H-product filtering-based isogeometric topology optimization method, apparatus and device, and medium

Abstract

The invention provides an isogeometric topology optimization method and device based on H-product filtering, equipment and a medium, and relates to the technical field of structure topology optimization, and the method comprises the steps: building parameter information according to a model of a to-be-optimized structure, taking the relative density of control points of the to-be-optimized structure as a design variable, and taking the minimum structure flexibility as an optimization target, and obtaining a design model of the to-be-optimized structure; constructing a preset isogeometric topology optimization model by taking the volume fraction of the material as a constraint, calculating the sensitivity of the preset isogeometric topology optimization model, updating the design variable by adopting an optimization criterion method based on the sensitivity until a preset convergence condition is met, and obtaining a target isogeometric topology optimization model based on the obtained target isogeometric topology optimization model. And obtaining target unit density distribution and a target topological configuration. By introducing the constraint condition into the filtering process of the design variable, the problem that a large number of constraints are introduced into topological optimization is solved, and the optimization result meeting the draft constraint can be explicitly obtained while the complexity of the optimization problem is not increased and the structural performance is not lost.

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, device, equipment 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 is required to have certain geometric features, otherwise the casting cannot be removed from the mold smoothly, resulting in casting failure. As an efficient, general and flexible structural optimization design method, since the topological optimization method of continuum structure based on homogenization was proposed, topological optimization has gradually attracted widespread attention from scholars, and topological optimization methods such as density method, level set method, and progressive structure method have emerged. And with the deepening of research, topological optimization can now handle most structural optimization design problems and can give good design results, but the analysis model used by the traditional finite element method is an approximation of the original geometric body, 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 optimal 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 for topological optimization design. The optimized structure obtained by topological optimization without considering manufacturing constraints is generally more complex and is 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] At present, the density method is often used for topological optimization design considering casting constraints. Under the framework of the density method, the main methods for realizing casting constraints include adjacent density constraints, reparameterization, and auxiliary physical models. Adjacent density constraints will introduce a large number of constraints and increase the computational cost; the reparameterization method uses different mapping strategies to reparameterize the design variables according to the castability requirements. The result is the result after reparameterization, which needs to be processed in a certain way to obtain the material distribution of the structure; and the auxiliary physical model needs to introduce additional physical fields, which increases 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, so as 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, taking the relative density of control points of the structure to be optimized as a design variable, taking the minimum structural flexibility as an optimization goal, and taking 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 by using an optimization criterion method until a preset convergence condition is met to obtain a target isogeometric topology optimization model;

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

[0012] According to the technical solution provided by the present application, the parameter information is constructed according to the model 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, including:

[0013] Based on the isogeometric analysis model, obtaining the 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 to construct a preset isogeometric topology optimization model of the structure to be optimized.

[0017] According to the technical solution provided by the present application, the model construction parameter information includes the NURBS basis function of the control point; accordingly, the first unit relative density of the structure to be optimized is obtained based on the relative density of the control point 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 basis function orders 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 the present application, the model construction parameter information also includes an H-product kernel, a projection curvature control parameter and a projection threshold; accordingly, the H-product filtering and threshold projection processing are performed on the first unit relative density to obtain the second unit relative density of the structure to be optimized, including:

[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 other 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 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.

[0028] According to the technical solution provided by the present 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 isogeometric analysis model according to the relative density of the second unit, 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 elastic 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 elastic modulus of the standard solid material, E min is the preset minimum Young's modulus.

[0032] According to the technical solution provided by the present 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 an optimization goal, and the volume fraction of the material is used as a constraint to construct a preset isogeometric topology optimization model of the structure to be optimized, 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 by the present 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 an optimization goal, and the volume fraction of the material is used as a constraint to construct a preset isogeometric topology optimization model of the structure to be optimized, including:

[0037] The preset isogeometric topology optimization model of the structure to be optimized is expressed as:

[0038]

[0039] 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.

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

[0041] A construction module is used to construct parameter information according to the model of the structure to be optimized, take the relative density of the control points of the structure to be optimized as the design variable, take the minimum structural flexibility as the optimization goal, take the volume fraction of the material as the constraint, and construct a preset isogeometric topology optimization model of the structure to be optimized;

[0042] A calculation module, used for calculating the sensitivity of the preset isogeometric topology optimization model;

[0043] An updating module, used for updating the design variables of the preset isogeometric topology optimization model by using an optimization criterion method based on the sensitivity until a preset convergence condition is met to obtain a target isogeometric topology optimization model;

[0044] The processing module is used to obtain the target unit density distribution and the target topological configuration based on the target isogeometric topological 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 embodiment of the present application provides an isogeometric topology optimization method, device, 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, and the optimization results that meet the draft constraints can be explicitly obtained without increasing the complexity of the optimization problem and losing the structural performance.

[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 features or beneficial effects means that specific technical features, technical solutions or beneficial effects are included in at least one embodiment. Therefore, the description of technical features, technical solutions or beneficial effects 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 realized 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 a specific embodiment that does not embody all embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solution in this embodiment, the drawings required for use in the description of the embodiment will be briefly introduced below. 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 paying creative work.

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

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

[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 a 2D simply supported beam design domain, applied loads and boundary conditions provided in an embodiment of the present application;

[0056] Figure 7 A schematic diagram of 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] Fig. 9 A schematic diagram showing the change of structural flexibility with the number of iterations in the process of optimizing a 2D simply supported beam provided in an embodiment of the present application;

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

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

[0061] Fig.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] Fig.13A schematic diagram of an isogeometric topology optimization device based on H-product filtering provided in an embodiment of the present application;

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

[0064] In order to enable those skilled in the art to better understand the technical solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings. The description in this section 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 embodiments of a part of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work should fall within the scope of protection of the present application.

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

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

[0067] In casting, the casting is required to have certain geometric features, otherwise the casting cannot be smoothly removed from the mold, resulting in casting failure. The geometric conditions that the casting needs to meet are called draft constraints. The direction in which the casting is taken out is called the removal (parting) direction, and its opposite direction is the draft (demolding) direction. Figure 1 and Figure 2 As shown, two geometric structures that should be avoided in castings are shown, namely internal holes and depressions perpendicular to the draft direction.

[0068] In the framework of density method, the main methods to realize casting constraints include adjacent density constraints, reparameterization, and auxiliary physical models. Adjacent density constraints will introduce a large number of constraints and increase the computational cost. The reparameterization method uses different mapping strategies to reparameterize the design variables according to the castability requirements. The result is the result after reparameterization, which requires certain processing to obtain the material distribution of the structure. The above all force 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 element 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 fact, we only need the relative density of the high-density element to meet the following requirements:

[0071] |ρ i -ρ i-1 |≤ε;

[0072] Among them, ε is a small value given artificially. Therefore, the above forced method will inevitably lose structural performance. The auxiliary physical model needs to introduce additional physical fields, which increases the complexity of the problem.

[0073] In view of this, the embodiment of the present application provides an isogeometric topology optimization method, device, 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, and takes the minimum structural flexibility as the optimization target; takes 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, and updates the design variables of the preset isogeometric topology optimization model based on the sensitivity using the optimization criterion method until the preset convergence condition is met, and obtains the target isogeometric topology optimization model, and then obtains the target unit density distribution and the target topological configuration based on the target isogeometric topology optimization model. 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, and the optimization results that meet the draft constraints can be explicitly obtained without increasing the complexity of the optimization problem and losing the structural performance.

[0074] In order to make the technical solution of the present application clearer and easier to understand, the application scenarios corresponding to the present 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 an embodiment of the present application is introduced below.

[0076] like Figure 3 As shown in FIG. 1 , the figure is a flow chart of an isogeometric topology optimization method based on H-product filtering provided in this embodiment, and the method comprises the following steps:

[0077] S101, constructing parameter information of the model of the structure to be optimized, taking the relative density of the control points of the structure to be optimized as the design variable, taking the minimum structural flexibility as the optimization target, and taking the volume fraction of the material as the constraint, constructing 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 elastic modulus of the structure to be optimized are obtained, the first unit relative density is subjected to H-product filtering and threshold projection processing, the second unit relative density of the structure to be optimized is obtained, parameter information, the control point relative density, the second unit relative density and the Young's elastic 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 taken as the optimization goal, and the volume fraction of the material is taken as the constraint, to construct a preset isogeometric topological optimization model of the structure to be optimized. Among them, the structure to be optimized is the design structure of the casting 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, a standard solid material Young's modulus, a 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 equal geometric topology optimization model is calculated based on the model construction parameter information. Since the optimization goal of the embodiment of the present application is to minimize the structural flexibility, the structural flexibility function is used as the objective function, and the sensitivity of the objective function is calculated.

[0081] S103, updating the design variables of the preset isogeometric topology optimization model by 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 implement iterative updates of the design variables of the preset isogeometric topology optimization model until the 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. Among them, the preset convergence condition package can be that the change amount of the design variable (that is, the relative density of the control point) 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 the actual situation, 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 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 is based on the model construction parameter information 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 the 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, and the optimization results that meet the draft constraints can be explicitly obtained without increasing the complexity of the optimization problem and losing the structural performance.

[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 target, 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, including:

[0087] Based on the isogeometric analysis model, obtaining the 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 point, 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 basis function orders 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 building 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 other 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 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.

[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 building 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 elastic 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 elastic modulus 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 to construct a preset isogeometric topology optimization model of the structure to be optimized.

[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 isogeometric 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] On the basis of the above embodiment, further, 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:

[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 basis function orders 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] On the basis of the above embodiment, further, 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:

[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 other 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 indexes in the x and y directions correspond to the indexes of the cells on the corresponding coordinate axes), the values ​​are

[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 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.

[0122] Specifically, the larger the value of the projection curvature control parameter β is, the greater the curvature of the projection function curve is. It is also an artificially set judgment standard for high-density units. Units with relative density greater than the projection threshold δ are high-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] On the basis of the above embodiment, further, 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 isogeometric analysis model according to the relative density of the second unit, including:

[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 elastic 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 elastic modulus 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, its value is set to 10 in the embodiment of the present application. -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 embodiment, further, 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 control point relative density, the second unit relative density and the Young's elastic modulus, the control point relative density of the structure to be optimized is used as a design variable, the minimum structural flexibility is used as an optimization target, 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:

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

[0130]

[0131] 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.

[0132] On the basis of the above embodiment, further, the calculating the sensitivity of the preset isogeometric topology optimization model includes:

[0133] According to the formula:

[0134]

[0135] Calculate the sensitivity of the preset isogeometric topology optimization model; wherein, is the sensitivity of the preset equal geometry 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 elastic modulus 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, and 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. a is the weight coefficient corresponding to the ath Gaussian 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, 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 its value is set to 0.3 in this embodiment, 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 to verify the technical effect of the present invention as follows:

[0145] like Figure 6 The simply supported beam structure shown in the figure has two ends of its bottom completely fixed, and a unit load F is applied vertically downward in the middle of its upper part. 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 relative density distribution of the unit obtained by the optimization result is shown in Figure 7 As shown in the figure, the result is cut by an isosurface with the same threshold and δ of 0.5, and the resulting topological configuration is as follows Figure 8 As shown, for example Fig.10 and Fig.11The density method is directly used to optimize the results shown in the figure. The structure obtained in the present application can be easily manufactured by a casting method. During the optimization process, the iterative curve of the present invention is as follows Fig. 9 As shown, the density method iteration curve is as follows Fig.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%. It is not difficult to see from the results of this specific example that the isogeometric topology optimization method based on H-product filtering provided by the present 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 and losing structural performance, it is possible to explicitly obtain optimization results that meet the draft constraints.

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

[0147] like Fig.13 As shown, the 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 used to construct parameter information according to the model of the structure to be optimized, take the relative density of the control points of the structure to be optimized as the design variable, take the minimum structural flexibility as the optimization target, take the volume fraction of the material as the constraint, and construct a preset isogeometric topology optimization model of the structure to be optimized;

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

[0150] An updating module 203 is used to update the design variables of the preset isogeometric topology optimization model by using an optimization criterion method based on the sensitivity until a preset convergence condition is met to obtain a target isogeometric topology optimization model;

[0151] The processing module 204 is used to obtain a target unit density distribution and a target topological configuration based on the target isogeometric topological 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, wherein 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 Fig.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 program stored in the ROM 302 or the program loaded from the storage part 308 to the RAM 303. In the RAM 303, various programs and data required for system operation are also stored. The CPU 301, the ROM 302 and the RAM 403 are connected to each other through the bus 304. The I / O interface 305 is also connected to the bus 304. Among them, 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, etc.; an output section 307 including a cathode ray tube, a liquid crystal display, etc., and a speaker, etc.; a storage section 308 including a hard disk, etc.; and a communication section 309 including a network interface card such as a LAN card, a modem, etc. 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. A removable medium 311, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 310 as needed, so that a computer program read therefrom is installed into 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 CPU301, 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, on which a computer program is stored. 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 embodiment; or it may exist independently without being assembled into the electronic device. The above computer-readable storage medium carries one or more programs, and when the above one or more programs are executed by an electronic device, the electronic device implements the isogeometric topology optimization method based on H-product filtering as described in the above embodiment.

[0159] It should be noted that the computer-readable storage medium shown in the present application may be a computer-readable signal medium or a computer-readable storage medium or any combination of the above two. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory, a read-only memory, an erasable programmable read-only memory, an optical fiber, a portable compact disk read-only memory, an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, device or device. In the present application, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, in which a computer-readable program code is carried. This propagated data signal may take a variety of forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination of the above.

[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 its 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 and the objective existence of infinite specific structures, ordinary technicians in this technical field can make several improvements, modifications or changes without departing from the principles of the present invention, 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 by using an optimization criterion method until a preset convergence condition is met to obtain a target isogeometric topology optimization model; Based on the target isogeometric topology optimization model, the target unit relative density distribution and the target topological configuration are obtained.

2. The method according to claim 1, characterized in that The method of constructing parameter information according to the model of the structure to be optimized, taking the relative density of the control points of the structure to be optimized as the design variable, taking the minimum structural flexibility as the optimization goal, and taking the volume fraction of the material as the constraint, constructing a preset isogeometric topology optimization model of the structure to be optimized, includes: Based on the isogeometric analysis model, obtaining the 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, 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 isogeometric topology optimization model of the structure to be optimized.

3. The method according to claim 2, characterized in that 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: 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 basis function orders 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.

4. The method according to claim 3, characterized in that The model building 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 other 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.

5. The method according to claim 4, characterized in that The model building 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 isogeometric analysis model according to the relative density of the second unit, including: According to the formula: Obtain the Young's elastic modulus of the structure to be optimized; wherein, E i is the Young's elastic 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 elastic modulus of the standard solid material, E min is the preset minimum Young's modulus.

6. The method according to claim 5, 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, 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 an 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: 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.

7. The method according to claim 6, characterized in that The calculating the sensitivity of the preset isogeometric topology optimization model includes: According to the formula: Calculate the sensitivity of the preset isogeometric topology optimization model; wherein, is the sensitivity of the preset equal geometry 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 elastic modulus 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, and 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. 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.

8. 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, take the relative density of the control points of the structure to be optimized as the design variable, take the minimum structural flexibility as the optimization goal, take the volume fraction of the material as the constraint, and construct a preset isogeometric topology optimization model of the structure to be optimized; A calculation module, used for calculating the sensitivity of the preset isogeometric topology optimization model; An updating module, used for updating the design variables of the preset isogeometric topology optimization model by using an optimization criterion method based on the sensitivity until a preset convergence condition is met to obtain a target isogeometric topology optimization model; The processing module is used to obtain the target unit density distribution and the target topological configuration based on the target isogeometric topological optimization model.

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

10. 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 7 is implemented.

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