CN117195606A - Part topology optimization method and system - Google Patents
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Abstract
The invention provides a part topology optimization method and a part topology optimization system, wherein the method comprises the following steps: establishing a first three-dimensional model based on the part parameters; performing grid division on the first three-dimensional model to obtain a grid model, and applying load and constraint to the grid model based on the stress state of the part; performing primary statics analysis on the grid model, and performing topological optimization on the grid model based on an optimization model: and carrying out re-modeling on the grid model based on the topological optimization result so as to obtain a second three-dimensional model. The first three-dimensional model is established based on the part parameters, the first three-dimensional model is subjected to grid division, loads and constraints are applied, the model is subjected to topological optimization through the optimization model, the optimized second three-dimensional model is obtained, and on the premise that the stress performance of the material is ensured, the cost is reduced and the material waste is reduced to a great extent, so that the material utilization rate is improved.
Description
Technical Field
The invention relates to the technical field of topology optimization, in particular to a part topology optimization method and system.
Background
The structural topology optimization is to give load and displacement boundary conditions in a designated design area, and provide a practical method for the optimal lightweight design by automatically removing low-efficiency materials in the design field under a certain design constraint condition. By using the topology optimization method, a designer can get rid of the experience design, so that a novel and special structural form can be developed more easily.
The SIMP method creatively converts the optimization problem into the optimal distribution problem of the material, greatly simplifies the complexity of problem solving, and has become the topology optimization technology which is relatively mature in current development and has the widest application because of higher calculation efficiency and stability.
The cam-driven scorpion deformation robot is a robot manufactured based on the principle of a bionic robot. The cam-driven scorpion deformation robot mainly simulates the body structure and movement form of the organism (commonly called scorpion) of the arachnoid order to design the mechanical structure.
In reality, the scorpion deformation robot driven by the cam has the disadvantage of competing in the market due to the fact that the quality is large and the material utilization rate is low. How to reduce the weight without changing the service performance and improve the material utilization becomes a new challenge.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a part topology optimization method and a part topology optimization system, and aims to solve the technical problem of low material utilization rate in the prior art.
In order to achieve the above object, the present invention is achieved by the following technical scheme: a method of part topology optimization comprising the steps of:
establishing a first three-dimensional model based on the part parameters;
performing grid division on the first three-dimensional model to obtain a grid model, and applying load and constraint to the grid model based on the stress state of the part;
performing primary statics analysis on the grid model, and performing topological optimization on the grid model based on the following optimization model:
；
；
；
in the method, in the process of the invention,，/>the material volume constraint function and the minimum size constraint function, respectively, D is the design variable vector, +.>Is the set to which the design variable vector D belongs;
and carrying out re-modeling on the grid model based on the topological optimization result so as to obtain a second three-dimensional model.
According to an aspect of the above technical solution, the step of performing topology optimization on the mesh model based on the following optimization model specifically includes:
solving an optimization problem of minimum compliance under minimum size constraints based on the following optimization model:
；
；
；
；
；
；
wherein R represents a design area, J is the minimum flexibility of the structure, f, u, t and epsilon are the volume density, actual displacement and Newman boundary of the solid material respectivelyThe upper surface force and the second order linear strain tensor, v is the unit volume of the solid material, d is the integral sign, q is an integer,/and>is Dirichlet boundary->Upper prescribed displacement,/->Representing a heuristic displacement field, +.>Representing the Heaviside function, +.>A topology description function set representing an overall component; e represents isotropic elastic modulus, +.>Is the upper limit of the constraint of the volume of the solid material, < + >>Representing distance constraint function, ++>Representing the maximum displacement, +.>Representing the minimum displacement.
According to an aspect of the foregoing technical solution, the calculation expression of the heuristic displacement field is:
；
in the method, in the process of the invention,representing each node in the design area, < > and>representing coordinate points on the dirichlet boundary.
According to an aspect of the foregoing technical solution, the calculation expression of the elastic modulus is:
；
wherein the superscript S represents a unit node, p is the Poisson' S ratio of the solid material,and->Four-order unit tensor and two-order unit tensor, respectively>Is->Function sum->Convolution of the function.
According to an aspect of the foregoing solution, after the step of re-modeling the mesh model based on the topology optimization result to obtain a second three-dimensional model, the method further includes:
and carrying out secondary statics analysis on the second three-dimensional model, comparing an analysis result with the result of the primary statics analysis, and optimizing and effectively if the difference value meets a preset range.
According to an aspect of the foregoing disclosure, the step of primary statics analysis or the secondary statics analysis specifically includes:
the structural response of the part under a fixed load was analyzed based on the following kinetic equation:
；
in the formula, [ M ]]Is a system quality matrix [ C ]]Is a system damping matrix [ K ]]Is a system stiffness matrix; f is an external force, and is a force,、/>and u represents system acceleration, velocity, and displacement, respectively.
In another aspect, the present invention also provides a part topology optimization system, including:
the first modeling module is used for establishing a first three-dimensional model based on the part parameters;
the constraint module is used for carrying out grid division on the first three-dimensional model to obtain a grid model, and applying load and constraint on the grid model based on the stress state of the part;
the optimization module is used for carrying out primary statics analysis on the grid model and carrying out topological optimization on the grid model based on the following optimization model:
；
；
；
in the method, in the process of the invention,，/>the material volume constraint function and the minimum size constraint function, respectively, D is the design variable vector, +.>Is the set to which the design variable vector D belongs;
and the second modeling module is used for carrying out re-modeling on the grid model based on the topological optimization result so as to obtain a second three-dimensional model.
According to an aspect of the foregoing technical solution, the optimization module is specifically configured to:
solving an optimization problem of minimum compliance under minimum size constraints based on the following optimization model:
；
；
；
；
；
；
wherein R represents a design area, J is the minimum flexibility of the structure, f, u, t and epsilon are the volume density, actual displacement and Newman boundary of the solid material respectivelyThe upper surface force and the second order linear strain tensor, v is the unit volume of the solid material, d is the integral sign, q is an integer,/and>is Dirichlet boundary->Upper prescribed displacement,/->Representing a heuristic displacement field, +.>Representing the Heaviside function, +.>A topology description function set representing an overall component; e represents isotropic elastic modulus, +.>Is the upper limit of the constraint of the volume of the solid material, < + >>Representing distance constraint function, ++>Representing the maximum displacement, +.>Representing the minimum displacement.
According to an aspect of the foregoing solution, the part topology optimization system further includes:
and the analysis module is used for carrying out secondary statics analysis on the second three-dimensional model, comparing an analysis result with the result of the primary statics analysis, and optimizing and effectively if the difference value meets a preset range.
According to an aspect of the foregoing solution, the optimizing module or the analyzing module is further configured to:
the structural response of the part under a fixed load was analyzed based on the following kinetic equation:
；
in the formula, [ M ]]Is a system quality matrix [ C ]]Is a system damping matrix [ K ]]Is a system stiffness matrix; f is an external force, and is a force,、/>and u represents system acceleration, velocity, and displacement, respectively.
Compared with the prior art, the invention has the beneficial effects that: the first three-dimensional model is established based on the part parameters, the first three-dimensional model is subjected to grid division, loads and constraints are applied, the model is subjected to topological optimization through the optimization model, the optimized second three-dimensional model is obtained, and on the premise that the stress performance of the material is ensured, the cost is reduced and the material waste is reduced to a great extent, so that the material utilization rate is improved.
Drawings
The foregoing and/or additional aspects and advantages of the invention 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 method of part topology optimization in a first embodiment of the invention;
FIG. 2 is a block diagram of a component topology optimization system in accordance with a second embodiment of the present invention;
description of main reference numerals:
a first modeling module 100, a constraint module 200, an optimization module 300, a second modeling module 400.
Detailed Description
In order that the invention may be readily understood, a more complete description of the invention will be rendered by reference to the appended drawings. Various embodiments of the invention are shown in the drawings. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.
It will be understood that when an element is referred to as being "mounted" on another element, it can be directly on the other element or intervening elements may also be present. When an element is referred to as being "connected" to another element, it can be directly connected to the other element or intervening elements may also be present. The terms "vertical," "horizontal," "left," "right," and the like are used herein for illustrative purposes only.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and/or" as used herein includes any and all combinations of one or more of the associated listed items.
Conveniently, the sole plate of the cam driven scorpion deformation robot acts to carry the weight of the whole machine and to protect the internal parts of the machine from damage. The tail base arranged on one side of the bottom plate is used for connecting the tail mechanical mechanism and the scorpion deformation robot main body driven by the cam. The current cam-driven scorpion deformation robot base plate and tail base are mostly based on the fact that experience design is not optimal in quality under the same function, and the lack of study on topological optimization design of the cam-driven scorpion deformation robot base plate and tail base is overcome.
In the embodiment, the scheme is mainly used for carrying out topological optimization on the bottom plate and the tail base of the scorpion deformation robot.
Referring to fig. 1, a part topology optimization method according to a first embodiment of the present invention includes the following steps:
step S100, a first three-dimensional model is built based on the part parameters. Specifically, in the present embodiment, the above-mentioned component parameters are the shape and size parameters of the conventional base plate and the tail base, and the like.
Step 200, mesh division is performed on the first three-dimensional model to obtain a mesh model, and load and constraint are applied to the mesh model based on the stress state of the part. Specifically, in this embodiment, the first three-dimensional model is imported into finite element analysis software and is subjected to mesh division, and mesh refinement is required to ensure mesh availability.
When loading and restraining are applied to the model in the finite element analysis software, the bottom plate is mainly subjected to downward gravity by the control system of the scorpion deformation robot driven by the upper cam, and the scorpion deformation robot driven by the cam is subjected to external gravity during the working process. The tail base is connected with the bottom plate, so that the contact area between the tail base and the bottom plate is fully restrained. When in operation, a certain clockwise moment is brought to the tail base.
Step S300, performing primary statics analysis on the grid model, and performing topological optimization on the grid model based on the following optimization model:
；
；
；
in the method, in the process of the invention,，/>the material volume constraint function and the minimum size constraint function, respectively, D is the design variable vector, +.>Is the set to which the design variable vector D belongs.
Further, in this embodiment, the statics analysis mainly analyzes the structural response under the action of a fixed load, and observes the deformation, strain and stress equivalent change conditions of the analysis object under the action of external force, where the dynamics equation of the system is:
the structural response of the part under a fixed load was analyzed based on the following kinetic equation:
；
in the formula, [ M ]]Is a system quality matrix [ C ]]Is a system damping matrix [ K ]]Is a system stiffness matrix; f is an external force, and is a force,、/>and u represents system acceleration, velocity, and displacement, respectively. Specifically, for the baseplate and the aft base in this embodiment, the system speed and acceleration during analysis is 0, the load is constant, and the equation can be expressed as: />。
Further, in the step S300, topology optimization is performed based on the statics analysis, and the cam-driven scorpion deformation robot base plate and the tail base are modified SIMP by a variable density method. The topological optimization model constrained by the smallest dimension of the objective function can be described as:
solving an optimization problem of minimum compliance under minimum size constraints based on the following optimization model:
；
；
；
；
；
；
wherein R represents a design area, J is the minimum flexibility of the structure, f, u, t and epsilon are the volume density, actual displacement and Newman boundary of the solid material respectivelyThe upper surface force and the second order linear strain tensor, v is the unit volume of the solid material, d is the integral sign, q is an integer,/and>is Dirichlet boundary->Upper prescribed displacement,/->Representing a heuristic displacement field, +.>Representing the Heaviside function, +.>A topology description function set representing an overall component; e represents isotropic elastic modulus, +.>Is the upper limit of the constraint of the volume of the solid material, < + >>Representing distance constraint function, ++>Representing the maximum displacement, +.>Representing the minimum displacement. In this embodiment, the value of q is 2.
Specifically, the above-mentioned calculation expression of the heuristic displacement field is:
；
in the method, in the process of the invention,representing each node in the design area, < > and>representing coordinate points on the dirichlet boundary.
The above-mentioned elastic modulus is calculated as:
；
wherein the superscript S represents a unit node, p is the Poisson' S ratio of the solid material,and->Respectively isFourth order unit tensor and second order unit tensor, < >>Is->Function sum->Convolution of the function.
And step S400, carrying out re-modeling on the grid model based on the topological optimization result so as to obtain a second three-dimensional model.
Preferably, in this embodiment, after the step S400, the method further includes:
and S500, performing secondary statics analysis on the second three-dimensional model, comparing an analysis result with a result of the primary statics analysis, and optimizing and effectively if the difference value meets a preset range. Specifically, in this embodiment, the bottom plate and the tail base of the scorpion deformation robot driven by the cam after topological optimization are subjected to statics analysis, and compared with the analysis in step S300, the maximum value and the maximum value position of the total deformation and the stress are observed, and if the maximum value position is displaced and the maximum value change is within + -5%, that is, the stress point corresponding to the relevant color in the static analysis chart is displaced, the topology is effective. In addition, the statics analysis in this step may refer to the above step S300, and will not be described herein.
In summary, in the part topology optimization method in the above embodiment of the present invention, by establishing a first three-dimensional model based on part parameters, meshing the first three-dimensional model, applying load and constraint, and performing topology optimization on the model by using an optimization model, an optimized second three-dimensional model is obtained, and on the premise of ensuring the stress performance of the material, the cost is reduced and the material waste is reduced to a great extent, thereby improving the material utilization rate.
Example two
A second embodiment of the present invention provides a part topology optimization system comprising:
a first modeling module 100 for building a first three-dimensional model based on the part parameters;
the constraint module 200 is configured to grid-divide the first three-dimensional model to obtain a grid model, and apply load and constraint to the grid model based on a stress state of the part;
the optimization module 300 is configured to perform a statics analysis on the mesh model, and perform topology optimization on the mesh model based on the following optimization model:
；
；
；
in the method, in the process of the invention,，/>the material volume constraint function and the minimum size constraint function, respectively, D is the design variable vector, +.>Is the set to which the design variable vector D belongs;
and the second modeling module 400 is configured to re-model the mesh model based on the topology optimization result, so as to obtain a second three-dimensional model.
Preferably, in this embodiment, the optimization module 300 is specifically configured to:
solving an optimization problem of minimum compliance under minimum size constraints based on the following optimization model:
；
；
；
；
；
；
wherein R represents a design area, J is the minimum flexibility of the structure, f, u, t and epsilon are the volume density, actual displacement and Newman boundary of the solid material respectivelyThe upper surface force and the second order linear strain tensor, v is the unit volume of the solid material, d is the integral sign, q is an integer,/and>is Dirichlet boundary->Upper prescribed displacement,/->Representing a heuristic displacement field, +.>Representing the Heaviside function, +.>Topology description function for representing integral componentsA number set; e represents isotropic elastic modulus, +.>Is the upper limit of the constraint of the volume of the solid material, < + >>Representing distance constraint function, ++>Representing the maximum displacement, +.>Representing the minimum displacement.
Preferably, in this embodiment, the part topology optimization system further includes:
and the analysis module is used for carrying out secondary statics analysis on the second three-dimensional model, comparing an analysis result with the result of the primary statics analysis, and optimizing and effectively if the difference value meets a preset range.
Preferably, in this embodiment, the optimizing module 300 or the analyzing module is further configured to:
the structural response of the part under a fixed load was analyzed based on the following kinetic equation:
；
in the formula, [ M ]]Is a system quality matrix [ C ]]Is a system damping matrix [ K ]]Is a system stiffness matrix; f is an external force, and is a force,、/>and u represents system acceleration, velocity, and displacement, respectively.
In summary, in the part topology optimization system in this embodiment, by setting the first modeling module 100, establishing the first three-dimensional model based on the part parameters, meshing the first three-dimensional model by the constraint module 200, applying load and constraint, performing topology optimization on the model based on the optimization model by the optimization module 300, and obtaining the optimized second three-dimensional model based on the second modeling module 400, on the premise of ensuring the stress performance of the material, the cost is reduced and the material waste is reduced to a great extent, thereby improving the material utilization rate.
In the description of the present specification, a description referring to terms "one embodiment," "some 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 present invention. 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.
The foregoing examples illustrate only a few embodiments of the invention and are described in detail herein without thereby limiting the scope of the invention. It should be noted that various modifications and improvements can be made by those skilled in the art without departing from the spirit of the invention, which falls within the scope of the present invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
Claims (10)
1. The part topology optimization method is characterized by comprising the following steps of:
establishing a first three-dimensional model based on the part parameters;
performing grid division on the first three-dimensional model to obtain a grid model, and applying load and constraint to the grid model based on the stress state of the part;
performing primary statics analysis on the grid model, and performing topological optimization on the grid model based on the following optimization model:
；
；
；
in the method, in the process of the invention,，/>the material volume constraint function and the minimum size constraint function, respectively, D is the design variable vector,is the set to which the design variable vector D belongs;
and carrying out re-modeling on the grid model based on the topological optimization result so as to obtain a second three-dimensional model.
2. The part topology optimization method according to claim 1, characterized in that the step of topology optimizing the mesh model based on the following optimization model specifically comprises:
solving an optimization problem of minimum compliance under minimum size constraints based on the following optimization model:
；
；
；
；
；
；
wherein R represents a design area, J is the minimum flexibility of the structure, f, u, t and epsilon are the volume density, actual displacement and Newman boundary of the solid material respectivelyThe upper surface force and the second order linear strain tensor, v is the unit volume of the solid material, d is the integral sign, q is an integer,/and>is Dirichlet boundary->Upper prescribed displacement,/->Representing a heuristic displacement field, +.>Representing the Heaviside function, +.>A topology description function set representing an overall component; e represents isotropic elastic modulus, +.>Is the upper limit of the constraint of the volume of the solid material, < + >>Representing distance constraint function, ++>Representing the maximum displacement, +.>Representing the minimum displacement.
3. The part topology optimization method of claim 2, wherein the heuristic displacement field is calculated as:
；
in the method, in the process of the invention,representing each node in the design area, < > and>representing coordinate points on the dirichlet boundary.
4. The part topology optimization method of claim 2, wherein the calculation expression of the elastic modulus is:
；
wherein the superscript S represents a unit node, p is the Poisson' S ratio of the solid material,and->Four-order unit tensor and two-order unit tensor, respectively>Is->Function sum->Convolution of the function.
5. The method of part topology optimization of claim 1, wherein after the step of re-modeling the mesh model based on the topology optimization result to obtain a second three-dimensional model, the method further comprises:
and carrying out secondary statics analysis on the second three-dimensional model, comparing an analysis result with the result of the primary statics analysis, and optimizing and effectively if the difference value meets a preset range.
6. The method of part topology optimization of claim 5, wherein the step of primary statics analysis or secondary statics analysis specifically comprises:
the structural response of the part under a fixed load was analyzed based on the following kinetic equation:
；
in the formula, [ M ]]Is a system quality matrix [ C ]]Is a system damping matrix [ K ]]Is a system stiffness matrix; f is an external force, and is a force,、/>and u represents the system acceleration,Speed and displacement.
7. A part topology optimization system, comprising:
the first modeling module is used for establishing a first three-dimensional model based on the part parameters;
the constraint module is used for carrying out grid division on the first three-dimensional model to obtain a grid model, and applying load and constraint on the grid model based on the stress state of the part;
the optimization module is used for carrying out primary statics analysis on the grid model and carrying out topological optimization on the grid model based on the following optimization model:
；
；
；
in the method, in the process of the invention,，/>the material volume constraint function and the minimum size constraint function, respectively, D is the design variable vector,is the set to which the design variable vector D belongs;
and the second modeling module is used for carrying out re-modeling on the grid model based on the topological optimization result so as to obtain a second three-dimensional model.
8. The part topology optimization system of claim 7, wherein the optimization module is specifically configured to:
solving an optimization problem of minimum compliance under minimum size constraints based on the following optimization model:
；
；
；
；
；
；
wherein R represents a design area, J is the minimum flexibility of the structure, f, u, t and epsilon are the volume density, actual displacement and Newman boundary of the solid material respectivelyThe upper surface force and the second order linear strain tensor, v is the unit volume of the solid material, d is the integral sign, q is an integer,/and>is Dirichlet boundary->Upper prescribed displacement,/->Representing a heuristic displacement field, +.>Representing the Heaviside function, +.>A topology description function set representing an overall component; e represents isotropic elastic modulus, +.>Is the upper limit of the constraint of the volume of the solid material, < + >>Representing distance constraint function, ++>Representing the maximum displacement, +.>Representing the minimum displacement.
9. The part topology optimization system of claim 7, wherein said part topology optimization system further comprises:
and the analysis module is used for carrying out secondary statics analysis on the second three-dimensional model, comparing an analysis result with the result of the primary statics analysis, and optimizing and effectively if the difference value meets a preset range.
10. The part topology optimization system of claim 9, wherein the optimization module or the analysis module is further configured to:
the structural response of the part under a fixed load was analyzed based on the following kinetic equation:
；
in the formula, [ M ]]Is a system quality matrix [ C ]]Is a system damping matrix [ K ]]Is a system stiffness matrix; f is an external force, and is a force,、/>and u represents system acceleration, velocity, and displacement, respectively.
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| CN116362079A (en) * | 2023-03-16 | 2023-06-30 | 大连理工大学 | Multi-material structure topology optimization method based on novel interpolation model |
| CN116757051A (en) * | 2023-08-14 | 2023-09-15 | 华东交通大学 | Topology optimization method and system for flexible hinge mechanism |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116362079A (en) * | 2023-03-16 | 2023-06-30 | 大连理工大学 | Multi-material structure topology optimization method based on novel interpolation model |
| CN116757051A (en) * | 2023-08-14 | 2023-09-15 | 华东交通大学 | Topology optimization method and system for flexible hinge mechanism |
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| Title |
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