, and the device includes:

[0148] A construction module 201 is configured to construct parameter information based on a model of a structure to be optimized, using the relative density of control points of the structure to be optimized as a design variable, minimizing structural flexibility as an optimization goal, and using the volume fraction of the material as a constraint to construct a preset isogeometric topology optimization model of the structure to be optimized;

[0149] A calculation module 202 is used to calculate the sensitivity of the preset geometric topology optimization model;

[0150] An updating module 203 is configured to update the design variables of the preset isogeometric topology optimization model using an optimization criterion method based on the sensitivity until a preset convergence condition is satisfied, thereby obtaining a target isogeometric topology optimization model;

[0151] The processing module 204 is configured to obtain a target unit density distribution and a target topological configuration based on the target isogeometric topology optimization model.

[0152] The isogeometric topology optimization device provided in the embodiment of the present application can correspond to executing the isogeometric topology optimization method based on H product filtering described in the embodiment of the present application, and the above functions of each module of the device correspond to realizing Figure 3 For the sake of brevity, the corresponding process of the method shown will not be repeated here.

[0153] An embodiment of the present application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the isogeometric topology optimization method based on H-product filtering as described in the above embodiment is implemented.

[0154] like Figure 14 As shown, the computer system 300 of the electronic device includes a CPU 301, which can perform various appropriate actions and processes according to the programs stored in the ROM 302 or the programs loaded from the storage unit 308 into the RAM 303. The RAM 303 also stores various programs and data required for system operation. The CPU 301, ROM 302, and RAM 403 are connected to each other via a bus 304. An I / O interface 305 is also connected to the bus 304. Here, CPU 301 represents a central processing unit, ROM 302 represents a read-only memory, RAM 403 represents a random access memory, and I / O represents input / output.

[0155] The following components are connected to the I / O interface 305: an input section 306 including a keyboard, a mouse, and the like; an output section 307 including devices such as a cathode ray tube, a liquid crystal display, and a speaker; a storage section 308 including devices such as a hard disk; and a communication section 309 including a network interface card such as a LAN card or a modem. The communication section 309 performs communication processing via a network such as the Internet. A drive 310 is also connected to the I / O interface 305 as needed. Removable media 311, such as a magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory, is installed in the drive 310 as needed, so that computer programs read from the media can be installed in the storage section 308 as needed.

[0156] In particular, the process of the isogeometric topology optimization method based on H-product filtering described in the above embodiment can be implemented as a computer software program. For example, an embodiment of the present application includes a computer program product, which includes a computer program carried on a computer-readable storage medium, and the computer program contains program code for executing the isogeometric topology optimization method based on H-product filtering described in the above embodiment. In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 309, and / or installed from the removable medium 311. When the computer program is executed by the CPU 301, the above functions defined in the present computer system 300 are executed.

[0157] An embodiment of the present application also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the isogeometric topology optimization method based on H-product filtering as described in the above embodiment is implemented.

[0158] Specifically, the computer-readable storage medium may be included in the electronic device described in the above embodiments, or may exist independently and not be incorporated into the electronic device. The computer-readable storage medium carries one or more programs. When executed by the electronic device, the one or more programs enable the electronic device to implement the isogeometric topology optimization method based on H-product filtering as described in the above embodiments.

[0159] It should be noted that the computer-readable storage medium described in this application may be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. Computer-readable storage media may include, for example, but are not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or components, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to, an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical fiber, a portable compact disk read-only memory, an optical storage device, a magnetic storage device, or any suitable combination thereof. In this application, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device, or component. Furthermore, in this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. This propagated data signal may take a variety of forms, including, but not limited to, electromagnetic signals, optical signals, or any suitable combination thereof.

[0160] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. The above is only the preferred implementation method of this application. It should be pointed out that due to the limitations of textual expression, there are objectively infinite specific structures. For ordinary technicians in this technical field, without departing from the principles of the present invention, they can also make several improvements, modifications or changes, and can also combine the above technical features in an appropriate manner; these improvements, modifications, changes or combinations, or the direct application of the inventive concept and technical solution to other occasions without improvement, should be regarded as the scope of protection of this application.

Claims

1. An isogeometric topology optimization method based on H-product filtering, characterized in that: include: According to the model construction parameter information of the structure to be optimized, the relative density of the control points of the structure to be optimized is used as the design variable, the minimum structural flexibility is used as the optimization goal, and the volume fraction of the material is used as the constraint to construct a preset geometric topology optimization model of the structure to be optimized; Calculating the sensitivity of the preset isogeometric topology optimization model; Based on the sensitivity, the design variables of the preset isogeometric topology optimization model are updated using an optimization criterion method until a preset convergence condition is satisfied, thereby obtaining a target isogeometric topology optimization model; Based on the target isogeometric topology optimization model, obtaining target unit relative density distribution and target topological configuration; The method constructs parameter information based on the model of the structure to be optimized, takes the relative density of the control points of the structure to be optimized as the design variable, takes the minimum structural flexibility as the optimization goal, and takes the volume fraction of the material as the constraint to construct a preset geometric topology optimization model of the structure to be optimized, including: Based on the isogeometric analysis model, obtaining a first unit relative density of the structure to be optimized according to the relative density of the control points; Performing H-product filtering and threshold projection processing on the first unit relative density to obtain a second unit relative density of the structure to be optimized; Based on the isogeometric analysis model, obtaining the Young's elastic modulus of the structure to be optimized according to the relative density of the second unit; Based on the model construction parameter information, the relative density of the control points, the relative density of the second unit, and the Young's elastic modulus, a preset isogeometric topology optimization model of the structure to be optimized is constructed with the relative density of the control points of the structure to be optimized as a design variable, with minimizing structural flexibility as an optimization goal, and with the volume fraction of the material as a constraint; The model construction parameter information also includes an H-product kernel, a projection curvature control parameter, and a projection threshold. Accordingly, performing H-product filtering and threshold projection processing on the first unit relative density to obtain the second unit relative density of the structure to be optimized includes: According to the formula: Performing H-product filtering on the first unit relative density to obtain the intermediate unit relative density of the structure to be optimized; wherein, is the relative density of the intermediate units of the structure to be optimized, Θ is the H product core, P i is a unit relative density matrix with the same size as the H product kernel, and its central position is the first relative density ρ of unit i i , the values ​​at other positions are the first relative densities of the adjacent units of unit i in the structure to be optimized, and the operator (·) represents the H product (Hadamard product) of the matrix, that is, the multiplication of elements at the same position; According to the formula: Performing threshold projection processing on the intermediate unit relative density to obtain the second unit relative density of the structure to be optimized; wherein, is the relative density of the second unit of the structure to be optimized, β is the projection curvature control parameter, δ is the projection threshold, is the relative density of the intermediate units of the structure to be optimized.

2. The method according to claim 1, characterized in that The model construction parameter information includes NURBS basis functions of control points; accordingly, the first unit relative density of the structure to be optimized is obtained according to the relative density of the control points based on the isogeometric analysis model, including: Based on the isogeometric analysis model, according to the formula: Represents the relationship between the relative density of the control point and the relative density of the corresponding first unit; where ρ i is the relative density of the first unit of unit i, x j represents the relative density of control point j, is the NURBS basis function corresponding to the control point j, r and l refer to the order of the basis function along the ξ and η directions respectively, and are the parameter coordinates along the ξ and η directions at the center of unit i, respectively.

3. The method according to claim 2, characterized in that The model construction parameter information also includes a penalty factor, a standard solid material Young's modulus, and a preset minimum Young's modulus. Accordingly, the Young's modulus of the structure to be optimized is obtained based on the relative density of the second unit based on the isogeometric analysis model, including: According to the formula: Obtain the Young's elastic modulus of the structure to be optimized; wherein, E i is the Young's modulus of the structure to be optimized, is the relative density of the second unit of the structure to be optimized, p is the penalty factor, E0 is the Young's modulus of elasticity of the standard solid material, E min is the preset minimum Young's modulus.

4. The method according to claim 3, characterized in that The model construction parameter information also includes a global displacement vector, an overall stiffness matrix, a global force vector, a unit displacement vector, a unit stiffness matrix, a material volume, a design domain volume, a volume fraction, a number of units, and a number of control points. Accordingly, based on the model construction parameter information, the relative density of the control points, the relative density of the second unit, and the Young's elastic modulus, a preset isogeometric topology optimization model of the structure to be optimized is constructed with the relative density of the control points of the structure to be optimized as a design variable, the minimum structural flexibility as an optimization goal, and the volume fraction of the material as a constraint, including: The preset isogeometric topology optimization model of the structure to be optimized is expressed as: Among them, c is the structural flexibility, U, K, and F represent the global displacement vector, the overall stiffness matrix, and the global force vector, respectively. is the relative density of the second unit of the structure to be optimized, E i is the Young's elastic modulus of the structure to be optimized, u i With k i are the unit displacement vector and the unit stiffness matrix respectively, V is the material volume, V0 is the design domain volume, VF represents the volume fraction, N and M are the number of units and the number of control points respectively.

5. The method according to claim 4, characterized in that The calculating the sensitivity of the preset isogeometric topology optimization model includes: According to the formula: Calculating the sensitivity of the preset isogeometric topology optimization model; wherein, is the sensitivity of the preset geometric topology optimization model, c is the structural flexibility, x j is the relative density of control point j, S j is the set of control point j participating in constituting the unit, is the relative density of the second unit of the structure to be optimized, p is the penalty factor, E0 is the Young's modulus of elasticity of the standard solid material, E min is the preset minimum Young's modulus, u i is the unit displacement vector, k0 is the unit stiffness matrix, B is the strain-displacement matrix, D0 is the elastic coefficient matrix, the Jacobian matrices J1 and J2 are the spatial variation relationships from the NURBS basis function parameter domain to the physical domain and from the integral domain to the parameter domain, respectively, ω a is the weight coefficient corresponding to the ath Gaussian integral point, N g is the number of Gaussian integration points, is the relative density of the intermediate units of the structure to be optimized, β is the projection curvature control parameter, δ is the projection threshold, θ i,t is the value of the corresponding position of unit t relative to unit i in the H product core, is the NURBS basis function corresponding to the control point j, and are the parameter coordinates along the ξ and η directions at the center of unit i, respectively.

6. An isogeometric topology optimization device based on H-product filtering, characterized in that: include: A construction module is used to construct parameter information according to the model of the structure to be optimized, use the relative density of the control points of the structure to be optimized as the design variable, minimize the structural flexibility as the optimization goal, and use the volume fraction of the material as the constraint to construct a preset geometric topology optimization model of the structure to be optimized; A calculation module, used for calculating the sensitivity of the preset geometric topology optimization model; An updating module is used to update the design variables of the preset isogeometric topology optimization model using an optimization criterion method based on the sensitivity until a preset convergence condition is met to obtain a target isogeometric topology optimization model; A processing module, configured to obtain a target unit density distribution and a target topological configuration based on the target isogeometric topology optimization model; The method constructs parameter information based on the model of the structure to be optimized, takes the relative density of the control points of the structure to be optimized as the design variable, takes the minimum structural flexibility as the optimization goal, and takes the volume fraction of the material as the constraint to construct a preset geometric topology optimization model of the structure to be optimized, including: Based on the isogeometric analysis model, obtaining a first unit relative density of the structure to be optimized according to the relative density of the control points; Performing H-product filtering and threshold projection processing on the first unit relative density to obtain a second unit relative density of the structure to be optimized; Based on the isogeometric analysis model, obtaining the Young's elastic modulus of the structure to be optimized according to the relative density of the second unit; Based on the model construction parameter information, the relative density of the control points, the relative density of the second unit, and the Young's elastic modulus, a preset isogeometric topology optimization model of the structure to be optimized is constructed with the relative density of the control points of the structure to be optimized as a design variable, with minimizing structural flexibility as an optimization goal, and with the volume fraction of the material as a constraint; The model construction parameter information also includes an H-product kernel, a projection curvature control parameter, and a projection threshold. Accordingly, performing H-product filtering and threshold projection processing on the first unit relative density to obtain the second unit relative density of the structure to be optimized includes: According to the formula: Performing H-product filtering on the first unit relative density to obtain the intermediate unit relative density of the structure to be optimized; wherein, is the relative density of the intermediate units of the structure to be optimized, Θ is the H product core, P i is a unit relative density matrix with the same size as the H product kernel, and its central position is the first relative density ρ of unit i i , the values ​​at other positions are the first relative densities of the adjacent units of unit i in the structure to be optimized, and the operator (·) represents the H product (Hadamard product) of the matrix, that is, the multiplication of elements at the same position; According to the formula: Performing threshold projection processing on the intermediate unit relative density to obtain the second unit relative density of the structure to be optimized; wherein, is the relative density of the second unit of the structure to be optimized, β is the projection curvature control parameter, δ is the projection threshold, is the relative density of the intermediate units of the structure to be optimized.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the method according to any one of claims 1 to 5 is implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 5 is implemented.

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