Size Control Method and Device in Multi-Material Topology Optimization Based on Density Method

Abstract

The embodiments of the present application disclose a size control method and device in multi-material topology optimization based on the density method. A projection variable field is constructed based on the variable field of the engineering structure, and the first type of constraint conditions and the second type of constraint conditions are constructed based on the projection variables of each phase material of the engineering structure. Then, under multiple first type of constraint conditions and at least one second type of constraint conditions, the value of the variable field is optimized by using a gradient-based optimization algorithm, so that the target property of the engineering structure reaches the optimum, achieving the purpose of controlling the maximum size of each phase material of the engineering structure during the topology optimization of the engineering structure composed of multi-materials, and improving the manufacturability and diversity of the engineering structure.

Description

Technical Field

[0001] The present application relates to the technical field of engineering structure design, and more specifically, to a method and device for size control in multi-material topology optimization based on the density method. Background Technique

[0002] Topology optimization technology has become the most effective lightweight and performance design tool in engineering fields such as aerospace. So far, topology optimization has been mainly implemented based on optimization frameworks such as the density method, the structural progressive method, or the level set method. For practical engineering problems, the topology optimization method based on the density method framework has been more widely used.

[0003] An important aspect of topology optimization is to control the size of engineering structures. The control of engineering structure size not only stems from the limitations of manufacturing processes but also includes indirect requirements in design. Engineering structure size control includes maximum member size control and minimum member size control, and can also be divided into solid size control and hole size control. Currently, in the topology optimization method under the density method optimization framework, considering the size control of single-material engineering structures cannot meet the requirements of topology optimization for considering the size control of multi-material engineering structures. Summary of the Invention

[0004] The purpose of the present application is to provide a method and device for size control in multi-material topology optimization based on the density method, including the following technical solutions:

[0005] A method for size control in multi-material topology optimization based on the density method, the method includes:

[0006] Obtain a variable field of the engineering structure to be optimized, where different variables in the variable field correspond to different units of the engineering structure; the engineering structure is composed of multiple-phase materials, and the variables are used to describe whether any one of the multiple-phase materials exists in the corresponding unit;

[0007] Based on the variable field, establish a projected variable field; wherein, the projected variables in the projected variable field of each phase material correspond one-to-one with the filtered variables in the filtered variable field of this phase material, and the projected variable field is obtained by processing the filtered variable field through a projection function; the filtered variable field of each phase material is obtained from the variable field and a filtering matrix of this phase material;

[0008] Utilize a gradient-based optimization algorithm to optimize the values of the variable field under multiple first-type constraints and at least one second-type constraint, so that the target attribute of the engineering structure reaches the optimal; wherein,

[0009] The multiple first - type constraint conditions include: the mass of the engineering structure calculated based on the projection variable field is less than or equal to the upper mass limit; the volume of the same - phase material calculated based on the projection variables of each unit corresponding to the same - phase material is less than or equal to the upper volume limit; the variables in the variable field are greater than zero and less than or equal to 1.

[0010] The at least one second - type constraint condition includes at least one of the following multiple second - type constraint conditions: for the i - th unit, the first porosity of the i - th unit calculated based on the projection variables of each unit corresponding to the same - phase material within the target search region centered on the i - th unit is greater than or equal to the lower first - porosity limit; the second porosity of the i - th unit calculated based on the projection variables of each unit corresponding to each phase material within the target search region is greater than or equal to the lower second - porosity limit; the material ratio of the i - th unit calculated based on the projection variables of each unit corresponding to each phase material within the target search region is greater than or equal to the lower material - ratio limit.

[0011] In the above method, preferably, the first porosity of the i - th unit calculated based on the projection variables of each unit corresponding to the j - th phase material within the target search region centered on the i - th unit is greater than or equal to the lower first - porosity limit, which includes:

[0012]

[0013] Or,

[0014]

[0015] Wherein,

[0016]

[0017]

[0018]

[0019] ξ ij represents the first porosity of the i - th unit calculated based on the projection variables of each unit corresponding to the j - th phase material within the target search region centered on the i - th unit; ξ L，j represents the lower first - porosity limit; Ω i ={1, 2,..., N}, where N is the total number of units within the target search region centered on the i - th unit; v k represents the volume of the k - th unit; represents the projection variable of the k - th unit corresponding to the j - th phase material; p is a preset penalty factor; p qis the exponent of the preset p-mean aggregation function; n is the number of units included in the engineering structure.

[0020] In the above method, preferably, the second porosity of the i-th unit calculated based on the projection variables of each unit within the target search region centered on the i-th unit is greater than or equal to the lower limit of the second porosity, and it includes:

[0021]

[0022] Or,

[0023]

[0024] Among them,

[0025]

[0026]

[0027]

[0028] ζ i represents the second porosity of the i-th unit calculated based on the projection variables of each unit within the target search region centered on the i-th unit; ζ L，0 represents the lower limit of the second porosity; Ω i = {1, 2,..., N}, where N is the total number of units within the target search region centered on the i-th unit; v k represents the volume of the k-th unit; represents the projection variable of the k-th unit corresponding to the j-th phase material; p is a preset penalty factor; p q is the exponent of the preset p-mean aggregation function; n is the number of units included in the engineering structure.

[0029] In the above method, preferably, the material ratio of the i-th unit calculated based on the projection variables of each unit within the target search region centered on the i-th unit is greater than or equal to the lower limit of the material ratio, and it includes:

[0030]

[0031] Or,

[0032]

[0033] Among them,

[0034]

[0035]

[0036]

[0037] Ψ i represents the material ratio of the i-th unit calculated based on the projection variables of each unit within the target search area centered on the i-th unit; Ψ L represents the lower limit of the material ratio; Ω i ={1, 2,..., N}, where N is the total number of units within the target search area centered on the i-th unit; v k represents the volume of the k-th unit; represents the projection variable of the k-th unit corresponding to the j-th phase material; p is a preset penalty factor; p q is the exponent of the preset p-mean aggregation function; n is the number of units included in the engineering structure.

[0038] For the above method, preferably, the multiple second-type constraint conditions further include at least one of the following three constraint conditions:

[0039] The first constraint condition:

[0040]

[0041]

[0042]

[0043] The second constraint condition:

[0044]

[0045]

[0046]

[0047] The third constraint condition:

[0048]

[0049]

[0050] Among them, is the filtering field variable of the i-th unit corresponding to the j-th phase material; is the preset threshold corresponding to the j-th phase material; is the preset upper limit value of the entity constraint corresponding to the j-th phase material; represents the projection variable of the i-th unit corresponding to the j-th phase material; is a preset parameter; R fThe filtering radius used to generate the filtering matrix for density; The spatial gradient of the i-th unit corresponding to the j-th phase material; The spatial gradient of the i-th unit corresponding to the overall engineering structure; The Hadamard product; The spatial perturbations added in the X, Y, and Z directions respectively; The spatial increments in the X, Y, and Z directions under the influence of spatial perturbations respectively; The preset threshold corresponding to the i-th unit; The upper limit value of the entity constraint corresponding to the i-th unit; η d The threshold in the projection function; ε MinV The upper limit value of the hole constraint corresponding to the i-th unit; n is the number of units included in the engineering structure; m is the number of materials included in the engineering structure.

[0051] In the above method, preferably, if the at least one second type of constraint condition includes a target constraint condition, and the target constraint condition includes at least one of the first constraint condition, the second constraint condition, and the third constraint condition, the use of the gradient-based optimization algorithm to optimize the value of the variable field under multiple first type of constraint conditions and at least one second type of constraint condition includes:

[0052] Initialize the variable field to obtain an initial variable field;

[0053] Establish a projected variable field based on the initial variable field;

[0054] Calculate the dispersion of the newly established projected variable field;

[0055] If the dispersion is less than the dispersion threshold, use the gradient-based optimization algorithm to perform one optimization on the value of the variable field under the multiple first type of constraint conditions and the at least one second type of constraint condition;

[0056] If the dispersion is greater than or equal to the dispersion threshold, use the gradient-based optimization algorithm to perform one optimization on the value of the variable field under the non-target constraint conditions among the multiple first type of constraint conditions and the at least one second type of constraint condition;

[0057] Establish a new projected variable field based on the optimized variable field, and return to execute the step of calculating the dispersion of the newly established projected variable field until the optimization end condition is met.

[0058] In the above method, preferably, the target search area is any one of a circular area, an elliptical area, and a rectangular area; or,

[0059] The target search area is any one of a spherical area, an ellipsoidal area, and a cuboid area;

[0060] The shapes of the target search areas centered on different units are the same or different.

[0061] In the above method, preferably, the method further includes:

[0062] In the case where the target property of the engineering structure needs to be calculated based on the Young's modulus of each unit of the engineering structure, for the i-th unit, interpolating the Young's modulus of each phase material for the i-th unit to obtain the Young's modulus interpolation result of the i-th unit;

[0063] Calculating the target property of the engineering structure based on the Young's modulus interpolation results of each unit of the engineering structure.

[0064] In the above method, preferably, the process of interpolating the Young's modulus of each phase material for the i-th unit to obtain the Young's modulus interpolation result of the i-th unit includes:

[0065] Based on the attention weights of each phase material for the i-th unit, weighted summing the Young's modulus of each phase material to obtain the Young's modulus interpolation result of the i-th unit;

[0066] Among them, the attention weight of the i-th unit to the j-th phase material is calculated by the following formula:

[0067]

[0068] where λ ij is the attention weight of the i-th unit to the j-th phase material; represents the projection variable of the i-th unit corresponding to the j-th phase material; represents the projection variable of the i-th unit corresponding to the ξ-th phase material; p is a penalty factor; m is the number of materials included in the engineering structure.

[0069] A size control device in multi-material topology optimization based on the density method, the device includes:

[0070] An acquisition module for acquiring a variable field of an engineering structure to be optimized, where different variables in the variable field correspond to different units of the engineering structure; the engineering structure is composed of multiple phase materials, and the variable is used to describe whether any one of the multiple phase materials exists in the corresponding unit;

[0071] A building module, configured to build a projected variable field based on the variable field; wherein, the projected variables in the projected variable field of each phase material correspond one-to-one with the filtered variables in the filtered variable field of this phase material, and the projected variable field is obtained by processing the filtered variable field through a projection function; the filtered variable field of each phase material is obtained from the variable field of this phase material and a filtering matrix;

[0072] An optimization module, configured to optimize the value of the variable field under multiple first-type constraint conditions and at least one second-type constraint condition by using a gradient-based optimization algorithm, so that the target property of the engineering structure reaches the optimum; wherein,

[0073] The multiple first-type constraint conditions include: the mass of the engineering structure calculated based on the projected variable field is less than or equal to the mass upper limit; the volume of the same phase material calculated based on the projected variables of each unit corresponding to the same phase material is less than or equal to the volume upper limit; the variables in the variable field are greater than zero and less than or equal to 1;

[0074] The at least one second-type constraint condition includes at least one of the following multiple second-type constraint conditions: for the i-th unit, the first porosity of the i-th unit calculated based on the projected variables of each unit corresponding to the same phase material within the target search area centered on the i-th unit is greater than or equal to the first porosity lower limit; the second porosity of the i-th unit calculated based on the projected variables of each unit corresponding to each phase material within the target search area is greater than or equal to the second porosity lower limit; the material ratio of the i-th unit calculated based on the projected variables of each unit corresponding to each phase material within the target search area is greater than or equal to the material ratio lower limit.

[0075] An electronic device, comprising:

[0076] A memory, configured to store a program;

[0077] A processor, configured to call and execute the program in the memory, and implement each step of the dimension control method in the multi-material topology optimization based on the density method as described in any one of the above.

[0078] A readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, each step of the dimension control method in the multi-material topology optimization based on the density method as described in any one of the above is implemented.

[0079] As can be seen from the above solution, a size control method and device in multi-material topology optimization based on the density method provided by the present application constructs a projection variable field based on the variable field of the engineering structure, constructs the first type of constraint condition and the second type of constraint condition based on the projection variables of each phase material of the engineering structure, and then, under multiple first type of constraint conditions and at least one second type of constraint condition, uses a gradient-based optimization algorithm to optimize the values of the variable field, so that the target attributes of the engineering structure reach the optimum, achieving the purpose of controlling the maximum size of each phase material of the engineering structure during the topology optimization of the engineering structure composed of multi-materials, and improving the manufacturability and diversity of the engineering structure. Description of the Drawings

[0080] To more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0081] Figure 1 It is a flowchart of an implementation of the size control method in multi-material topology optimization based on the density method provided by the embodiments of the present application;

[0082] Figure 2a It is an example diagram of a circular search area constructed with the i-th unit x i as the center;

[0083] Figure 2b It is an example diagram of an elliptical search area constructed with the i-th unit x i as the center;

[0084] Figure 2c It is an example diagram of a rectangular search area constructed with the i-th unit x i as the center;

[0085] Figure 3a It is an example diagram of an engineering structure to be optimized provided by the embodiments of the present application;

[0086] Figure 3b It is for the embodiments of the present application Figure 3a An example diagram of the effect of controlling the maximum physical size of each phase material of the shown engineering structure;

[0087] Figure 3c It is for the embodiments of the present application Figure 3a An example diagram of the effect of controlling the maximum physical size of Material 1 of the shown engineering structure;

[0088] Figure 3d An example diagram of the effect of controlling the maximum material size for the overall engineering structure provided by the embodiment of the present application; Figure 3a

[0089] Figure 3e An example diagram of the effect of controlling the maximum material size for the overall engineering structure and each phase material provided by the embodiment of the present application; Figure 3a

[0090] Figure 4a An example diagram of the effect of controlling the maximum material size for the overall engineering structure to be optimized provided by the embodiment of the present application;

[0091] Figure 4b An example diagram of the effect of controlling the maximum material size for the overall engineering structure to be optimized and controlling the minimum material size for Material 1 provided by the embodiment of the present application; Figure 4a

[0092] Figure 4c An example diagram of the effect of controlling the maximum and minimum material sizes for the overall engineering structure to be optimized provided by the embodiment of the present application; Figure 4a

[0093] Figure 5a Another example diagram of the engineering structure to be optimized provided by the embodiment of the present application;

[0094] Figure 5b An example diagram of the effect of controlling the maximum hole size for the overall engineering structure shown provided by the embodiment of the present application; Figure 5a

[0095] Figure 5c Another example diagram of the effect of controlling the maximum hole size for the overall engineering structure shown provided by the embodiment of the present application; Figure 5a

[0096] Figure 5d Another example diagram of the effect of controlling the maximum hole size for the overall engineering structure shown provided by the embodiment of the present application; Figure 5a

[0097] Figure 6a Another example diagram of the engineering structure to be optimized provided by the embodiment of the present application;

[0098] Figure 6b An example diagram of the effect of controlling the minimum material size for Material 1 of the engineering structure shown provided by the embodiment of the present application; Figure 6a

[0099] Figure 6c ​​​​​​​​An effect example diagram provided by an embodiment of the present application for controlling the minimum entity size of the overall engineering structure shown Figure 6a ;

[0100] Figure 6d An effect example diagram provided by an embodiment of the present application for controlling the minimum hole size of the overall engineering structure shown Figure 6a ;

[0101] Figure 6e An effect example diagram provided by an embodiment of the present application for controlling the minimum entity size and the minimum hole size of the overall engineering structure shown Figure 6a ;

[0102] Figure 7 A structural schematic diagram of a size control device in multi-material topology optimization based on the density method provided by an embodiment of the present application

[0103] Figure 8 A structural schematic diagram of an electronic device provided by an embodiment of the present application

[0104] Terms such as "first", "second", "third", "fourth", etc. (if any) in the specification, claims and the above-mentioned drawings are used to distinguish similar parts, and do not necessarily describe a specific order or sequence. It should be understood that such used data can be interchanged under appropriate circumstances so that the embodiments of the present application described herein can be implemented in an order other than that illustrated herein Specific embodiments

[0105] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the protection scope of the present application

[0106] As Figure 1 shown, a flowchart of an implementation of a size control method in multi-material topology optimization based on the density method provided by an embodiment of the present application may include:

[0107] Step S101: Obtain the variable field of the engineering structure to be optimized

[0108] Among them, different variables in the variable field correspond to different units of the engineering structure; the engineering structure is composed of multi-phase materials, and each variable is used to describe whether any one of the above multi-phase materials exists in the corresponding unit

[0109] The engineering structure to be optimized can be an engineering structure in the field of aerospace, or an engineering structure in other engineering fields (such as, the field of ocean engineering, the field of rail transit, etc.).

[0110] The engineering structure can be subjected to finite element mesh division to obtain a number of elements of the engineering structure. Each element is located within a grid. Each element of the engineering structure is characterized by a variable to obtain a variable field of the engineering structure. Each variable is used to describe whether any one of the above-mentioned multiphase materials exists in the element corresponding to the variable. Assuming that the engineering structure is composed of m-phase materials, each variable has m + 1 possible values, and each value characterizes that the element corresponding to the variable does not contain any one of the above-mentioned m-phase materials (i.e., a hole), or characterizes that the element corresponding to the variable contains one of the above-mentioned m-phase materials.

[0111] The optimization objective of this application is to determine the optimal value of each variable.

[0112] Step S102: Establish a projection variable field based on the variable field of the engineering structure.

[0113] Among them, the projection variables in the projection variable field of each phase material correspond one-to-one with the filtering variables in the filtering variable field of the phase material. The projection variable field is obtained by processing the filtering variable field through a projection function; the filtering variable field of each phase material is obtained from the variable field of the phase material and a filtering matrix.

[0114] Optionally, for the j-th phase material, from the variable field x of the j-th phase material (j) to obtain the filtering variable field of the j-th phase material The process can be expressed by the formula as follows:[[]]

[0115]

[0116] Among them, n is the number of designable elements in the engineering structure to be optimized; x ij is the design variable of the i-th element of the engineering structure to be optimized corresponding to the j-th phase material, and its value characterizes whether the i-th element contains the j-th phase material;

[0117] is the filtering matrix;

[0118] W ik is the weight coefficient of the k-th element with respect to the i-th element, and its expression is:[[]]

[0119]

[0120] w ik = max{R f - d ik , 0} (3)

[0121] Among them, V k is the volume of the k-th unit, R f is the pre-given filtration radius, d ik is the center distance between the k-th unit and the i-th unit.

[0122] After obtaining the filtration variable field of the j-th phase material it is possible to process the filtration variable field through a projection function to obtain the projection variable field of the j-th phase material As an example, the Heaviside function can be used to process the filtration variable field to obtain the projection variable field of the j-th phase material which can be expressed by the formula as:

[0123]

[0124]

[0125] Among them, β is used to control the steepness of the projection, which is a parameter to be optimized and its value will be updated during the optimization process. Optionally, at the initial stage of optimization, the value of β is relatively small, indicating that the steepness of the projection is relatively small, and at the later stage of optimization, the value of β is relatively large, indicating that the steepness of the projection is relatively large. η is a preset threshold. As an example, the value of η can be 0.5.

[0126] Step S103: Using a gradient-based optimization algorithm, optimize the value of the variable field under multiple first-type constraint conditions and at least one second-type constraint condition, so that the target property of the engineering structure reaches the optimum.

[0127] Optionally, the target property may include but is not limited to at least one of the following: the overall stiffness of the engineering structure, or the heat transfer capacity, or the deformation capacity, or the stress level, etc.

[0128] Taking the overall stiffness of the engineering structure as an example, the overall stiffness of the engineering structure can be characterized by the overall compliance of the engineering structure. The lower the overall compliance of the engineering structure, the higher the overall stiffness of the engineering structure is characterized. Otherwise, the higher the overall compliance of the engineering structure, the lower the overall stiffness of the engineering structure is characterized. The overall compliance of the engineering structure to be optimized can be expressed by the formula as:

[0129] C = F T u(6)

[0130] F = Ku(7)

[0131] Among them, C represents the overall compliance of the engineering structure to be optimized; F is the load vector of the engineering structure to be optimized; u is the displacement vector of each element of the engineering structure to be optimized under the action of the above load; K is the stiffness matrix of the engineering structure to be optimized.

[0132] The overall compliance of the engineering structure to be optimized reaching the optimum includes: the overall compliance C of the engineering structure to be optimized is the smallest.

[0133] The gradient-based optimization algorithm can be any of the following algorithms: the gradient-based GCMMA (The globally convergent version of the method of moving asymptot) optimization algorithm, the gradient-based ConLin (Convex Linearization) optimization algorithm, the gradient-based MDPA (MCL (Markov cluster algorithm) differential privacy algorithm) optimization algorithm, the gradient-based SLP (The method of sequential linear programming) optimization algorithm, the gradient-based QP (Quadratic programming) optimization algorithm. Among them, the specific process of optimization using the gradient-based optimization algorithm can refer to the existing optimization process, which will not be elaborated here.

[0134] Among them, multiple first-type constraint conditions can include:

[0135] First-type constraint condition 1: The mass of the engineering structure to be optimized calculated based on the projected variable field is less than or equal to the mass upper limit. It can be expressed by the formula:

[0136]

[0137] Among them, is the mass of the engineering structure to be optimized calculated based on the projected variable field; ρ (j) represents the density of the j-th phase material; V i is the volume of the i-th element; is the mass upper limit of the engineering structure to be optimized; n is the number of elements included in the engineering structure to be optimized; m is the number of materials included in the engineering structure to be optimized.

[0138] First-type constraint condition 2: The volume of the same-phase material calculated based on the projected variables corresponding to each element of the same-phase material is less than the volume upper limit. It can be expressed by the formula:

[0139]

[0140] Among them, represents the volume of the j-th phase material calculated based on the projection variables of each unit corresponding to the j-th phase material; V i is the volume of the i-th unit; is the upper volume limit corresponding to the j-th phase material. The upper volume limit corresponding to each phase material can be determined according to actual design requirements.

[0141] The first type of constraint condition 3: The variables in the variable field are greater than zero and less than or equal to 1. Optionally, the initial values of the variables in the variable field can all be set to 0.1.

[0142] In an optional embodiment, when the calculation of the target attribute involves the stiffness matrix of the engineering structure, in order to avoid singularity of the stiffness matrix during the optimization process, a lower limit of the design variable is introduced, that is, the variables in the variable field are greater than the lower limit of the design variable and less than or equal to 1. As an example, the lower limit of the design variable can be 10 -3 .

[0143] At least one of the above-mentioned second type of constraint conditions includes at least one of the following multiple second type of constraint conditions:

[0144] The second type of constraint condition 1: For each unit (for the convenience of description, denoted as the i-th unit), the first porosity of the i-th unit calculated based on the projection variables of the units corresponding to the same phase material within the target search area centered on the i-th unit is greater than or equal to the lower limit of the first porosity. This second type of constraint condition is used to control the maximum solid size of each phase material of the engineering structure to be optimized, and can be called the maximum solid size control constraint considering a single phase material.

[0145] In the embodiments of the present application, a target search area related to the unit is established with each unit as the center.

[0146] When the optimization of the engineering structure belongs to a two-dimensional plane optimization problem, the target search area can be any one of a circular search area, an elliptical search area, and a rectangular search area.

[0147] When the optimization of the engineering structure belongs to a three-dimensional solid optimization problem, the target search area can be any one of a spherical search area, an ellipsoidal search area, and a cuboid search area.

[0148] Whether it is a two-dimensional plane optimization problem or a three-dimensional solid optimization problem, the shapes of the target search areas centered on different units can be the same or different.

[0149] Such as Figures 2a - 2c shown, Figure 2a is the x of the i-th unit provided by the embodiments of the present application iExample diagram of a circular search area constructed centered thereon; Figure 2b For the i-th unit x provided in the embodiment of the present application i Example diagram of an elliptical search area constructed centered thereon; Figure 2c For the i-th unit x provided in the embodiment of the present application i Example diagram of a rectangular search area constructed centered thereon.

[0150] Figures 2a - 2c Among them, each square grid represents a unit, where □ represents a hole, represents Material 1, represents Material 2.

[0151] Figure 2a The circular area shown can be expressed by the formula:

[0152]

[0153] Among them, and are the coordinates of the center of the i-th unit x i on the X-axis and Y-axis respectively; and are the coordinates of the center of the k-th unit in the circular area on the X-axis and Y-axis respectively; R Max is the radius of the pre-given circular area, and the specific value is set according to actual design needs.

[0154] Figure 2b The elliptical area shown can be expressed by the formula:

[0155]

[0156] Among them, and are the coordinates of the center of the i-th unit x i on the X-axis and Y-axis respectively; and are the coordinates of the center of the k-th unit in the elliptical area on the X-axis and Y-axis respectively; a is the length of the major axis of the pre-given ellipse, b is the length of the minor axis of the pre-given ellipse; θ is the angle between the major axis of the ellipse and the X-axis. The sizes of the major and minor axes of the specific ellipse, and the angle between the major axis and the X-axis are set according to actual design needs.

[0157] As Figure 2c shown, the rectangular area is obtained by a combination of a circle and a straight line l. Among them, the circular area centered on the i-th unit x i can be determined by formula (10), and the expression of the straight line l passing through the i-th unit x i can be:

[0158]

[0159] Among them, and are the coordinates of the center of the i-th unit on the X-axis and Y-axis of x i respectively; and are the coordinates of the center of the k-th unit in the elliptical area on the X-axis and Y-axis respectively; α is the included angle between the straight line l and the X-axis, and the specific value is set according to the actual design requirements.

[0160] The rectangular area (essentially a quasi-rectangular area) obtained by mixing control based on a circle and a straight line l can be expressed by the formula:

[0161] d ik <R Max (13)

[0162]

[0163] Among them, d ik is the distance from the k-th unit to the i-th unit; is the distance from the i-th unit to the straight line l; is the preset upper limit of the distance.

[0164] The second type of constraint condition 2: The second porosity of the i-th unit calculated based on the projection variables of each unit corresponding to each phase material in the target search area is greater than or equal to the lower limit of the second porosity. This second type of constraint condition is used to control the overall maximum entity size of the engineering structure to be optimized, and can be called the maximum entity size control constraint considering the overall engineering structure.

[0165] The second type of constraint condition 3: The material ratio of the i-th unit calculated based on the projection variables of each unit corresponding to each phase material in the target search area is greater than or equal to the lower limit of the material ratio. This second type of constraint condition is used to control the overall maximum hole size of the engineering structure to be optimized, and can be called the maximum hole size control constraint considering the overall engineering structure.

[0166] Optionally, an implementation manner of optimizing the value of the variable field under multiple first-type constraint conditions and at least one second-type constraint condition by using the gradient-based optimization algorithm can be:

[0167] Initialize the variable field to obtain the initial variable field.

[0168] Establish a projection variable field based on the initial variable field.

[0169] Based on the newly established projection variable field, using a gradient-based optimization algorithm, the values of the latest variable field are optimized once under multiple first-type constraint conditions and at least one second-type constraint condition. Among them, the newly established projection variable field is the projection variable field established based on the latest variable field. When this step is executed for the first time, the latest variable field is the initial variable field. When this step is executed non-first time, the latest variable field is the optimized variable field obtained from the previous execution of this step.

[0170] If the optimization end condition is not satisfied, a new projection variable field is established based on the optimized variable field, and the process returns to execute the above step of optimizing the values of the variable field using a gradient-based optimization algorithm under multiple first-type constraint conditions and at least one second-type constraint condition until the optimization end condition is satisfied.

[0171] The size control method in the multi-material topology optimization based on the density method provided by the embodiments of the present application constructs a projection variable field based on the variable field of the engineering structure to be optimized, constructs first-type constraint conditions and second-type constraint conditions based on the projection variables of each phase material of the engineering structure, and then optimizes the values of the variable field using a gradient-based optimization algorithm under multiple first-type constraint conditions and at least one second-type constraint condition, so that the target attributes of the engineering structure reach the optimal, achieving the purpose of controlling the maximum size of each phase material of the engineering structure during the topology optimization of the engineering structure composed of multiple materials, and improving the manufacturability and diversity of the engineering structure.

[0172] In an optional embodiment, for the i-th (i = 1, 2,..., n) unit, the first porosity of the i-th unit calculated based on the projection variables of each unit corresponding to the j-th phase material within the target search region centered on the i-th unit being greater than or equal to the lower limit of the first porosity may include:

[0173]

[0174]

[0175] Among them, ζ ij represents the first porosity of the i-th unit calculated based on the projection variables of each unit corresponding to the j-th phase material within the target search region centered on the i-th unit; ζ L，j represents the lower limit of the first porosity; Ω i ={1, 2,..., N}, where N is the total number of units within the target search region centered on the i-th unit; v k represents the volume of the k-th unit; represents the projection variable of the k-th unit corresponding to the j-th phase material; p is a preset penalty factor.

[0176] The constraint conditions represented by Formulas (15)-(16) are to consider the maximum material condition size of the single-phase material to control the local constraint conditions (i.e., the constraint conditions corresponding to each element). Since each element corresponds to a local constraint condition, there will be many local constraint conditions, which will result in a relatively slow optimization rate. To improve the optimization rate, the p-mean aggregation function is used in this application to aggregate all the local constraints into a global single variable. According to the definition of the aggregation function, construct Its expression is:

[0177]

[0178] The expression of the p-mean aggregation function is:

[0179]

[0180] where p q is the exponent of the preset p-mean aggregation function.

[0181] According to Formulas (15)-(18), the global constraint condition considering the maximum material condition size of the j-th phase material can be determined:

[0182]

[0183] That is to say, based on the projection variables of each element corresponding to the j-th phase material within the target search area centered on the i-th element, the first porosity of the i-th element calculated to be greater than or equal to the lower limit of the first porosity can be represented by Formulas (15)-(16), or can also be represented by Formulas (17)-(19), where

[0184] In an optional embodiment, for the i-th (i = 1, 2,..., n) element, that the second porosity of the i-th element calculated based on the projection variables of each element corresponding to each phase material within the target search area centered on the i-th element is greater than or equal to the lower limit of the second porosity may include:

[0185]

[0186]

[0187] where ζ i represents the second porosity of the i-th element calculated based on the projection variables of each element within the target search area centered on the i-th element; ζ L，0 represents the lower limit of the second porosity; Ω i= {1, 2, ..., N}, where N is the total number of cells within the target search area centered on the i-th cell; v k represents the volume of the k-th cell; represents the projection variable of the k-th cell corresponding to the j-th phase material; p is a preset penalty factor.

[0188] The constraint conditions represented by formulas (20)-(21) are the maximum entity size control local constraint conditions (i.e., the constraint conditions corresponding to each cell) for all materials of the engineering structure to be optimized. Since each cell corresponds to a local constraint condition, there will be many local constraint conditions, which will result in a relatively slow optimization rate. To improve the optimization rate, the p-mean aggregation function is used in this application to aggregate all local constraints into a global single variable. According to the definition of the aggregation function, construct Its expression is:

[0189]

[0190] The expression of the p-mean aggregation function is:

[0191]

[0192] where p q is the exponent of the preset p-mean aggregation function.

[0193] According to formulas (20)-(23), the global constraint condition for the maximum entity size control of all materials of the engineering structure to be optimized can be determined:

[0194]

[0195] That is to say, the second porosity of the i-th cell calculated based on the projection variables of each cell corresponding to each phase material within the target search area centered on the i-th cell is greater than or equal to the lower limit of the second porosity, which can be represented by formulas (20)-(21), or can also be represented by formulas (22)-(24), where

[0196] In an optional embodiment, for the i-th (i = 1, 2, ……, n) cell, the material rate of the i-th cell calculated based on the projection variables of each cell corresponding to each phase material within the target search area centered on the i-th cell being greater than or equal to the lower limit of the material rate may include:

[0197]

[0198]

[0199] where Ψ iIt represents the material ratio of the \(i\)-th unit calculated based on the projection variables of each unit corresponding to each phase material within the target search area centered on the \(i\)-th unit; \(\varPsi\) L It represents the lower limit of the material ratio; \(\varOmega\) i \(=\{1, 2, \ldots, N\}\), where \(N\) is the total number of units within the target search area centered on the \(i\)-th unit; \(v\) k It represents the volume of the \(k\)-th unit; It represents the projection variable of the \(k\)-th unit corresponding to the \(j\)-th phase material; \(p\) is a preset penalty factor.

[0200] The constraint conditions represented by Formulas (25)-(26) are local constraint conditions for controlling the maximum hole size of all materials of the engineering structure to be optimized (i.e., the constraint conditions corresponding to each unit). Since each unit corresponds to a local constraint condition, there will be many local constraint conditions, which will cause the optimization rate to be relatively slow. To improve the optimization rate, in this application, a \(p\)-mean aggregation function is used to aggregate all local constraints into a global single variable. According to the definition of the aggregation function, \(m\) is constructed i \(\in[0, 1]\), and its expression is:

[0201]

[0202] The expression of the \(p\)-mean aggregation function is:

[0203]

[0204] According to Formulas (25)-(28), the global constraint conditions for controlling the maximum hole size of all materials of the engineering structure to be optimized can be determined:

[0205]

[0206] where \(p\) q is the exponent of the preset \(p\)-mean aggregation function.

[0207] That is to say, the material ratio of the \(i\)-th unit calculated based on the projection variables of each unit corresponding to each phase material within the target search area centered on the \(i\)-th unit being greater than or equal to the lower limit of the material ratio can be characterized by Formulas (25)-(26), or can also be characterized by Formulas (27)-(29), where

[0208] The above is an embodiment of controlling the maximum size of the entity and holes of the engineering structure. In addition to controlling the maximum size of the entity and holes of the engineering structure, this application can also control the minimum size of the entity and holes of the engineering structure. Based on this, the foregoing multiple second-type constraint conditions may further include at least one of the following three constraint conditions:

[0209] The first constraint condition is the minimum feature size control constraint for single-phase materials considering the engineering structure:

[0210]

[0211]

[0212]

[0213] Among them, is the filtering field variable of the i-th element corresponding to the j-th phase material; is the preset threshold corresponding to the j-th phase material; is the upper limit value of the entity constraint corresponding to the j-th phase material; represents the projection variable of the i-th element corresponding to the j-th phase material; is a preset parameter. As an example, the value can be 10 -4 ; R f is the filtering radius used to generate the aforementioned filtering matrix; is the spatial gradient of the i-th element corresponding to the j-th phase material; is the Hadamard product; are the spatial perturbations added in the X, Y, and Z directions respectively, and this perturbation is artificially added; are the spatial increments in the X, Y, and Z directions under the influence of the spatial perturbation respectively.

[0214] The second constraint condition is the minimum feature size control constraint considering the entire engineering structure:

[0215]

[0216]

[0217]

[0218] Among them, is the filtering field variable of the i-th element corresponding to the j-th phase material; is the preset threshold corresponding to the i-th element; is the upper limit value of the entity constraint corresponding to the i-th element; represents the projection variable of the i-th element corresponding to the j-th phase material; is a preset parameter. As an example, its value can be 10 -4 ; R f is the filtering radius used to generate the aforementioned filtering matrix; is the spatial gradient of the i-th element corresponding to the entire engineering structure; is the Hadamard product; Spatial perturbations increased in the X, Y, and Z directions respectively, which are artificially increased; Spatial increments in the X, Y, and Z directions respectively under the influence of spatial perturbations.

[0219] The third constraint condition, which is the minimum hole size control constraint considering the overall engineering structure:

[0220]

[0221]

[0222] Wherein, is the filtering field variable corresponding to the j-th phase material of the i-th unit; represents the projection variable corresponding to the j-th phase material of the i-th unit; is a preset parameter. As an example, its value can be 10 -4 ; R f is the filtering radius used to generate the aforementioned filtering matrix; is the spatial gradient corresponding to the overall engineering structure of the i-th unit; The calculation of is shown in formula (35); is the Hadamard product; η d is the threshold η in the projection function; ε MinV is the upper limit value of the hole constraint corresponding to the i-th unit preset.

[0223] In this application, the above at least one second type of constraint condition may include target constraint conditions (including at least one of the aforementioned first constraint condition, second constraint condition, and third constraint condition), or may not include target constraint conditions. In this application, if at least one second type of constraint condition includes target constraint conditions, one implementation manner of optimizing the value of the variable field under multiple first type of constraint conditions and at least one second type of constraint condition by using the gradient-based optimization algorithm can be:

[0224] Initialize the variable field to obtain the initial variable field.

[0225] Establish a projection variable field based on the initial variable field.

[0226] Calculate the dispersion of the newly established projection variable field. When this step is executed for the first time, the newly established projection variable field is the projection variable field established based on the initial variable field; when this step is executed non-first time, the newly established projection variable field is the projection variable field established based on the variable field obtained from the previous optimization.

[0227] If the dispersion is less than the dispersion threshold, based on the newly established projection variable field, using a gradient-based optimization algorithm, the values of the variable field are optimized once under multiple first-type constraint conditions and at least one second-type constraint condition. That is to say, only when the dispersion is less than the dispersion threshold, will the target constraint conditions be imposed on the engineering structure to optimize and control the minimum size of the engineering structure.

[0228] If the dispersion is greater than or equal to the dispersion threshold, based on the newly established projection variable field, using a gradient-based optimization algorithm, the values of the variable field are optimized once under multiple first-type constraint conditions and the non-target constraint conditions among at least one second-type constraint condition. That is to say, if the dispersion is greater than or equal to the dispersion threshold, the target constraint conditions will not be imposed on the engineering structure, that is, the minimum size optimization control of the engineering structure will not be carried out.

[0229] If the optimization end condition is not satisfied, a new projection variable field is established based on the optimized variable field, and the step of calculating the dispersion of the newly established projection variable field is returned and executed until the optimization end condition is satisfied.

[0230] If the optimization end condition is satisfied, the above optimization process is ended.

[0231] In practical application scenarios, the calculation of some target properties of the engineering structure (such as the overall stiffness of the engineering structure, etc.) involves the Young's modulus of each unit of the engineering structure. In order to make the size control of the engineering structure more accurate, the present application interpolates the Young's modulus of each unit. Specifically, the size control method in the multi-material topology optimization based on the density method provided by the present application may further include:

[0232] In the case where the target property of the engineering structure needs to be calculated based on the Young's modulus of each unit of the engineering structure, for each unit, the Young's modulus of each phase material is used to interpolate the unit to obtain the Young's modulus interpolation result of the unit.

[0233] Optionally, for the i-th unit, the Young's modulus of each phase material can be weighted and summed based on the attention weight of the i-th unit to each phase material to obtain the Young's modulus interpolation result of the i-th unit. It can be expressed by the formula:

[0234]

[0235]

[0236] where, E i is the Young's modulus interpolation result of the i-th unit; λ ij is the attention weight of the i-th unit to the j-th phase material; E (j) is the Young's modulus of the j-th phase material; Denote the projection variable of the $i$-th unit corresponding to the $j$-th phase material; Denote the projection variable of the $i$-th unit corresponding to the $\xi$-th phase material; $p$ is the penalty factor. As an example, the value of $p$ can be 3.

[0237] Calculate the target property of the engineering structure based on the interpolation results of the Young's modulus of each unit of the engineering structure.

[0238] To better illustrate the effect of the size control method in the multi-material topology optimization based on the density method of the present application, the following gives the effect example diagrams of size control of the engineering structure with the overall stiffness of the engineering structure as the optimization target under different second-class constraints. Among them, □ represents a hole, represents Material 1, represents Material 2, represents Material 3.

[0239] As shown in 3a, it is an example diagram of the engineering structure to be optimized provided by the embodiment of the present application. Figure 3a The described engineering structure involves two materials, namely Material 1 and Material 2.

[0240] As Figures 3b - 3e shown, it is an example diagram of the effect of maximum physical size control on the Figure 3a described engineering structure by the size control method in the multi-material topology optimization based on the density method of the present application. Among them,

[0241] Figure 3b is an example diagram of the effect provided by the embodiment of the present application for Figure 3a the maximum physical size control of each phase material of the engineering structure shown in Figure 3b (marked with in Figure 3a ). Specifically, it is based on considering the maximum physical size control constraint of Material 1 (that is, for each unit, the first porosity of the unit calculated based on the projection variables of each unit corresponding to Material 1 within the target search area centered on the unit is greater than or equal to the lower limit of the first porosity), and considering the maximum size control constraint of Material 2 (that is, for each unit, the first porosity of the unit calculated based on the projection variables of each unit corresponding to Material 2 within the target search area centered on the unit is greater than or equal to the lower limit of the first porosity). These two second-class constraints are used to Figure 3a carry out the effect example diagram of the maximum physical size control of the engineering structure shown.

[0242] Figure 3c is an example diagram of the effect provided by the embodiment of the present application for Figure 3a the maximum physical size control of Material 1 of the engineering structure shown in Figure 3c (marked with An exemplary diagram of an effect for the maximum material size control (marked with Figure 3a ), specifically, it is an exemplary diagram of the effect of maximum material size control on the engineering structure shown below, based on only considering the maximum material size control constraint of Material 1 (i.e., for each unit, the first porosity of the unit calculated based on the projection variables of Material 1 corresponding to each unit within the target search area centered on this unit is greater than or equal to the lower limit of the first porosity), which is a second - type constraint condition.

[0243] Figure 3d This is provided by an embodiment of the present application for Figure 3a the overall maximum material size control of the engineering structure shown below ( Figure 3d marked with in the figure), specifically, it is an exemplary diagram of the effect of maximum material size control on the engineering structure shown below, based on considering the overall maximum material size control constraint (i.e., for each unit, the second porosity of the unit calculated based on the projection variables of Material 1 corresponding to each unit within the target search area centered on this unit and the projection variables of Material 2 corresponding to each unit is greater than or equal to the lower limit of the second porosity), which is a second - type constraint condition. Figure 3a An exemplary diagram of the effect of maximum material size control on the engineering structure shown below.

[0244] Figure 3e This is provided by an embodiment of the present application for Figure 3a the overall maximum material size control of the engineering structure shown below and a single - phase material ( Figure 3e marked with in the figure), specifically, it is an exemplary diagram of the effect of maximum material size control on the engineering structure shown below by simultaneously considering the maximum size control constraints of the overall engineering structure and Material 1. That is to say, Figure 3a it is an exemplary diagram of the effect of maximum material size control on the engineering structure shown below based on considering the maximum material size control constraint of Material 1 (i.e., for each unit, the first porosity of the unit calculated based on the projection variables of Material 1 corresponding to each unit within the target search area centered on this unit is greater than or equal to the lower limit of the first porosity), and considering the overall maximum material size control constraint (i.e., for each unit, the second porosity of the unit calculated based on the projection variables of Material 1 corresponding to each unit within the target search area centered on this unit and the projection variables of each unit based on Material 2 is greater than or equal to the lower limit of the second porosity), which are two second - type constraint conditions. Figure 3e An exemplary diagram of the effect of maximum material size control on the engineering structure shown below. Figure 3a An exemplary diagram of the effect of maximum material size control on the engineering structure shown below.

[0245] Figure 4a This is provided by an embodiment of the present application for the overall maximum material size control of a certain engineering structure to be optimized ( Figure 4a marked with in the figure), Figure 4aThe engineering structure shown involves three materials, namely Material 1, Material 2, and Material 3. Figure 4a For the embodiment of this application, Figure 4a This is an example diagram of the effect of controlling the maximum material condition size of the entire engineering structure to be optimized involved, specifically based on considering the constraint of controlling the maximum material condition size of the whole (that is, for each unit, the second porosity of the unit calculated based on the projection variables of Material 1, the projection variables of Material 2, and the projection variables of Material 3 corresponding to each unit within the target search area centered on this unit is greater than or equal to the lower limit of the second porosity), which is a second - type constraint condition for Figure 4a the effect example diagram of controlling the maximum material condition size of the engineering structure shown. Since Figures 4a - 4c it is to illustrate the difference between only controlling the maximum size of the engineering structure and applying both maximum size control and minimum size control simultaneously, therefore, an example diagram of a certain engineering structure to be optimized involved is not given here. Figure 4a the example diagram of a certain engineering structure to be optimized involved.

[0246] Figure 4b For the embodiment of this application, Figure 4a This is an example diagram of the effect of controlling the maximum material condition size of the entire engineering structure to be optimized involved ( Figure 4b marked with ) and controlling the minimum material condition size of Material 1 ( Figure 4b marked with ), specifically based on considering the constraint of controlling the maximum material condition size of the whole (that is, for each unit, the second porosity of the unit calculated based on the projection variables of Material 1, the projection variables of Material 2, and the projection variables of Material 3 corresponding to each unit within the target search area centered on this unit is greater than or equal to the lower limit of the second porosity), and only considering the constraint of controlling the minimum material condition size of Material 1 (that is, the first constraint condition), these two second - type constraint conditions for Figure 4a the effect example diagram of controlling the material condition size of the engineering structure shown.

[0247] Figure 4c For the embodiment of this application, Figure 4a This is an example diagram of the effect of controlling the maximum material condition size of the entire engineering structure to be optimized involved ( Figure 4c marked with ) and controlling the minimum material condition size of the whole ( Figure 4c marked with An example diagram of an effect for a (marked) engineering structure, specifically based on considering the overall maximum entity size control constraint (i.e., for each unit, the second porosity of the unit calculated based on the projection variables of material 1, the projection variables of material 2, and the projection variables of material 3 corresponding to each unit within the target search area centered on this unit is greater than or equal to the lower limit of the second porosity), and considering the overall minimum entity size control constraint (i.e., the second constraint condition), these two second - type constraint conditions are applied to Figure 4a An example diagram of the effect of entity size control on the shown engineering structure.

[0248] As shown in 5a, it is another example diagram of the engineering structure to be optimized provided by the embodiment of the present application. Figure 5a The described engineering structure involves two materials, namely material 1 and material 2.

[0249] Figure 5b For the embodiment of the present application to Figure 5a An example diagram of the effect of maximum hole size control on the overall shown engineering structure ( Figure 5b marked with and ). Specifically, it is based on considering the overall maximum hole size control constraint (i.e., for each unit, the material rate of the unit calculated based on the projection variables of each phase material corresponding to each unit within the target search area centered on this unit is greater than or equal to the lower limit of the material rate).

[0250] Figure 5c For the embodiment of the present application to Figure 5a An example diagram of another effect of maximum hole size control on the overall shown engineering structure ( Figure 5c marked with MaxLSC - V in ).

[0251] Figure 5d For the embodiment of the present application to Figure 5a An example diagram of yet another effect of maximum hole size control on the overall shown engineering structure ( Figure 5d marked with MaxLSC - V in ).

[0252] Obviously, Figure 5c the holes in the maximum hole size control result shown are larger than Figure 5b the holes in the maximum hole size control result described; Figure 5d the holes in the maximum hole size control result shown are larger than Figure 5c the holes in the maximum hole size control result described.

[0253] The size of the holes in the maximum hole size control result is affected by the size of the target search area. Therefore, the size of the holes can be adjusted by adjusting the size of the target search area. For example, the target search area is a circular area, and the radii of the circular areas are r1, r2, and r3 in sequence, where r1 < r2 < r3. Then, for the overall engineering structure shown in Figure 5a the holes in the control result of the maximum hole size control are smaller than those in the control result of the maximum hole size control for the overall engineering structure shown in Figure 5a based on the circular target search area with a radius of r2. For the overall engineering structure shown in Figure 5a the holes in the control result of the maximum hole size control are smaller than those in the control result of the maximum hole size control for the overall engineering structure shown in Figure 5a based on the circular target search area with a radius of r3.

[0254] As shown in 6a, it is another example diagram of the engineering structure to be optimized provided by the embodiment of the present application. Figure 6a The described engineering structure involves two materials, namely Material 1 and Material 2.

[0255] Figure 6b For the embodiment of the present application, it is an example diagram of the effect of minimum feature size control ( Figure 6a marked with Figure 6b in ) for Material 1 of the engineering structure shown. Specifically, it is an example diagram of the effect of minimum feature size control for the engineering structure shown based on considering only one constraint condition, that is, the minimum feature size control constraint of Material 1 (i.e., the first constraint condition). Figure 6a

[0256] Figure 6c For the embodiment of the present application, it is an example diagram of the effect of minimum feature size control ( Figure 6a marked with Figure 6c in ) for the overall engineering structure shown. Specifically, it is an example diagram of the effect of minimum feature size control for the engineering structure shown based on considering only one constraint condition, that is, the minimum feature size control constraint of the overall (i.e., the second constraint condition). Figure 6a

[0257] Figure 6d For the embodiment of the present application, it is an example diagram of the effect of minimum hole size control ( Figure 6a marked with Figure 6d in ​​An example diagram of an effect for a (certain identifier), specifically an example diagram of the effect of controlling the minimum hole size for the Figure 6a shown engineering structure based on considering only one constraint condition, i.e., the overall minimum hole size control constraint (i.e., the third constraint condition).

[0258] Figure 6e This is an example diagram of the effect of controlling the minimum solid size for the overall Figure 6a shown engineering structure and controlling the minimum hole size for the overall Figure 6e in the identified) provided by an embodiment of the present application. Specifically, based on considering the overall minimum solid size control constraint (i.e., the second constraint condition) and the overall minimum hole size control constraint (i.e., the third constraint condition), these two constraint conditions are used to Figure 6e in the identified) for the shown engineering structure. This is an example diagram of the effect of controlling the minimum solid size. Figure 6a shown engineering structure.

[0259] Corresponding to the method embodiment, an embodiment of the present application also provides a size control device in multi-material topology optimization based on the density method. As Figure 7 shown, this is a schematic structural diagram of a size control device in multi-material topology optimization based on the density method provided by an embodiment of the present application, including:

[0260] an acquisition module 701, a construction module 702, and an optimization module 703; wherein,

[0261] The acquisition module 701 is used to acquire the variable field of the engineering structure to be optimized. Different variables in the variable field correspond to different units of the engineering structure. The engineering structure is composed of multiple-phase materials, and the variables are used to describe whether any one of the multiple-phase materials exists in the corresponding unit;

[0262] The construction module 702 is used to construct a projected variable field based on the variable field. Wherein, the projected variables in the projected variable field of each phase material correspond one-to-one with the filtering variables in the filtering variable field of this phase material. The projected variable field is obtained by processing the filtering variable field through a projection function. The filtering variable field of each phase material is obtained from the variable field of this phase material and a filtering matrix;

[0263] The optimization module 703 is used to optimize the values of the variable field under multiple first-class constraint conditions and at least one second-class constraint condition by using a gradient-based optimization algorithm, so that the target attribute of the engineering structure reaches the optimum; wherein,

[0264] The multiple first - type constraint conditions include: the mass of the engineering structure calculated based on the projection variable field is less than or equal to the upper mass limit; the volume of the same - phase material calculated based on the projection variables of each unit corresponding to the same - phase material is less than or equal to the upper volume limit; the variables in the variable field are greater than zero and less than or equal to 1.

[0265] The at least one second - type constraint condition includes at least one of the following multiple second - type constraint conditions: for the i - th unit, the first porosity of the i - th unit calculated based on the projection variables of each unit corresponding to the same - phase material within the target search region centered on the i - th unit is greater than or equal to the lower first - porosity limit; the second porosity of the i - th unit calculated based on the projection variables of each unit corresponding to each phase material within the target search region is greater than or equal to the lower second - porosity limit; the material ratio of the i - th unit calculated based on the projection variables of each unit corresponding to each phase material within the target search region is greater than or equal to the lower material - ratio limit.

[0266] The size - control device in the multi - material topology optimization based on the density method provided by the embodiments of the present application constructs a projection variable field based on the variable field of the engineering structure to be optimized, constructs the first - type constraint conditions and the second - type constraint conditions based on the projection variables of each phase material of the engineering structure, and then, under the multiple first - type constraint conditions and at least one second - type constraint condition, uses a gradient - based optimization algorithm to optimize the values of the variable field, so that the target attributes of the engineering structure reach the optimum, achieving the purpose of controlling the maximum size of each phase material of the engineering structure during the topology optimization of the engineering structure composed of multiple materials, and improving the manufacturability and diversity of the engineering structure.

[0267] The specific implementation processes of each module (i.e., the obtaining module 701, the establishing module 702, and the optimizing module 703) can refer to the foregoing method embodiments and will not be elaborated here.

[0268] Corresponding to the method embodiment, the present application also provides an electronic device. A schematic structural diagram of the electronic device is as Figure 8 shown, and may include: at least one processor 1, at least one communication interface 2, at least one memory 3, and at least one communication bus 4.

[0269] In the embodiments of the present application, the number of the processor 1, the communication interface 2, the memory 3, and the communication bus 4 is at least one, and the processor 1, the communication interface 2, and the memory 3 complete mutual communication through the communication bus 4.

[0270] The processor 1 may be a central processing unit (CPU), or an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application, etc.

[0271] The memory 3 may include a high-speed RAM memory, and may also include a non-volatile memory, such as at least one disk memory.

[0272] Among them, the memory 3 stores a program, and the processor 1 can call the program stored in the memory 3. The program is used for:

[0273] Obtaining a variable field of an engineering structure to be optimized, where different variables in the variable field correspond to different units of the engineering structure; the engineering structure is composed of multiphase materials, and the variables are used to describe whether any one of the multiphase materials exists in the corresponding unit;

[0274] Establishing a projection variable field based on the variable field; where, the projection variables in the projection variable field of each phase material correspond one-to-one with the filtering variables in the filtering variable field of this phase material, and the projection variable field is obtained by processing the filtering variable field through a projection function; the filtering variable field of each phase material is obtained from the variable field of this phase material and a filtering matrix;

[0275] Using a gradient-based optimization algorithm, under multiple first-type constraint conditions and at least one second-type constraint condition, optimizing the values of the variable field so that the target attribute of the engineering structure reaches the optimum; where,

[0276] The multiple first-type constraint conditions include: the mass of the engineering structure calculated based on the projection variable field is less than or equal to the mass upper limit; the volume of the same phase material calculated based on the projection variables of each unit corresponding to the same phase material is less than or equal to the volume upper limit; the variables in the variable field are greater than zero and less than or equal to 1;

[0277] The at least one second-type constraint condition includes at least one of the following multiple second-type constraint conditions: for the i-th unit, the first porosity of the i-th unit calculated based on the projection variables of each unit corresponding to the same phase material within a target search region centered on the i-th unit is greater than or equal to the first porosity lower limit; the second porosity of the i-th unit calculated based on the projection variables of each unit corresponding to each phase material within the target search region is greater than or equal to the second porosity lower limit; the material ratio of the i-th unit calculated based on the projection variables of each unit corresponding to each phase material within the target search region is greater than or equal to the material ratio lower limit.

[0278] Optionally, the refinement function and extension function of the program may refer to the above description.

[0279] The embodiment of the present application further provides a storage medium, which can store a program suitable for execution by a processor, and the program is used for:

[0280] Obtain the variable field of the engineering structure to be optimized, where different variables in the variable field correspond to different units of the engineering structure; the engineering structure is composed of multiphase materials, and the variable is used to describe whether any one of the multiphase materials exists in the corresponding unit;

[0281] Establish a projection variable field based on the variable field; wherein, the projection variables in the projection variable field of each phase material are in one-to-one correspondence with the filtering variables in the filtering variable field of this phase material, and the projection variable field is obtained by processing the filtering variable field through a projection function; the filtering variable field of each phase material is obtained from the variable field of this phase material and a filtering matrix;

[0282] Using a gradient-based optimization algorithm, under multiple first-type constraint conditions and at least one second-type constraint condition, optimize the values of the variable field so that the target attribute of the engineering structure reaches the optimal; wherein,

[0283] The multiple first-type constraint conditions include: the mass of the engineering structure calculated based on the projection variable field is less than or equal to the mass upper limit; the volume of the same phase material calculated based on the projection variables of each unit corresponding to the same phase material is less than or equal to the volume upper limit; the variables in the variable field are greater than zero and less than or equal to 1;

[0284] The at least one second-type constraint condition includes at least one of the following multiple second-type constraint conditions: for the i-th unit, the first porosity of the i-th unit calculated based on the projection variables of each unit corresponding to the same phase material within the target search area centered on the i-th unit is greater than or equal to the first porosity lower limit; the second porosity of the i-th unit calculated based on the projection variables of each unit corresponding to each phase material within the target search area is greater than or equal to the second porosity lower limit; the material ratio of the i-th unit calculated based on the projection variables of each unit corresponding to each phase material within the target search area is greater than or equal to the material ratio lower limit.

[0285] Optionally, the refinement function and extension function of the program may refer to the above description.

[0286] Those of ordinary skill in the art will realize that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are executed in hardware or software depends on the specific application and design constraints of the technical solution. A professional technician can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of this application.

[0287] In several embodiments provided in this application, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. Additionally, the couplings or direct couplings or communication connections shown or discussed among each other can be through some interfaces, and the indirect couplings or communication connections of devices or units can be in electrical, mechanical, or other forms.

[0288] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they can be located in one place, or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0289] In addition, in each embodiment of this application, the functional units can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit.

[0290] It should be understood that in the embodiments of this application, the dependent claims, each embodiment, and features can be combined with each other to achieve the solution of the aforementioned technical problems.

[0291] If the described functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in each embodiment of this application. The aforementioned storage medium includes: USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs and other various media that can store program codes.

[0292] The foregoing description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for size control in multi-material topology optimization based on density method, characterized in that, the method includes: obtaining a variable field of an engineering structure to be optimized, where different variables in the variable field correspond to different units of the engineering structure; the engineering structure is composed of multiple-phase materials, and the variables are used to describe whether any one of the multiple-phase materials exists in the corresponding unit; establishing a projected variable field based on the variable field; wherein, the projected variables in the projected variable field of each phase material correspond one-to-one with the filtered variables in the filtered variable field of this phase material, and the projected variable field is obtained by processing the filtered variable field through a projection function; the filtered variable field of each phase material is obtained from the variable field of this phase material and a filtering matrix; using a gradient-based optimization algorithm, under multiple first-type constraints and at least one second-type constraint, optimizing the values of the variable field so that the target property of the engineering structure reaches the optimum; wherein, the multiple first-type constraints include: the mass of the engineering structure calculated based on the projected variable field is less than or equal to the mass upper limit; the volume of the same phase material calculated based on the projected variables of each unit corresponding to the same phase material is less than or equal to the volume upper limit; the variables in the variable field are greater than zero and less than or equal to 1; the at least one second-type constraint includes at least one of the following multiple second-type constraints: for the i-th unit, the first porosity of the i-th unit calculated based on the projected variables of each unit corresponding to the same phase material within a target search region centered on the i-th unit is greater than or equal to the first porosity lower limit; the second porosity of the i-th unit calculated based on the projected variables of each unit corresponding to each phase material within the target search region is greater than or equal to the second porosity lower limit; the material ratio of the i-th unit calculated based on the projected variables of each unit corresponding to each phase material within the target search region is greater than or equal to the material ratio lower limit.

2. The method according to claim 1, characterized in that, the first porosity of the i-th unit calculated based on the projected variables of each unit corresponding to the j-th phase material within a target search region centered on the i-th unit being greater than or equal to the first porosity lower limit includes: Or, wherein, ζ ij represents the first porosity of the i-th unit calculated based on the projection variables of each unit corresponding to the j-th phase material within the target search area centered on the i-th unit; ζ L，j represents the lower limit of the first porosity; Ω i ={1, 2,..., N}, where N is the total number of units within the target search area centered on the i-th unit; v k represents the volume of the k-th unit; represents the projection variable of the k-th unit corresponding to the j-th phase material; p is a preset penalty factor; p q is the exponent of the preset p-mean aggregation function; n is the number of units included in the engineering structure.

3. The method according to claim 1, characterized in that, the second porosity of the i-th unit calculated based on the projected variables of each unit corresponding to each phase material within a target search region centered on the i-th unit being greater than or equal to the second porosity lower limit includes: Or, wherein, ζ i represents the second porosity of the i-th unit calculated based on the projection variables of each unit corresponding to each phase material within the target search area centered on the i-th unit; ζ L，0 represents the lower limit of the second porosity; Ω i ={1, 2,..., N}, where N is the total number of units within the target search area centered on the i-th unit; v k represents the volume of the k-th unit; represents the projection variable of the k-th unit corresponding to the j-th phase material; p is a preset penalty factor; p q is the exponent of the preset p-mean aggregation function; n is the number of units included in the engineering structure.

4. The method according to claim 1, characterized in that, the material ratio of the i-th unit calculated based on the projected variables of each unit corresponding to each phase material within a target search region centered on the i-th unit being greater than or equal to the material ratio lower limit includes: Or, wherein, Ψ i represents the material ratio of the i-th unit calculated based on the projection variables of each unit corresponding to each phase material within the target search region centered on the i-th unit; Ψ L represents the lower limit of the material ratio; Ω i ={1, 2,..., N}, where N is the total number of units within the target search region centered on the i-th unit; v k represents the volume of the k-th unit; represents the projection variable of the k-th unit corresponding to the j-th phase material; p is a preset penalty factor; p q is the exponent of the preset p-mean aggregation function; n is the number of units included in the engineering structure.

5. The method according to any one of claims 1-4, characterized in that, the multiple second-type constraints further include at least one of the following three constraints: The first constraint: Second constraint condition: Third constraint condition: Among them, is the filtering field variable corresponding to the j-th phase material of the i-th unit; is the preset threshold corresponding to the j-th phase material; is the upper limit value of the entity constraint corresponding to the j-th phase material preset; represents the projection variable corresponding to the i-th unit corresponding to the j-th phase material; is a preset parameter; R f is the filtering radius used to generate the filtering matrix; is the spatial gradient corresponding to the i-th unit corresponding to the j-th phase material; is the spatial gradient corresponding to the i-th unit corresponding to the overall engineering structure; is the Hadamard product; are the spatial perturbations added in the X, Y, and Z directions respectively; are the spatial increments in the X, Y, and Z directions under the influence of the spatial perturbation respectively; is the preset threshold corresponding to the i-th unit; is the upper limit value of the entity constraint corresponding to the i-th unit preset; η d is the threshold in the projection function; ε MivV is the upper limit value of the hole constraint corresponding to the i-th unit preset; n is the number of units included in the engineering structure; m is the number of materials included in the engineering structure.

6. The method according to claim 5, wherein, if at least one of the second type of constraint conditions includes a target constraint condition, and the target constraint condition includes at least one of the first constraint condition, the second constraint condition, and the third constraint condition, the optimizing the value of the variable field under multiple first type of constraint conditions and at least one second type of constraint condition by using a gradient-based optimization algorithm includes: Initializing the variable field to obtain an initial variable field; Establishing a projected variable field based on the initial variable field; Calculating the dispersion of the newly established projected variable field; If the dispersion is less than the dispersion threshold, using a gradient-based optimization algorithm to perform one optimization on the value of the variable field under the multiple first type of constraint conditions and the at least one second type of constraint condition; If the dispersion is greater than or equal to the dispersion threshold, using a gradient-based optimization algorithm to perform one optimization on the value of the variable field under the non-target constraint conditions among the multiple first type of constraint conditions and the at least one second type of constraint condition; Establishing a new projected variable field based on the optimized variable field, and returning to execute the step of calculating the dispersion of the newly established projected variable field until the optimization end condition is satisfied.

7. The method according to claim 1, wherein, the target search area is any one of a circular area, an elliptical area, and a rectangular area; or, the target search area is any one of a spherical area, an ellipsoidal area, and a cuboid area; The shapes of the target search areas centered on different units are the same or different.

8. The method according to claim 1, wherein, the method further includes: When the target property of the engineering structure needs to be calculated based on the Young's modulus of each unit of the engineering structure, for the i-th unit, interpolating the Young's modulus of the i-th unit by using the Young's modulus of each phase material to obtain the Young's modulus interpolation result of the i-th unit; Calculating the target property of the engineering structure based on the Young's modulus interpolation results of each unit of the engineering structure.

9. The method according to claim 8, wherein, the process of interpolating the Young's modulus of the i-th unit by using the Young's modulus of each phase material to obtain the Young's modulus interpolation result of the i-th unit includes: Based on the attention weight of each phase material of the i-th unit, weighted summing the Young's modulus of each phase material to obtain the Young's modulus interpolation result of the i-th unit; wherein, the attention weight of the i-th unit to the j-th phase material is calculated by the following formula: where λ ij is the attention weight of the i-th unit to the j-th phase material; represents the projection variable of the i-th unit corresponding to the j-th phase material; represents the projection variable of the i-th unit corresponding to the ξ-th phase material; p is the penalty factor; m is the number of materials included in the engineering structure.

10. A size control device in multi-material topology optimization based on the density method, wherein, the device includes: An obtaining module, configured to obtain a variable field of an engineering structure to be optimized, where different variables in the variable field correspond to different units of the engineering structure; the engineering structure is composed of multiple phase materials, and the variable is used to describe whether any one of the multiple phase materials exists in the corresponding unit; A building module for building a projected variable field based on the variable field; wherein, the projected variables in the projected variable field of each phase material correspond one-to-one with the filtering variables in the filtering variable field of this phase material, and the projected variable field is obtained by processing the filtering variable field through a projection function; the filtering variable field of each phase material is obtained from the variable field of this phase material and a filtering matrix; An optimization module for optimizing the value of the variable field under multiple first-class constraints and at least one second-class constraint by using a gradient-based optimization algorithm, so that the target property of the engineering structure reaches the optimum; wherein, The multiple first-class constraints include: the mass of the engineering structure calculated based on the projected variable field is less than or equal to the mass upper limit; the volume of the same phase material calculated based on the projected variables of each unit corresponding to the same phase material is less than or equal to the volume upper limit; the variables in the variable field are greater than zero and less than or equal to 1; The at least one second-class constraint includes at least one of the following multiple second-class constraints: for the i-th unit, the first porosity of the i-th unit calculated based on the projected variables of each unit corresponding to the same phase material within the target search area centered on the i-th unit is greater than or equal to the first porosity lower limit; the second porosity of the i-th unit calculated based on the projected variables of each unit corresponding to each phase material within the target search area is greater than or equal to the second porosity lower limit; the material ratio of the i-th unit calculated based on the projected variables of each unit corresponding to each phase material within the target search area is greater than or equal to the material ratio lower limit.

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