CN114239363A - Variable density topology optimization method based on ABAQUS secondary development Python language - Google Patents
Variable density topology optimization method based on ABAQUS secondary development Python language Download PDFInfo
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Abstract
The invention relates to a method, a device, electronic equipment and a storage medium for variable density topology optimization based on ABAQUS secondary development Python language, wherein the method takes minimum strain energy as an objective function and takes volume fraction as a constraint condition, and comprises the following steps: establishing a finite element model and determining a design domain; acquiring topology optimization parameters, wherein the topology optimization parameters comprise volume fraction, filtering radius and penalty factor; establishing a unit stiffness matrix according to the preset initial relative density of each unit, and assembling an integral stiffness matrix; carrying out finite element analysis, and extracting a node displacement field and unit strain energy; calculating sensitivity and obtaining unit relative density according to a criterion method of a variable density topological optimization algorithm; and continuously repeating finite element analysis and optimization iterative computation according to the topological optimization parameters until the objective function and the constraint condition are met.
Description
Technical Field
The invention relates to the field of structure optimization, in particular to a variable density topology optimization method and device based on ABAQUS secondary development Python language, electronic equipment and a storage device.
Background
The topological optimization is one of the structural optimization, is a conceptual design stage in product design, can break through the limitation of the traditional design, creates a new configuration, and is a research direction with the greatest difficulty and the greatest vitality and challenge in the structural optimization. The topological optimization is based on engineering practice, loads and constraint conditions are given in a certain design domain, an optimal material distribution form is sought, the purposes of reducing weight, reducing displacement or stress level and the like are taken as targets, the material utilization rate is improved, and the purposes of light weight design and cost reduction are finally achieved. In recent years, the variable density topological optimization method is widely applied to the fields of automobiles, airplanes, ships, machinery and the like, and therefore, certain commercial finite element software such as TOSCA, ABAQUS, HyperWorks, ANSYS and the like in the market introduces a topological optimization function. Among these commercial finite element software, ABAQUS is widely recognized as the most powerful finite element software that can analyze complex solid mechanical structural mechanics systems, and in particular can handle very large and complex problems and simulate highly nonlinear problems.
However, when topology optimization is performed through ABAQUS, when a plurality of parts need topology optimization, or the same part does not determine optimization control parameter values, and multiple optimization needs to be performed, if the topology optimization function of the ABAQUS is used, many optimization tasks need to be established, multiple settings of objective functions, constraints and the like are performed, and the work is repeated and tedious, and the efficiency is low.
Although the use of commercial finite element software such as ABAQUS can complete topology optimization, it is a "black box" for users, and it has no knowledge about the structure and logic for implementing the topology optimization function, and cannot understand the topology optimization algorithm from depth, so that users cannot clearly understand the parameter setting and result extraction method. In addition, when the ABAQUS is used for topology optimization, more parameters need to be input, and the process is relatively complicated.
Disclosure of Invention
Based on the method, the device, the electronic equipment and the storage medium, the variable density topology optimization method, the device, the electronic equipment and the storage medium based on the ABAQUS secondary development Python language simplify parameter input, improve readability of an optimization process, are suitable for multiple optimization tasks and improve optimization efficiency.
The invention is realized by the following scheme:
in a first aspect, the present invention provides a method for variable density topology optimization based on ABAQUS quadratic development Python language, which takes minimum strain energy as an objective function and takes a volume fraction as a constraint condition, and the method includes the following steps:
establishing a finite element model and determining a design domain;
acquiring topology optimization parameters which comprise volume fractions, filter radii and penalty factors;
establishing a unit stiffness matrix according to the preset initial relative density of each unit, and assembling an integral stiffness matrix;
carrying out finite element analysis, and extracting a node displacement field and unit strain energy;
calculating sensitivity and obtaining unit relative density according to a criterion method of a variable density topological optimization algorithm;
and continuously repeating finite element analysis and optimization iterative computation according to the topological optimization parameters until the objective function and the constraint condition are met.
Further, establishing a finite element model and determining a design domain, comprising:
defining material properties, dividing networks, applying boundary conditions and applying loads;
an optimized region and a non-optimized region are determined.
Further, according to the preset initial relative density of each unit, a unit stiffness matrix is established, and an overall stiffness matrix is assembled, wherein the method comprises the following steps:
the initial relative density of the cells is defined to be 0.5 and the relative density of each cell is defined to vary from 0 to 1.
Further, continuously repeating the finite element analysis and the optimization iterative computation according to the topology optimization parameters, comprising:
keeping units with large contribution rate to the rigidity of the structure, wherein the relative density of the units is equal to 1 or approaches to 1;
and deleting the units with small contribution rate to the structural rigidity, wherein the relative density of the units is equal to 0 or approaches to 0.
Further, the volume fraction Vf is set to 0.2.
Further, the filter radius rmin is set to 3.
Further, the penalty factor P is set to 3.0.
In a second aspect, the present invention provides an apparatus for variable density topology optimization based on ABAQUS second development Python language, the apparatus comprising:
the model establishing module is used for establishing a finite element model and determining a design domain;
the parameter acquisition module is used for acquiring topology optimization parameters, and the topology optimization parameters comprise volume fractions, filter radii and penalty factors;
the rigidity matrix establishing module is used for establishing a unit rigidity matrix according to the preset initial relative density of each unit and assembling an integral rigidity matrix;
the finite element analysis module is used for carrying out finite element analysis and extracting a node displacement field and unit strain energy;
the sensitivity calculation module is used for calculating sensitivity and obtaining the relative density of the unit according to a criterion method of a variable density topological optimization algorithm;
and the optimization iteration module is used for continuously repeating finite element analysis and optimization iteration calculation according to the topology optimization parameters until the objective function and the constraint condition are met.
In a third aspect, the present invention provides an electronic device, comprising:
at least one memory and at least one processor;
the memory for storing one or more programs;
when executed by the at least one processor, cause the at least one processor to implement the steps of the method for variable density topology optimization based on ABAQUS second development Python language according to the first aspect.
In a fourth aspect, the present invention provides a computer readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the steps of the method for performing variable density topology optimization based on ABAQUS second development Python language according to the first aspect.
The variable density topology optimization method based on ABAQUS secondary development Python language provided by the embodiment of the invention is suitable for an optimization design domain with any shape and has universality; when a plurality of optimization tasks are faced, the process automation can be realized, the problem of repeated complexity is effectively solved, the labor is saved, and the efficiency and the precision are improved; meanwhile, the variable density SIMP topological optimization algorithm is realized in a Python language mode, so that the learning of a topological optimization theory and the algorithm can be facilitated, the defects of the algorithm can be found, the optimization and the improvement of the algorithm can be carried out, and the black box trouble caused by the existing finite element software can be avoided; meanwhile, the minimum strain energy is taken as an objective function, the volume fraction is taken as a constraint condition, and when the topology optimization is performed on the input model, compared with the existing finite element software, the optimization can be performed only by inputting the volume fraction Vf and the filtering radius R, the optimization result of the iteration step can be checked, and the readability is improved.
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Drawings
FIG. 1 is a flowchart of the steps of a method for variable density topology optimization based on ABAQUS secondary development Python language provided by the present invention;
FIG. 2 is a model illustration of a three-dimensional cantilever structure;
FIG. 3 is a schematic structural diagram of a three-dimensional cantilever structure after topological optimization by ABAQUS software;
fig. 4 is a schematic structural diagram after topology optimization is performed by a method for variable density topology optimization based on ABAQUS secondary development Python language provided by the present invention;
fig. 5 is a schematic diagram of a variable density topology optimization device based on ABAQUS secondary development Python language provided by the present invention;
fig. 6 is a schematic structural diagram of an electronic device provided in the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more clear, embodiments of the present application will be described in further detail below with reference to the accompanying drawings.
It should be understood that the embodiments described are only some embodiments of the present application, and not all embodiments. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments in the present application without any creative effort belong to the protection scope of the embodiments in the present application.
The terminology used in the embodiments of the present application is for the purpose of describing particular embodiments only and is not intended to be limiting of the embodiments of the present application. As used in the examples of this application and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.
When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the application, as detailed in the appended claims. In the description of the present application, it is to be understood that the terms "first," "second," "third," and the like are used solely to distinguish one from another similar human body, and are not necessarily used to describe a particular order or sequence, nor are they to be construed as indicating or implying relative importance. The specific meaning of the above terms in the present application can be understood by those of ordinary skill in the art as appropriate.
Further, in the description of the present application, "a plurality" means two or more unless otherwise specified. "and/or" describes an associative relationship with a human body, meaning that there may be three relationships, e.g., a and/or B, which may mean: a exists alone, A and B exist simultaneously, and B exists alone. The character "/" generally indicates that the context of the associated human is an "or" relationship.
To solve the technical problems in the background art, an embodiment of the present application provides a method for variable density topology optimization based on ABAQUS secondary development Python language, which takes minimum strain energy as an objective function and takes a volume fraction as a constraint condition, as shown in fig. 1, and the method includes the following steps:
s101: establishing a finite element model and determining a design domain;
s102: acquiring topology optimization parameters, wherein the topology optimization parameters comprise volume fraction, filtering radius and penalty factor;
s103: establishing a unit stiffness matrix according to the preset initial relative density of each unit, and assembling an integral stiffness matrix;
s104: carrying out finite element analysis, and extracting a node displacement field and unit strain energy;
s105: calculating sensitivity and obtaining unit relative density according to a criterion method of a variable density topological optimization algorithm;
s106: and continuously repeating finite element analysis and optimization iterative computation according to the topological optimization parameters until the objective function and the constraint condition are met.
In a preferred embodiment, step S101 specifically includes:
defining material properties, dividing networks, applying boundary conditions and applying loads;
an optimized region and a non-optimized region are determined.
In a preferred embodiment, step S103 specifically includes:
the initial relative density of the cells is defined to be 0.5 and the relative density of each cell is defined to vary from 0 to 1.
In a preferred embodiment, step S106 specifically includes:
keeping units with large contribution rate to the rigidity of the structure, wherein the relative density of the units is equal to 1 or approaches to 1;
the cells with small contribution rate to the structural rigidity are deleted, and the relative density of the cells is equal to 0 or approaches to 0.
In a preferred embodiment, step S102 specifically includes:
setting the volume fraction Vf to 0.2, the filtering radius rmin to 3 and the penalty factor P to 3.0.
In a specific example, the topology optimization is performed by taking a three-dimensional cantilever beam structure as shown in fig. 2 as an example.
The dimensions length, width and height of the three-dimensional cantilever beam structure are 60 x 4 x 20(mm3), and the structure is assumed to be a linear elastic material, the elastic modulus is 210000MPa, and the Poisson ratio is 0.3. The boundary conditions were set such that the left end face was completely fixed, a concentrated force of 300N was applied to the center below the right end face, the initial density of the material was set to 0.7, the number of divided meshes was 2000, and an optimized region and a non-optimized region were designated. Next, the target volume fraction Vf is set to 0.2, the filter radius rmin is set to 3, and the penalty factor P is set to 3.0.
And then, carrying out the finite element calculation for once extraction, extracting the deformation and the strain energy of each grid unit node in the model, and then carrying out sensitivity calculation according to a criterion method of a variable density topological optimization algorithm. The element density obtained by the last calculation can be automatically input into the next iterative calculation, and then the finite element calculation and the optimization iteration are repeated continuously until the optimization target and the constraint condition are met.
In the variable density topological optimization, the relative density of each unit is defined to be changed in a range of 0-1, the relative density of each unit is initially assumed to be 0.5, the units with high contribution rate to the structural rigidity in the model are gradually reserved in a plurality of iteration processes, the corresponding unit relative density is equal to 1 or approaches to 1, the unit relative density with low contribution rate to the structural rigidity is gradually equal to 0 or approaches to 0, finally, a region with low contribution rate to an objective function is found through a plurality of optimization iterations, and the structural lightweight can be realized by deleting the region.
As shown in fig. 3 and 4, fig. 3 is a topological structure obtained by optimizing through existing ABAQUS software, fig. 4 is a topological structure obtained by optimizing through a method for variable density topological optimization based on a secondary ABAQUS development Python language provided by an embodiment of the present invention, and comparing fig. 3 and 4, it can be seen that the topological structure obtained by performing topological optimization through the embodiment of the present invention has higher precision and better effect.
The variable density topology optimization method based on ABAQUS secondary development Python language provided by the embodiment of the invention is suitable for an optimization design domain with any shape and has universality; when a plurality of optimization tasks are faced, the process automation can be realized, the problem of repeated complexity is effectively solved, the labor is saved, and the efficiency and the precision are improved; meanwhile, the variable density SIMP topological optimization algorithm is realized in a Python language mode, so that the learning of a topological optimization theory and the algorithm can be facilitated, the defects of the algorithm can be found, the optimization and the improvement of the algorithm can be carried out, and the black box trouble caused by the existing finite element software can be avoided; meanwhile, the minimum strain energy is taken as an objective function, the volume fraction is taken as a constraint condition, and when the topology optimization is performed on the input model, compared with the existing finite element software, the optimization can be performed only by inputting the volume fraction Vf and the filtering radius R, the optimization result of the iteration step can be checked, and the readability is improved.
As shown in fig. 5, an embodiment of the present application further provides an apparatus 500 for variable density topology optimization based on ABAQUS secondary development Python language, where the apparatus 500 includes:
a model establishing module 501, configured to establish a finite element model and determine a design domain;
a parameter obtaining module 502, configured to obtain topology optimization parameters, where the topology optimization parameters include a volume fraction, a filter radius, and a penalty factor;
a stiffness matrix establishing module 503, configured to establish a cell stiffness matrix according to a preset initial relative density of each cell, and assemble an overall stiffness matrix;
a finite element analysis module 504, configured to perform finite element analysis and extract a node displacement field and a unit strain energy;
a sensitivity calculation module 505, configured to calculate sensitivity and obtain a relative cell density according to a criterion method of a variable density topology optimization algorithm;
and an optimization iteration module 506, configured to continuously repeat finite element analysis and optimization iteration calculation according to the topology optimization parameters until the objective function and the constraint condition are satisfied.
In an exemplary embodiment, model building module 501 includes:
the parameter definition unit is used for defining material properties, dividing networks, applying boundary conditions and applying loads;
and the area determining unit is used for determining an optimized area and a non-optimized area.
In an exemplary embodiment, the stiffness matrix establishing module 503 includes:
and the relative density defining unit is used for defining the initial relative density of the unit to be 0.5 and defining that the relative density of each unit is changed in a range of 0-1.
In an exemplary embodiment, the optimization iteration module 506 includes:
the region reserving unit is used for reserving units with high contribution rate to the rigidity of the structure, and the relative density of the units is equal to 1 or approaches to 1;
and the area deleting unit is used for deleting the units with small contribution rate to the structural rigidity, and the relative density of the units is equal to 0 or approaches to 0.
In an exemplary embodiment, the parameter obtaining module 502, the topology optimization parameter includes the following settings:
setting the volume fraction Vf to 0.2, the filtering radius rmin to 3 and the penalty factor P to 3.0.
As shown in fig. 6, fig. 6 is a block diagram of an electronic device according to an exemplary embodiment of the present application.
The electronic device includes a processor 610 and a memory 620. The number of the processors 610 in the main control chip may be one or more, and one processor 610 is taken as an example in fig. 6. The number of the memories 620 in the main control chip may be one or more, and one memory 620 is taken as an example in fig. 6.
The memory 620 is used as a computer readable storage medium, and can be used to store a software program, a computer executable program, and a module, such as a program of the method for performing the variable density topology optimization based on the ABAQUS secondary development Python language according to any embodiment of the present application, and a program instruction/module corresponding to the method for performing the variable density topology optimization based on the ABAQUS secondary development Python language according to any embodiment of the present application. The memory 620 may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required for at least one function; the storage data area may store data created according to use of the device, and the like. Further, the memory 620 may include high speed random access memory, and may also include non-volatile memory, such as at least one magnetic disk storage device, flash memory device, or other non-volatile solid state storage device. In some examples, the memory 620 can further include memory located remotely from the processor 610, which can be connected to the device over a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
The processor 610 executes various functional applications and data processing of the device by running software programs, instructions and modules stored in the memory 620, that is, the method for implementing the variable density topology optimization based on the ABAQUS secondary development Python language described in any of the above embodiments is implemented.
The present application further provides a computer-readable storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the method for performing variable density topology optimization based on ABAQUS secondary development Python language according to any of the foregoing embodiments.
The present invention may take the form of a computer program product embodied on one or more storage media including, but not limited to, disk storage, CD-ROM, optical storage, and the like, having program code embodied therein. Computer readable storage media, which include both non-transitory and non-transitory, removable and non-removable media, may implement any method or technology for storage of information. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of the storage medium of the computer include, but are not limited to: phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium may be used to store information that may be accessed by a computing device.
It is to be understood that the embodiments of the present application are not limited to the precise arrangements described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the embodiments of the present application is limited only by the following claims.
The above-mentioned embodiments only express a few embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for those skilled in the art, variations and modifications can be made without departing from the concept of the embodiments of the present application, and these embodiments are within the scope of the present application.
Claims (10)
1. A method for carrying out variable density topological optimization based on ABAQUS quadratic development Python language, which takes minimum strain energy as an objective function and takes volume fraction as a constraint condition, is characterized by comprising the following steps:
establishing a finite element model and determining a design domain;
acquiring topology optimization parameters which comprise volume fractions, filter radii and penalty factors;
establishing a unit stiffness matrix according to the preset initial relative density of each unit, and assembling an integral stiffness matrix;
carrying out finite element analysis, and extracting a node displacement field and unit strain energy;
calculating sensitivity and obtaining unit relative density according to a criterion method of a variable density topological optimization algorithm;
and continuously repeating finite element analysis and optimization iterative computation according to the topological optimization parameters until the objective function and the constraint condition are met.
2. The method of claim 1, wherein the establishing a finite element model and determining a design domain comprises:
defining material properties, dividing networks, applying boundary conditions and applying loads;
an optimized region and a non-optimized region are determined.
3. The ABAQUS quadratic development Python language-based variable density topology optimization method according to claim 2, wherein the establishing of the cell stiffness matrix according to the preset initial relative density of each cell and the assembling of the overall stiffness matrix comprises:
the initial relative density of the cells is defined to be 0.5 and the relative density of each cell is defined to vary from 0 to 1.
4. The method of claim 3, wherein the continuously repeating finite element analysis and iterative optimization calculation according to the topology optimization parameters comprises:
keeping units with large contribution rate to the rigidity of the structure, wherein the relative density of the units is equal to 1 or approaches to 1;
and deleting the units with small contribution rate to the structural rigidity, wherein the relative density of the units is equal to 0 or approaches to 0.
5. The method of claim 4, wherein the ABAQUS-based method for performing the variable density topology optimization of Python language by secondary development comprises the following steps:
setting the volume fraction Vf to 0.2.
6. The method of claim 5, wherein the ABAQUS-based method for performing the variable density topology optimization of Python language by secondary development comprises the following steps:
the filtration radius rmin is set to 3.
7. The method of claim 6, wherein the ABAQUS-based method for performing the variable density topology optimization of Python language by secondary development comprises the following steps:
and setting the penalty factor P to be 3.0.
8. An apparatus for variable density topology optimization based on ABAQUS quadratic development Python language, the apparatus comprising:
the model establishing module is used for establishing a finite element model and determining a design domain;
the parameter acquisition module is used for acquiring topology optimization parameters, and the topology optimization parameters comprise volume fractions, filter radii and penalty factors;
the rigidity matrix establishing module is used for establishing a unit rigidity matrix according to the preset initial relative density of each unit and assembling an integral rigidity matrix;
the finite element analysis module is used for carrying out finite element analysis and extracting a node displacement field and unit strain energy;
the sensitivity calculation module is used for calculating sensitivity and obtaining the relative density of the unit according to a criterion method of a variable density topological optimization algorithm;
and the optimization iteration module is used for continuously repeating finite element analysis and optimization iteration calculation according to the topology optimization parameters until the objective function and the constraint condition are met.
9. An electronic device, comprising:
at least one memory and at least one processor;
the memory for storing one or more programs;
when executed by the at least one processor, the one or more programs cause the at least one processor to perform the steps of the method for variable density topology optimization based on the ABAQUS secondary development Python language of any of claims 1 to 7.
10. A computer readable storage medium storing a computer program, wherein the computer program when executed by a processor implements the steps of the method for ABAQUS secondary development Python language based variable density topology optimization according to any of claims 1 to 7.
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