CN113536491B - Lattice structure topology optimization design method, device and computer readable storage medium - Google Patents
Lattice structure topology optimization design method, device and computer readable storage medium Download PDFInfo
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Abstract
The application discloses a lattice structure topology optimization design method, a device and a computer readable storage medium, wherein the method comprises the following steps: discretizing the design area by adopting a finite element theory to obtain material points in the design area; defining material points in the design area as initial topological design variables; correcting the topology design variable by adopting a two-phase projection method to obtain a final topology design variable; carrying out material interpolation treatment on the final topological design variable, and carrying out unit stiffness matrix calculation by adopting a constitutive model of a high-order continuous strain gradient theory to obtain unit stiffness matrix information; based on the sensitivity information, updating the topology design variable until the topology design variable meets the convergence condition to output a topology optimization result. Through the technical scheme, an accurate and efficient lattice structure topology design scheme can be provided for a micro-scale or nano-scale structure considering scale effects.
Description
Technical Field
The present application relates to the field of topology optimization design, and in particular, to a method and apparatus for topology optimization design of a lattice structure, and a computer readable storage medium.
Background
In the traditional macro-scale topological optimization design scheme, the constitutive model does not contain any parameter capable of predicting scale effect, so that accurate response analysis cannot be effectively provided for a micro-scale or nano-scale structure. On the other hand, the direct method of quantum mechanics or atomic simulation consumes a large computational cost to process the micro-scale structure. Therefore, the topological optimization design based on the framework of the continuum medium theory of the existing theory cannot meet the structural design requirements of micro-scale or nano-scale.
Disclosure of Invention
The present application aims to solve at least one of the technical problems existing in the prior art.
Therefore, the application provides a topological optimization design method of a lattice structure, which can provide an accurate and efficient topological design scheme for a micro-scale or nano-scale structure.
The application also provides a lattice structure topology optimization design device applying the lattice structure topology optimization design method.
The application also provides a computer readable storage medium applying the lattice structure topology optimization design method.
According to an embodiment of the first aspect of the application, the method for topological optimization design of the lattice structure comprises the following steps:
discretizing a design area by adopting a finite element theory to obtain material points in the design area, applying external load to the design area, and fixing the boundary degree of freedom of the design area to obtain boundary conditions;
defining material points in the design area as initial topological design variables;
correcting the topological design variable by adopting a two-phase projection method to obtain a final topological design variable;
performing material interpolation treatment on the final topological design variable, and performing unit stiffness matrix calculation by adopting a constitutive model of a high-order continuous strain gradient theory to obtain unit stiffness matrix information;
integrating the unit rigidity matrix information to obtain overall rigidity matrix information;
according to the external load and the boundary condition, a node displacement vector is obtained from the integral rigidity matrix information;
obtaining structural target performance information according to the node displacement vector;
performing sensitivity analysis on the structural target performance and constraint information to obtain corresponding sensitivity information;
and updating the topological design variable based on the sensitivity information until the topological design variable meets a convergence condition to output a topological optimization result.
The lattice structure topology optimization design method provided by the embodiment of the application has at least the following beneficial effects: firstly, discretizing a design area by adopting a finite element theory to obtain material points in the design area; applying an external load to the design area, and fixing the boundary degree of freedom of the design area to obtain boundary conditions; defining material points in the design area as initial topological design variables; correcting the initial topological design variable by adopting a two-phase projection method to obtain a final topological design variable; performing material interpolation treatment on the final topological design variable, and performing unit stiffness matrix calculation by adopting a constitutive model of a high-order continuous strain gradient theory to obtain unit stiffness matrix information; then integrating the unit rigidity matrix information to obtain overall rigidity matrix information; then according to the external load and boundary conditions, node displacement vectors are obtained from the overall rigidity matrix information; obtaining structural target performance information according to the node displacement vector; then, performing sensitivity analysis on the structural target performance and constraint information to obtain corresponding sensitivity information; and finally, updating the topology design variable based on the sensitivity information until the topology design variable meets a convergence condition to output a topology optimization result. Through the technical scheme, an accurate and efficient topological design scheme can be provided for a micro-scale or nano-scale structure.
According to some embodiments of the application, the correcting the initial topology design variable to obtain a final topology design variable includes:
performing first re-density filtering and projection processing on the initial topological design variable to obtain first topological variable information;
performing second density filtering and projection processing on the first topological variable information to obtain second topological variable information;
and superposing the first topological variable information and the second topological variable information to obtain the final topological design variable.
According to some embodiments of the present application, the performing material interpolation processing on the final topological design variable uses a constitutive model of a high-order continuous strain gradient theory to perform unit stiffness matrix calculation, to obtain unit stiffness matrix information, including:
performing material interpolation treatment on the final topological design variable to obtain a topological optimization relationship under a high-order continuous strain gradient theoretical frame;
and carrying out unit stiffness matrix calculation on the final topological design variable based on the topological optimization relation under the high-order strain gradient theoretical frame to obtain the unit stiffness matrix information.
According to some embodiments of the application, updating the topology design variable based on the sensitivity information until the topology design variable satisfies a convergence condition to output a topology optimization result includes:
updating the topological design variable based on the sensitivity information to obtain a topological design updating variable;
judging whether the topology design updating variable meets a convergence condition, if so, outputting the topology optimization result, and if not, replacing the topology design variable by the topology design updating variable.
According to some embodiments of the present application, the performing a first re-density filtering and projection on the initial topology design variable to obtain first topology variable information includes:
filtering the initial topology design variable by using a first filtering function to obtain first topology filtering information;
and processing the first topology filtering information by using a first projection function to obtain the first topology variable information.
According to some embodiments of the present application, the performing second density filtering and projection processing on the first topology variable information to obtain second topology variable information includes:
filtering the first topological variable information by using a second filtering function to obtain second topological filtering information;
and processing the second topology filtering information by using a second projection function to obtain the second topology variable information.
According to some embodiments of the application, the first filter function is a Helmholtz type partial differential equation and the first projection function is a differential projection function.
According to a second aspect of the present application, a lattice structure topology optimization design device includes:
the method comprises the steps of a first module, performing discretization processing on a design area by adopting a finite element theory to obtain material points in the design area, applying external load on the design area, and fixing the boundary degree of freedom of the design area to obtain boundary conditions;
a second module for defining material points in the design area as initial topological design variables;
the third module is used for correcting the initial topological design variable by adopting a two-phase projection method to obtain a final topological design variable;
a fourth module, configured to perform material interpolation processing on the final topology design variable, and perform unit stiffness matrix calculation by using a constitutive model of a high-order continuous strain gradient theory, so as to obtain unit stiffness matrix information;
a fifth module, configured to integrate the unit stiffness matrix information to obtain overall stiffness matrix information;
a sixth module, configured to obtain a node displacement vector from the overall stiffness matrix information according to the external load and the boundary condition;
a seventh module, configured to obtain structural target performance constraint information according to the node displacement vector;
an eighth module, configured to perform sensitivity analysis on the structural target performance constraint information to obtain corresponding sensitivity information;
and a ninth module, configured to update the topology design variable based on the sensitivity information until the topology design variable meets a convergence condition, and output a topology optimization result.
According to some embodiments of the application, the third module comprises:
a tenth module, configured to perform first re-density filtering and projection processing on the initial topology design variable to obtain first topology variable information;
an eleventh module, configured to perform second density filtering and projection processing on the first topology variable information to obtain second topology variable information;
and a twelfth module, configured to perform superposition processing on the first topology variable information and the second topology variable information, to obtain the final topology design variable.
According to an embodiment of the third aspect of the present application, the computer-readable storage medium stores computer-executable instructions that, when executed by the control processor, implement the lattice structure topology optimization design method as described above.
Additional aspects and advantages of the application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the application.
Drawings
The foregoing and/or additional aspects and advantages of the application will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
FIG. 1 is a flow chart of a topology optimization design method of a lattice structure according to an embodiment of the present application;
FIG. 2 is a flowchart illustrating variable correction in a topology optimization design method of a lattice structure according to an embodiment of the present application;
FIG. 3 is a flowchart of material interpolation and cell stiffness matrix calculation according to a topology optimization design method of lattice structure according to an embodiment of the present application;
FIG. 4 is a specific flowchart of topology design variable optimization of a lattice structure topology optimization design method according to an embodiment of the present application;
FIG. 5 is a flowchart illustrating variable correction according to one embodiment of the present application;
FIG. 6 is a flowchart illustrating variable correction according to another embodiment of the present application;
FIG. 7 is a flowchart of a topology optimization design method for a lattice structure according to another embodiment of the present application;
FIG. 8 is a schematic diagram of a design area of a cantilever beam and its loading and boundary conditions according to one embodiment of the present application;
FIG. 9 is a graph showing the topology optimization results for different intrinsic lengths of materials according to one embodiment of the present application;
fig. 10 is a graph showing objective function values of final topology for different intrinsic lengths of materials according to one embodiment of the present application.
Detailed Description
Embodiments of the present application are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the application.
In the description of the present application, it should be understood that references to orientation descriptions such as upper, lower, front, rear, left, right, etc. are based on the orientation or positional relationship shown in the drawings, are merely for convenience of description of the present application and to simplify the description, and do not indicate or imply that the apparatus or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus should not be construed as limiting the present application.
In the description of the present application, a number means one or more, a number means two or more, and greater than, less than, exceeding, etc. are understood to not include the present number, and above, below, within, etc. are understood to include the present number. The description of the first and second is for the purpose of distinguishing between technical features only and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or implicitly indicating the precedence of the technical features indicated.
In the description of the present application, unless explicitly defined otherwise, terms such as arrangement, installation, connection, etc. should be construed broadly and the specific meaning of the terms in the present application can be reasonably determined by a person skilled in the art in combination with the specific contents of the technical scheme.
Referring to fig. 1, an embodiment according to the first aspect of the present application provides a lattice structure topology optimization design method, including but not limited to step S100, step S200, step S300, step S400, step S500, step S600, step S700, step S800, and step S900.
Step S100, discretizing a design area by adopting a finite element theory to obtain material points in the design area, applying external load to the design area, and fixing the boundary degree of freedom of the design area to obtain boundary conditions;
step S200, defining material points in a design area as initial topological design variables;
step S300, correcting the initial topological design variable by adopting a two-phase projection method to obtain a final topological design variable;
step S400, carrying out material interpolation processing on the final topological design variable, and carrying out unit stiffness matrix calculation by adopting a constitutive model of a high-order continuous strain gradient theory to obtain unit stiffness matrix information;
step S500, integrating the unit rigidity matrix information to obtain overall rigidity matrix information;
step S600, obtaining a node displacement vector from the overall stiffness matrix information according to the external load and the boundary condition;
step S700, obtaining structural target performance constraint information according to the node displacement vector;
step S800, performing sensitivity analysis on the structural target performance constraint information to obtain corresponding sensitivity information;
and step S900, updating the topological design variable based on the sensitivity information until the topological design variable meets the convergence condition to output a topological optimization result.
In an embodiment, the embodiment of the application firstly adopts finite element theory to discretize a design area to obtain material points in the design area; applying an external load to the design area, and fixing the boundary degree of freedom of the design area to obtain boundary conditions; defining material points in the design area as initial topological design variables; correcting the topology design variable by adopting a two-phase projection method to obtain a final topology design variable; then carrying out material interpolation treatment on the final topological design variable, and carrying out unit stiffness matrix calculation by adopting a constitutive model of a high-order continuous strain gradient theory to obtain unit stiffness matrix information; then integrating the unit rigidity matrix information to obtain overall rigidity matrix information; then according to the external load and boundary conditions, node displacement vectors are obtained from the overall rigidity matrix information; obtaining structural target performance information according to the node displacement vector; then, carrying out sensitivity analysis on the structural target performance and constraint information to obtain corresponding sensitivity information; and finally, updating the topology design variable based on the sensitivity information until the topology design variable meets a convergence condition to output a topology optimization result. Through the technical scheme, an accurate and efficient topological design scheme can be provided for a micro-scale or nano-scale structure.
Referring to fig. 2, the variable is corrected in the above step S300, including but not limited to step S310, step S320, and step S330.
Step S310, performing first re-density filtering and projection processing on the initial topological design variable to obtain first topological variable information;
step S320, performing second density filtering and projection processing on the first topological variable information to obtain second topological variable information;
and step S330, performing superposition processing on the first topological variable information and the second topological variable information to obtain a final topological design variable.
In an embodiment, the embodiment of the application firstly carries out first dense filtering and projection processing on topology design variables to obtain first topology variable information; then, performing second density filtering and projection processing on the first topological variable information to obtain second topological variable information; and finally, superposing the first topological variable information and the second topological variable information to obtain a final topological design variable.
It should be noted that, the first filtering and projection process is mainly used to ensure stability of numerical computation, and is generally used to overcome numerical instability problems such as grid singularities, grid dependencies, and the like. The second filtering function adopts an averaging method to carry out averaging topological variable processing on the first reprojection topological variable; the second projection function adopts a low-pass projection function for determining the topology variable with the local topology variable threshold below a specified boundary value, and the final topology design variable can be obtained.
Referring to fig. 3, the material interpolation and cell stiffness matrix calculation in step S400 described above may include, but is not limited to, step S410 and step S420.
Step S410, carrying out material interpolation processing on the final topological design variable to obtain topological optimization relation information under a high-order continuous strain gradient theoretical frame;
and step S420, carrying out unit stiffness matrix calculation on the final topological design variable based on the topological optimization relation under the high-order strain gradient theoretical frame to obtain unit stiffness matrix information.
In an embodiment, material interpolation processing is performed on a final topological design variable to obtain a topological optimization relationship under a high-order continuous strain gradient theory framework, wherein the topological optimization relationship under the high-order strain gradient theory framework is used for representing the connection between the strain gradient theory and the topological optimization theory; and then constructing a unit stiffness matrix according to the strain gradient theory to obtain unit stiffness matrix information.
Referring to fig. 4, the optimization of the topology design variables in step 900 may include, but is not limited to, step S910 and step S920.
Step S910, updating the topology design variable based on the sensitivity information to obtain a topology design update variable;
and step S920, judging whether the topology design updating variable meets the convergence condition, if so, outputting a topology optimization result, and if not, replacing the topology design variable with the topology design updating variable.
In an embodiment, the embodiment of the application updates the topology design variable based on the sensitivity information, so as to obtain a topology design update variable; and judging whether the topology design updating variable meets the convergence condition, if so, outputting a topology optimization result, if not, replacing the original topology design variable with the topology design updating variable, and then continuing to repeat the steps to update the topology design variable until the obtained topology design updating variable meets the convergence condition.
Referring to fig. 5, the variable correction specific step in step 310 may include, but is not limited to, step S311 and step S312.
Step S311, filtering the initial topology design variable by using a first filtering function to obtain first topology filtering information;
step S312, the first topology filtering information is processed by using the first projection function, so as to obtain first topology variable information.
In an embodiment, the first filtering and projection processing in the embodiment of the present application is mainly used to ensure stability of numerical computation, and is generally used to overcome numerical instability problems such as grid singularities, grid dependencies, and the like. The first filtering function adopts a Helmholtz partial differential equation to filter topological variables, and the first reprojection function adopts a differentiable projection function to filter topological variables.
Referring to fig. 6, the variable correction specific step in step 320 may include, but is not limited to, step S321 and step S322.
Step S321, filtering the first topology variable information by using a second filtering function to obtain second topology filtering information;
step S322, the second topology filtering information is processed by using the second projection function to obtain second topology variable information.
In an embodiment, the embodiment of the application utilizes a second filtering function to filter the first topology variable information to obtain second topology filtering information; and then processing the second topology filtering information by using a second projection function, and finally obtaining second topology variable information. The second filtering function adopts an averaging method to carry out averaging topology variable processing on the first reprojection topology variable; the second projection function adopts a low-pass projection function for determining the topology variable with the local topology variable threshold below a specified boundary value, and the final topology design variable can be obtained.
In some embodiments of the application, the first filter function is a Helmholtz type partial differential equation and the first projection function is a differential projection function.
The following description of the above embodiment of the present application will be given by way of example only, and should not be construed as limiting the scope of the application.
The structure is first defined as a designed area and an un-designed area, and the corresponding loads and boundary conditions are applied to the structure. The structure is treated with discrete elements using finite element theory and each discrete element in the design area is given an initial topological design variable x. Furthermore, an objective function F (e.g., stiffness maximization) and constraint gi (e.g., lightweight design requirements) of the structure are defined.
First, carrying out first re-density filtering and projection processing on an initial topological design variable x, wherein the first re-filtering and projection scheme is mainly used for guaranteeing the stability of numerical calculation and is usually used for overcoming the numerical instability problems such as grid singularity, grid dependence and the like. The first filtering function is obtained by adopting Helmholtz partial differential equation to filter topological variablesThe first reprojection function is processed using a differentiable projection function>A second gravity average filtering strategy and a low-pass projection function are then employed, which function is primarily used to control the distribution of material within the neighborhood of material points. The second filtering function adopts an average scheme method to perform an average topological variable treatment on the first reprojection topological variable to obtain +.>Second projection functionTopology variables for determining that the local topology variable threshold is below a specified boundary value can be obtained by using a low-pass projection function>After the initial topology design variables are subjected to double filtering and double projection function processing, final corrected topology variable values are obtained. The evolution process of its topological design variables can be expressed as:
in order to ensure that the final topological structure generates the required non-uniformly distributed lattice structure, a first-stage projection variable and a correction topological variable are adopted to carry out superposition operation to obtain a final topological design variable phi, which can be expressed as:
the final topological design variable value is subjected to material interpolation scheme treatment, so that an effective connection between the topological variable and the strain gradient theory can be constructed. The material interpolation scheme can be written as:
E i ＝φ p E 0
after the material interpolation model is built, the topology variables are taken into finite element analysis for direct calculation. In this finite element analysis approach, the scale effect of the structure on both the microscopic and macroscopic scales needs to be reflected. Therefore, a constitutive model of strain gradient theory is introduced, and structural property changes caused by scale effects are described through dimensionless intrinsic length parameters of materials. According to a continuous medium theoretical model based on the strain gradient theory, the stiffness matrix of the unit is composed of two parts, wherein one part is a unit stiffness matrix ke in classical mechanics, and the other part is a unit stiffness matrix ks generated by the strain gradient theory. Thus for a particular cell i, its cell stiffness matrix can be expressed as:
after the cell stiffness is calculated, it can be assembled to form a calculation of the overall stiffness matrix. Then, according to the applied load and constraint conditions, node displacement of the structure is calculated, and then, according to the obtained node displacement, target performance of the structure can be calculated. In the present method, taking the minimum flexibility as an objective function and the light weight requirement as constraints, the following optimization formula can be calculated:
find：x＝[x 1 ,x 2 ,...,x N ]
minimize：
subjectto：K eq U＝F
φ i v i ＝V *
0<x min ≤x i ≤1,(i＝1,...,N)
wherein W is a target flexibility value, U is node displacement, keq is an overall structural rigidity matrix, and U is an overall displacement vector. F is the external load vector v is the volume of the corresponding cell. V is the specified volume.
Since the method is based on a variable density method model for topology optimization calculation, the gradient of the objective function and the constraint condition must be deduced. Therefore, according to the optimization list above, the gradient information of the objective function and the constraint condition is biased according to the chain rule and the concomitant variable method, and the corresponding sensitivity analysis can be obtained. For sensitivity information of its objective function, we can get:
the sensitivity information of the objective function to the topological design variables will be subjected to the cell stiffness matrix of classical mechanics and strain gradient theory, which can be written as:
the sensitivity information of the constraint condition to the topological design variable can also be continuously related by changing the objective function into the constraint condition. After obtaining a sensitivity analysis of the constraints of the objective function, a large number of topology design variables may be involved in the topology optimization method due to the finite element. Therefore, in the framework of the method, in order to improve the efficiency of optimization calculation, a moving asymptote method is adopted to update the topological optimization design variables. And finally, iterating repeatedly until the method reaches a convergence condition so as to output the final topological configuration of the lattice structure.
Generally, the application is mainly used for providing an active topological optimization conceptual design scheme for micro-scale or nano-scale lattice structure design. The constitutive equation is described according to the strain gradient theory due to structural performance change caused by the size effect, so that an accurate simulation scheme can be provided for the design of the constitutive equation, and the effectiveness of a final topological design structure is ensured. The theory is combined with the double filtering and projection method, so that the fully-connected lattice structure can be effectively generated, and the topological formation of the lattice structure is directly related to a load path, so that the excellent performance of the structure under the working condition can be more exerted.
In particular, with reference to fig. 7 to 10, another specific embodiment is presented below to supplement the description of the embodiment of the present application.
First, a cantilever design area is defined, which has a length of 200 and a height of 100. In this example, non-dimensionality will be applied to the data. An external load of 1 is applied to the lower right corner thereof and fixes all degrees of freedom of the left boundary of the design area, as shown in fig. 8. The modulus of elasticity and poisson's ratio are defined as 1 and 0.3, respectively. All material points in the area are defined as a design area, and the design area is discretized by adopting a finite element method to obtain a finite number of discrete elements. And defining topology design variables for each discrete cell within the design area. In order to study the influence of different scale effects, different intrinsic lengths of materials are selected to describe the difference of the influence of the scale effects.
And according to the defined initial topological design variable, carrying out topological variable correction processing on the topological design variable by adopting a double filtering and double projection method to obtain a final topological design variable. The topological design variable is used for establishing a connection between a strain gradient theory and a topological optimization theory in a material interpolation model. And then constructing a unit stiffness matrix according to a strain gradient theory, and assembling an integrated overall stiffness matrix. And then solving the displacement vector of the integral structure according to the applied load and the boundary condition. The following optimization formula is then calculated:
find：x＝[x 1 ,x 2 ,...,x N ]
minimize：
subjectto：K eq U＝F
φ i v i ＝V * /V
0<x min ≤x i ≤1,(i＝1,...,N)
wherein the specified target volume fraction is defined as v=0.5 and x min =0.001. And then performing sensitivity analysis of the objective function and constraint conditions according to the calculation result. After obtaining their corresponding sensitivity information, the topology design variables are updated using a moving asymptote method based on the gradient information. Then judging whether the topological variable value of the structure meets the convergence condition, and if so, outputting a final topological optimization result; if the topology variable value does not meet the requirement, the updated topology variable value is assigned to the initial topology design variable to continue calculation until the convergence condition is met.
Fig. 9 shows the results of topological optimization for different intrinsic material lengths, which means the ratio of the dimensions of the structure to the dimensions of the material points. When the intrinsic length of the material is large, the topological optimization result and the objective function value of the material are close to those of the traditional classical mechanics. However, when the intrinsic length of the material increases, it means that the dimensional effect between the size of the material point and the structural size thereof is not negligible, and both the topology optimization result and the objective function value are affected by the dimensional effect, as shown in fig. 9 and 10. According to the objective function curve, when the intrinsic length of the material is smaller, namely the structural dimension is larger relative to the dimension of the material, the objective function of the structure is similar to the traditional topology optimization design method, but when the intrinsic length of the material is larger, the structural dimension is equal to the dimension of the material, the scale effect in the structure is highlighted, so that the stress-strain distribution is influenced, and different topology optimization results are generated. Therefore, the structure can be designed effectively and accurately in consideration of the influence caused by the size effect in the method.
By the technical scheme, the influence of the scale effect of the structure is considered, and a reasonable design scheme is provided for the design of the micro-scale or nano-scale lattice structure by combining the strain gradient theory, the projection technology and the topology optimization technology.
The application provides a lattice structure topology optimization design method considering scale effect. In the method, the influence caused by the size effect is considered, the strain gradient effect of the structure is described through the rotation gradient and the stretching gradient in the structure, the performance influence caused by the scale effect is described by introducing intrinsic parameters of materials, and then the strain gradient theory is combined with a variable density method, so that the lattice structure is designed efficiently through a double projection technology. Therefore, compared with the traditional macro-scale topological optimization design method, the method can provide an accurate and efficient topological concept design scheme for micro-scale or nano-scale structural design.
Generally, the application is mainly used for providing an active topological optimization conceptual design scheme for micro-scale or nano-scale lattice structure design. The constitutive equation is described according to the strain gradient theory due to structural performance change caused by the size effect, so that an accurate simulation scheme can be provided for the design of the constitutive equation, and the effectiveness of a final topological design structure is ensured. The theory is combined with the double filtering and projection method, so that the fully-connected lattice structure can be effectively generated, and the topological formation of the lattice structure is directly related to a load path, so that the excellent performance of the structure under the working condition can be more exerted.
According to an embodiment of the second aspect of the present application, there is provided a lattice structure topology optimization design device, including:
the first module is used for carrying out discretization treatment on the design area by adopting a finite element theory to obtain material points in the design area, applying external load on the design area, and fixing the boundary degree of freedom of the design area to obtain boundary conditions;
a second module for defining material points in the design area as initial topological design variables;
the third module is used for correcting the initial topological design variable by adopting a two-phase projection method to obtain a final topological design variable;
the fourth module is used for carrying out material interpolation processing on the final topological design variable, and carrying out unit stiffness matrix calculation by adopting a constitutive model of a high-order continuous strain gradient theory to obtain unit stiffness matrix information;
the fifth module is used for integrating the unit rigidity matrix information to obtain the whole rigidity matrix information;
a sixth module, configured to obtain a node displacement vector from the overall stiffness matrix information according to the external load and the boundary condition;
a seventh module, configured to obtain structural target performance constraint information according to the node displacement vector;
an eighth module, configured to perform sensitivity analysis on the structural target performance constraint information to obtain corresponding sensitivity information;
and a ninth module, configured to update the topology design variable based on the sensitivity information until the topology design variable meets a convergence condition, and output a topology optimization result.
In some embodiments of the application, the third module comprises:
a tenth module, configured to perform first re-density filtering and projection processing on the initial topology design variable to obtain first topology variable information;
the eleventh module is used for performing second density filtering and projection processing on the first topological variable information to obtain second topological variable information;
and the twelfth module is used for carrying out superposition processing on the first topological variable information and the second topological variable information to obtain a final topological design variable.
It should be noted that, since the lattice structure topology optimization design device in the present embodiment and the lattice structure topology optimization design method in the foregoing embodiments are based on the same inventive concept, the corresponding content in the method embodiment is also applicable to the system embodiment, and will not be described in detail herein.
An embodiment according to a third aspect of the present application provides a computer-readable storage medium storing computer-executable instructions that when executed by a control processor implement the lattice structure topology optimization design method in the above embodiment. For example, the above-described method steps S100 to S900 in fig. 1, method steps S310 to S330 in fig. 2, or method steps S410 to S420 in fig. 3, or method steps S910 to S920 in fig. 4, or method steps S311 to S312 in fig. 5, or method steps S321 to S322 in fig. 6 are performed.
It should be noted that, since the computer readable storage medium in the present embodiment and the lattice structure topology optimization design method in the above embodiment are based on the same inventive concept, the corresponding content in the method embodiment is also applicable to the system embodiment, and will not be described in detail herein.
Those of ordinary skill in the art will appreciate that all or some of the steps, systems, and methods disclosed above may be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application specific integrated circuit. Such software may be distributed on computer readable media, which may include computer storage media (or non-transitory media) and communication media (or transitory media). The term computer storage media includes both volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data, as known to those skilled in the art. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital Versatile Disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by a computer. Furthermore, as is well known to those of ordinary skill in the art, communication media typically include computer readable instructions, data structures, program modules, or other data in a modulated data signal, such as a carrier wave or other transport mechanism, and may include any information delivery media.
In the description of the present specification, reference to the terms "one embodiment," "some embodiments," "illustrative embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present application have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the application, the scope of which is defined by the claims and their equivalents.
Claims (7)
1. The topological optimization design method for the lattice structure is characterized by comprising the following steps of:
discretizing a design area by adopting a finite element theory to obtain material points in the design area, applying external load to the design area, and fixing the boundary degree of freedom of the design area to obtain boundary conditions;
defining material points in the design area as initial topological design variables;
correcting the initial topological design variable by adopting a biphase projection method to obtain a final topological design variable;
performing material interpolation processing on the final topological design variable, and performing unit stiffness matrix calculation by adopting a constitutive model of a high-order continuous strain gradient theory to obtain unit stiffness matrix information;
integrating the unit rigidity matrix information to obtain overall rigidity matrix information;
according to the external load and the boundary condition, a node displacement vector is obtained from the integral rigidity matrix information;
obtaining structural target performance constraint information according to the node displacement vector;
performing sensitivity analysis on the structural target performance constraint information to obtain corresponding sensitivity information;
updating the topological design variable based on the sensitivity information until the topological design variable meets a convergence condition to output a topological optimization result;
the correcting the initial topological design variable by adopting a biphase projection method to obtain a final topological design variable comprises the following steps:
performing first re-density filtering and projection processing on the initial topological design variable to obtain first topological variable information;
performing second density filtering and projection processing on the first topological variable information to obtain second topological variable information;
superposing the first topological variable information and the second topological variable information to obtain the final topological design variable;
the method for calculating the unit stiffness matrix by adopting the constitutive model of the high-order continuous strain gradient theory to obtain the unit stiffness matrix information comprises the following steps:
performing material interpolation processing on the final topological design variable to construct topological optimization under a strain gradient theoretical frame
Transforming the relationship;
based on the topological optimization relation under the strain gradient theoretical frame, carrying out unit stiffness matrix calculation on the final topological design variable to obtain the unit stiffness matrix information;
the first re-density filtering and projection processing are carried out on the initial topological design variable to obtain first topological variable information, which comprises the following steps:
filtering the initial topology design variable by using a first filtering function to obtain first topology filtering information;
processing the first topology filtering information by using a first projection function to obtain first topology variable information;
wherein the final topology design variable φ is represented as:is the variable resulting from the first re-projection function,is a variable obtained by the second re-projection function;
the cell stiffness matrix is expressed as:is a classical mechanical cell stiffness matrix, +.>Is a cell stiffness matrix of the strain gradient.
2. The method for topological optimization design of a lattice structure according to claim 1, wherein updating the topological design variable based on the sensitivity information until the topological design variable satisfies a convergence condition to output a topological optimization result comprises:
updating the topological design variable based on the sensitivity information to obtain a topological design updating variable;
judging whether the topology design updating variable meets a convergence condition, if so, outputting the topology optimization result, and if not, replacing the topology design variable by the topology design updating variable.
3. The method for optimizing the design of the lattice structure topology according to claim 1, wherein the performing second dense filtering and projection processing on the first topological variable information to obtain second topological variable information comprises:
filtering the first topological variable information by using a second filtering function to obtain second topological filtering information;
and processing the second topology filtering information by using a second projection function to obtain the second topology variable information.
4. The topological optimization design method of a lattice structure according to claim 1, wherein the first filtering function is a Helmholtz type partial differential equation, and the first projection function is a differential projection function.
5. The utility model provides a lattice structure topology optimization design device which characterized in that includes:
the first module is used for carrying out discretization treatment on the design area by adopting a finite element theory to obtain material points in the design area, applying external load on the design area, and fixing the boundary degree of freedom of the design area to obtain boundary conditions;
a second module for defining material points in the design area as initial topological design variables;
the third module is used for correcting the initial topological design variable by adopting a two-phase projection method to obtain a final topological design variable;
a fourth module, configured to perform material interpolation processing on the final topology design variable, and perform unit stiffness matrix calculation by using a constitutive model of a high-order continuous strain gradient theory, so as to obtain unit stiffness matrix information;
a fifth module, configured to integrate the unit stiffness matrix information to obtain overall stiffness matrix information;
a sixth module, configured to obtain a node displacement vector from the overall stiffness matrix information according to the external load and the boundary condition;
a seventh module, configured to obtain structural target performance constraint information according to the node displacement vector;
an eighth module, configured to perform sensitivity analysis on the structural target performance constraint information to obtain corresponding sensitivity information;
a ninth module, configured to update the topology design variable based on the sensitivity information until the topology design variable meets a convergence condition to output a topology optimization result;
the correcting the initial topological design variable by adopting a biphase projection method to obtain a final topological design variable comprises the following steps:
performing first re-density filtering and projection processing on the initial topological design variable to obtain first topological variable information;
performing second density filtering and projection processing on the first topological variable information to obtain second topological variable information;
superposing the first topological variable information and the second topological variable information to obtain the final topological design variable;
the method for calculating the unit stiffness matrix by adopting the constitutive model of the high-order continuous strain gradient theory to obtain the unit stiffness matrix information comprises the following steps:
performing material interpolation processing on the final topological design variable to construct topological optimization under a strain gradient theoretical frame
Transforming the relationship;
based on the topological optimization relation under the strain gradient theoretical frame, carrying out unit stiffness matrix calculation on the final topological design variable to obtain the unit stiffness matrix information;
the first re-density filtering and projection processing are carried out on the initial topological design variable to obtain first topological variable information, which comprises the following steps:
filtering the initial topology design variable by using a first filtering function to obtain first topology filtering information;
processing the first topology filtering information by using a first projection function to obtain first topology variable information;
wherein the final topology design variable φ is represented as:is the variable resulting from the first re-projection function,is a variable obtained by the second re-projection function;
the cell stiffness matrix is expressed as:is a classical mechanical cell stiffness matrix, +.>Is a cell stiffness matrix of the strain gradient.
6. The lattice structure topology optimization design device of claim 5, wherein said third module comprises:
a tenth module, configured to perform first re-density filtering and projection processing on the initial topology design variable to obtain first topology variable information;
an eleventh module, configured to perform second density filtering and projection processing on the first topology variable information to obtain second topology variable information;
and a twelfth module, configured to perform superposition processing on the first topology variable information and the second topology variable information, to obtain the final topology design variable.
7. A computer-readable storage medium storing computer-executable instructions, wherein the computer-executable instructions, when executed by a control processor, implement the lattice structure topology optimization design method of any one of claims 1 to 4.
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