CN114021497A - Compressible turbulent flow fluid topology optimization method based on automatic differentiation - Google Patents

Compressible turbulent flow fluid topology optimization method based on automatic differentiation Download PDF

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CN114021497A
CN114021497A CN202111294234.8A CN202111294234A CN114021497A CN 114021497 A CN114021497 A CN 114021497A CN 202111294234 A CN202111294234 A CN 202111294234A CN 114021497 A CN114021497 A CN 114021497A
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邱若凡
周涛
尤延铖
周康
闫成
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Abstract

A compressible turbulent flow fluid topology optimization method based on automatic differentiation relates to topology optimization. Establishing a geometric model corresponding to the topological optimization of the flow channel; obtaining basic parameters of a topology optimization object, and constructing a CFD topology optimization model; constructing an objective function according to the basic parameters to form a nonlinear programming problem; deriving a sensitivity equation based on a companion method; solving a fluid control equation to obtain a flow field result and a value of an objective function, and outputting a new flow field result; constructing a Jacobian matrix and a gradient vector by utilizing an automatic differentiation technology; constructing a matrix form adjoint equation to obtain an adjoint multiplier; substituting the new flow field result and the adjoint multiplier into a sensitivity equation to solve the sensitivity; establishing a mathematical model by using an MMA (methyl methacrylate) numerical optimization method and combining a nonlinear programming problem; and carrying out optimization solution on the flow channel, updating the design variables to obtain an optimal solution, and outputting an optimal two-dimensional topological configuration. The problems that the manual derivation of compressible fluid is not enough in equation flexibility, complex in process, prone to error and the like are solved.

Description

Compressible turbulent flow fluid topology optimization method based on automatic differentiation
Technical Field
The invention belongs to the technical field of fluid topology optimization in computational fluid mechanics, and particularly relates to a compressible turbulent fluid topology optimization method based on automatic differentiation.
Background
Compressibility is one of the inherent properties of all fluids, usually in water and other liquids, which is neglected, and gases like air, where compressibility is one of the most important considerations at high velocities and pressures. High velocity compressible fluid flow is widely found in the aerospace field, and fluid compressibility must be considered in aerodynamic designs such as engine flowpath parts, aircraft profiles, airfoil profiles, turbomachinery, and the like. Meanwhile, with the development of computer technology, optimization methods for compressible streams have emerged in succession, Cummings et al ([1] Cummings R M, Yang H T, Oh Y H supersonics, turbo flow calculation and drive optimization for axiomatic afterbodies [ J ]. Computers & flows, 1995,24(4):487 507) proposed size optimization for compressible Fluids, and burgreand bay ([2] burgreg w.three-dimensional affinity processing optimization using size optimization.
The fluid topology optimization method is different from size optimization and shape optimization, can realize the change of the topological configuration of an optimized object, and has great advantages in the initial concept design stage. Borrval and Petersson ([3] Borrval T, Petersson J. topology optimization of Fluids in stocks flow [ J ]. International Journal for Numerical Methods in Fluids,2003,41(1):77-107) have for the first time proposed a fluid topology optimization method and applied to the topology optimization problem of fluid channels. Since then, the fluid topology optimization method is widely applied to various flows. While the current fluid topology optimization is mainly focused on the field of incompressible flow. Recently, LFN S et al ("4 LFN S a, Okubo C M, silver e. poling Optimization of subsonic compressible flows [ J ] Structural and Multidisciplinary Optimization,2021(6)) achieved subsonic compressible fluid topology Optimization, but no description was given of the specific process of auto-differentiating to achieve dispersion, and no consideration was given to the effects of turbulence. In many scientific research and engineering fields, the working environments of wing airfoils, turbine blades, internal flow channels of engines and the like are high-speed compressible turbulent flow. Therefore, it is highly desirable to develop a compressible fluid topology optimization method that takes into account the turbulence model.
The solution of sensitivity in fluid topology optimization usually adopts a continuous or discrete adjoint method, and A. Carnarius et al. ([5] Carnarius A, Thiele F, Oezkaya E, et al. Adjoint errors For Optimal Flow Control [ C ]//5th Flow Control reference.2010) introduces the advantages and disadvantages of the two methods. For complex CFD solvers that employ separation and iterative solution methods, manually deriving discrete adjoint equations is an important and error-prone task. The automatic differentiation method is a technology for accurately solving the function gradient by using a computer program, and has the characteristics of strong flexibility, accurate calculation and the like. The automatic differentiation method is described in detail in R.general. ([6] R.general, T.Kaminski, strategies for additive code construction, ACM Trans.Math.Softw.24(4) (1998) 437-474). The Cetin B. Dilgen et al. ([7] Dilgen CB, Dilgen S B, Fuhrman D R, et al. topology optimization of turboflow [ J ]. Computer Methods in Applied Mechanics and Engineering,2018,331(APR.1):363-393) proposed the optimization of the incompressible turbulence topology based on the automatic differentiation method. The invention discloses a compressible fluid accompanying equation solving method by utilizing an automatic differentiation method, and provides a compressible fluid topological optimization method based on automatic differentiation and considering a turbulence model.
Disclosure of Invention
The invention aims to provide a compressible turbulent fluid topology optimization method based on automatic differentiation, which can realize fluid topology optimization aiming at compressible fluid, considers the influence of a turbulent model on the optimization, constructs an adjoint equation through an automatic differentiation method, efficiently and accurately displays and generates a Jacobian matrix by utilizing the characteristics of the automatic differentiation method, and avoids the problems of insufficient flexibility, complicated process, easy error and the like of manually deriving the adjoint equation of the compressible fluid.
The invention comprises the following steps:
step 1: establishing a geometric model corresponding to the topological optimization of the flow channel according to the actual requirement of the optimized object, and determining the positions of an optimized design region omega and the inlet and outlet of the flow channel;
step 2: obtaining basic parameters of a topological optimization object, and constructing a CFD topological optimization model based on a compressible fluid control equation;
and step 3: converting optimization objective and fluid control equation into weak form according to basic parameters
Figure BDA0003335913410000021
Constructing a target function to form a nonlinear programming problem;
and 4, step 4: deriving a sensitivity equation based on a companion method;
and 5: setting appropriate design variables and initial values of intermediate variables, solving a fluid control equation to obtain a flow field result and a value of an objective function, and outputting a new flow field result;
step 6: in order to solve the adjoint equation, a Jacobian matrix and a gradient vector are constructed by utilizing an automatic differentiation technology;
and 7: constructing a matrix form adjoint equation by the Jacobian matrix and the gradient vector obtained in the step 6 to obtain an adjoint multiplier;
and 8: substituting the new flow field result obtained in the step 5 and the adjoint multiplier obtained in the step 7 into the sensitivity equation in the step 4, and solving the sensitivity;
and step 9: using an MMA (methyl methacrylate) numerical optimization method, and building a mathematical model by combining a known topological optimization nonlinear programming problem;
step 10: performing optimization solution on the flow channel by using an MMA algorithm, updating design variables, obtaining an optimal solution if iteration is converged, and outputting an optimal two-dimensional topological configuration; otherwise, jumping to step 5, and setting the flow field result as a new initial value.
In step 2, the obtaining of the basic parameters of the topology optimization object mainly includes: optimizing targets, fluid properties, inflow conditions, boundary conditions, heat conduction parameters; the specific steps of constructing the CFD topology optimization model based on the compressible fluid control equation may be:
(1) the material density is designated as a design variable gamma based on a variable density topological optimization method, a source term f is added in a fluid control equation to represent the resistance brought by the porous medium, and the function of the resistance and the design variable is as follows:
f＝-au
α(γ)＝αmin+(αmax-αmin)q(1-γ)/(q+γ)
wherein alpha is a permeability coefficient, and the larger the alpha value is, the larger the resistance caused by the porous medium to the fluid is; u is the fluid velocity field, q is a penalty parameter, and γ is the material density.
(2) Constructing a CFD topological optimization model based on a compressible fluid control equation:
Min:J(u,p,T,γ)；
Figure BDA0003335913410000031
Figure BDA0003335913410000032
Figure BDA0003335913410000033
wherein:
Figure BDA0003335913410000034
Figure BDA0003335913410000035
0≤γ≤1
wherein E is energy density, ρ is mass density, u is fluid velocity field, p is fluid pressure field, T is fluid temperature field, k is thermal conductivity coefficient,
Figure BDA0003335913410000036
is the viscosity tensor, μ is the kinetic viscosity, μTSolving the resulting turbulence viscosity, V, for the turbulence modelθThe volume fraction upper limit.
In step 3, the specific steps of constructing the objective function and constructing the nonlinear programming problem may be: converting optimization objective and fluid control equation into weak form according to basic parameters
Figure BDA0003335913410000037
And construct an objective function
Figure BDA0003335913410000038
Converting volume fraction limits to constraints
Figure BDA0003335913410000041
Wherein, a design variable γ, i.e. a function independent variable x, then constitutes the following nonlinear programming problem:
Minimize f0(x)
Subject to fi(x)≤0，i＝1,…,m
in step 4, the sensitivity equation is derived based on the adjoint method as follows:
Figure BDA0003335913410000042
Figure BDA0003335913410000043
Figure BDA0003335913410000044
wherein, U is an intermediate variable comprising U, p and T;
let adjoint equation
Figure BDA0003335913410000045
Obtaining a sensitivity equation:
Figure BDA0003335913410000046
in step 6, the specific method of the jacobian matrix and the gradient vector may be:
(1) assembling a jacobian matrix with a highly sparse structure by an automatic differential method:
Figure BDA0003335913410000047
the expansion form is as follows:
Figure BDA0003335913410000048
wherein: m is the number of intermediate variables, and n is the dimension of the design variable.
(2) Assembling a gradient vector L by an automatic differential method, wherein the value of the gradient vector L is the partial derivative of the target function to the intermediate variable:
Figure BDA0003335913410000049
in step 7, the matrix form is accompanied by the equation:
Figure BDA00033359134100000410
and solving the equation to obtain a value of the adjoint multiplier, and outputting the adjoint multiplier lambda.
In step 8, the solution sensitivity is as follows;
Figure BDA0003335913410000051
in step 9, the key parameters of the mathematical model include flow field results u, p, T, accompanying multiplier λ, sensitivity
Figure BDA0003335913410000052
And first-order and second-order differential expressions of the objective function and the constraint condition, and the like.
In step 10, it is determined whether the iteration has converged, and the maximum relative design variable change value of each grid cell before and after updating is compared with a set iteration termination condition as a convergence criterion.
The method aims at the compressible fluid to carry out fluid topology optimization, considers a turbulence model in a fluid control equation, and solves an adjoint equation in sensitivity analysis by adopting an automatic differentiation method. The compressible Navier-Stokes equation is coupled with a penalty equation based on a variable density material; and carrying out fluid topology optimization according to set constraint conditions such as a target function, volume limitation and the like, wherein the gradient in the optimization algorithm realizes discrete accompaniment through automatic differentiation, and then solving is carried out. The method has the advantages that the automatic differentiation method is utilized to realize and simplify the sensitivity solution of compressible fluid topology optimization under the consideration of the turbulence model, the burden of software development and maintainers is reduced, and the maintainability and flexibility of the fluid topology optimization application program are improved. The compressible turbulent flow fluid topology optimization method based on automatic differentiation provides a solving means for fluid topology optimization application in the engineering fields of aerospace and the like. The invention is suitable for the fluid topology optimization of compressible laminar flow and turbulent flow.
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FIG. 1 is a flowchart of an embodiment of a compressible fluid topology optimization method based on automatic differential solution with sensitivity.
Fig. 2 is a schematic view of a topology optimization design of a compressible turbulent two-dimensional straight-through flow channel provided by an embodiment of the present invention.
FIG. 3 is a graph of the convergence of the objective function and the volume constraint during the optimization process according to an embodiment of the present invention. Wherein, (a) is an objective function convergence diagram; (b) is a volume fraction convergence diagram.
Fig. 4 is a diagram of an optimal flow channel topology after solving according to an embodiment of the present invention.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth in order to provide a thorough understanding of the present invention.
The compressible fluid topological optimization method based on the automatic differential solution with the sensitivity is mainly constructed in a flow chart shown in figure 1 by taking the compressible turbulence optimization in a simple two-dimensional straight channel as an embodiment. The main method of the embodiment is as follows:
1. a square design field omega is constructed as required by the straight channel embodiment, fig. 2. The left side is an inlet, the right side is an outlet, and the width of the inlet is twice of that of the outlet;
2. setting basic parameters of a topology optimization object, mainly comprising: and (3) specifying the material density as gamma of a design variable, an optimization target, fluid properties, inflow conditions, boundary conditions and the like based on the variable density topological optimization method. Wherein the optimization objective is flow loss, the fluid property is air, and the boundary conditions are no-slip and thermal insulation boundaries:
designing variables: material density gamma
Intermediate variables: u, p, T
Permeability coefficient:
Figure BDA0003335913410000061
reynolds number:
Figure BDA0003335913410000062
darcy number:
Figure BDA0003335913410000063
an objective function:
Figure BDA0003335913410000064
wherein μ is dynamic viscosity, μTSolving the obtained turbulence viscosity for the turbulence model;
constraint conditions are as follows:
Figure BDA0003335913410000065
wherein, VθIs an artificial limit value for the volume fraction.
In this example, the reynolds number Re is 2.6 × 106The inlet velocity is parabolic and umax167m/s, Mach number Ma 0.5, volume constraint upper limit Vθ＝0.8。
3. The constraint conditions of the fluid topology optimization are divided into equality constraint conditions and inequality constraint conditions, wherein the equality constraint conditions comprise a fluid control equation after a source term f ═ au is added:
Figure BDA0003335913410000066
Figure BDA0003335913410000067
Figure BDA0003335913410000068
wherein:
Figure BDA0003335913410000069
the inequality constraints include volume fraction upper limits:
Figure BDA0003335913410000071
in summary, the optimization objective and the fluid control equation are transformed into weak form
Figure BDA0003335913410000072
And construct an objective function
Figure BDA0003335913410000073
Converting volume fraction limits to constraints
Figure BDA0003335913410000074
Wherein, a design variable γ, i.e. a function independent variable x, then constitutes the following nonlinear programming problem:
Minimize f0(x)
Subject to fi(x)≤0，i＝1,…,m
4. deriving a sensitivity equation based on the adjoint method:
Figure BDA0003335913410000075
Figure BDA0003335913410000076
Figure BDA0003335913410000077
wherein, U is an intermediate variable comprising U, p and T;
let adjoint equation
Figure BDA0003335913410000078
Obtaining a sensitivity equation:
Figure BDA0003335913410000079
5. setting appropriate design variables and initial values of intermediate variables, solving a fluid control equation to obtain a flow field result and a value of an objective function, and outputting fluid velocity fields u, p and J (u, p, T and gamma);
6. simplification using autodifferentiation techniques for solving adjoint equations
Figure BDA00033359134100000710
Solving:
a) assembling elegance with highly sparse structure by auto-differential methodComparable matrices:
Figure BDA00033359134100000711
its unfolded shape
The formula is as follows:
Figure BDA00033359134100000712
wherein: m is the number of intermediate variables, and n is the dimension of the design variable.
b) Assembling a gradient vector L by an automatic differential method, wherein the value of the gradient vector L is the partial derivative of the target function to the intermediate variable:
Figure BDA0003335913410000081
7. and (3) forming a matrix form adjoint equation by the Jacobian matrix K obtained in the step 6 and the gradient vector L:
Figure BDA0003335913410000082
solving an equation to obtain a value of an adjoint multiplier, and outputting lambda;
8. substituting the flow field result u obtained in the step 4 and the adjoint multiplier lambda obtained in the step 7 into the sensitivity equation in the step 5, and solving the sensitivity;
Figure BDA0003335913410000083
9. and (3) constructing a mathematical model by using an MMA (methyl methacrylate) numerical optimization method and combining a known topological optimization nonlinear programming problem. The key parameters of the mathematical model comprise flow field results obtained by solving the steps: u, p, T, adjoint multiplier: λ, sensitivity:
Figure BDA0003335913410000084
and first-order and second-order differential expressions of the objective function and the constraint condition, and the like.
10. And (3) performing optimization solution on the straight-through flow channel through an MMA algorithm, continuously updating design variables, comparing the maximum relative design variable change value of each grid unit before and after updating with a set iteration termination condition as a convergence basis, and if the iteration is not converged, jumping to the step 5 and setting a flow field result as a new initial value. And stopping calculation until iterative convergence to obtain an optimal solution, and outputting the two-dimensional straight-through flow channel topological configuration with the lowest energy loss. In the optimization process, penalty parameters q and alphamaxDetermines the quality of the optimized result, namely q and alphamaxWhen the selection is not proper, the problem of unclear fluid-solid boundary can occur. FIG. 3 shows an example of the present invention where q is 0.1 and α ismaxThe objective function and the volume constraint convergence map under 10000 parameter settings. As can be seen from the figure, the change amplitude of the first 10 steps in the optimization process is large, and gradually converges from the 10 th step to the 60 th step. Wherein, the objective function convergence diagram (a) shows the topological configuration under different iteration steps. Fig. 4 is the result of the topology configuration after the final optimization convergence.
The invention provides a compressible fluid topology optimization method based on automatic differentiation, which is characterized in that an automatic differentiation technology is utilized to solve an adjoint equation in sensitivity analysis. The method not only realizes the compressible fluid topology optimization considering the turbulence influence, but also has the characteristic of realizing the discrete adjoint by automatic differentiation, so that repeated derivation is not needed according to target functions and boundary conditions of different research objects, and the method has obvious superiority compared with a fussy manual derivation adjoint equation method.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. This need not be, nor should it be exhaustive of all examples. Any modification and improvement within the spirit of the invention are considered to be within the scope of the invention.

Claims (10)

1. An automatic differential based compressible turbulent fluid topology optimization method is characterized by comprising the following steps:
step 1: establishing a geometric model corresponding to the topological optimization of the flow channel according to the actual requirement of the optimized object, and determining the positions of an optimized design region omega and the inlet and outlet of the flow channel;
step 2: obtaining basic parameters of a topological optimization object, and constructing a CFD topological optimization model based on a compressible fluid control equation;
and step 3: converting optimization objective and fluid control equation into weak form according to basic parameters
Figure RE-FDA0003369283070000011
Constructing a target function to form a nonlinear programming problem;
and 4, step 4: deriving a sensitivity equation based on a companion method;
and 5: setting appropriate design variables and initial values of intermediate variables, solving a fluid control equation to obtain a flow field result and a value of an objective function, and outputting a new flow field result;
step 6: in order to solve the adjoint equation, a Jacobian matrix and a gradient vector are constructed by utilizing an automatic differentiation technology;
and 7: constructing a matrix form adjoint equation by the Jacobian matrix and the gradient vector obtained in the step 6 to obtain an adjoint multiplier;
and 8: substituting the new flow field result obtained in the step 5 and the adjoint multiplier obtained in the step 7 into the sensitivity equation in the step 4, and solving the sensitivity;
and step 9: using an MMA (methyl methacrylate) numerical optimization method, and building a mathematical model by combining a known topological optimization nonlinear programming problem;
step 10: performing optimization solution on the flow channel by using an MMA algorithm, updating design variables, obtaining an optimal solution if iteration is converged, and outputting an optimal two-dimensional topological configuration; otherwise, jumping to step 5, and setting the flow field result as a new initial value.
2. The compressible turbulent fluid topological optimization method based on automatic differentiation according to claim 1, wherein in step 2, the obtaining of basic parameters of a topological optimization object comprises: optimization objectives, fluid properties, inflow conditions, boundary conditions, heat transfer parameters.
3. The compressible turbulent fluid topology optimization method based on automatic differentiation according to claim 1, wherein in step 2, the concrete steps of constructing the CFD topology optimization model based on the compressible fluid control equation are as follows:
(1) the material density is designated as a design variable gamma based on a variable density topological optimization method, a source term f is added in a fluid control equation to represent the resistance brought by the porous medium, and the function of the resistance and the design variable is as follows:
f＝-au
α(γ)＝αmin+(αmax-αmin)q(1-γ)/(q+γ)
wherein alpha is a permeability coefficient, and the larger the alpha value is, the larger the resistance caused by the porous medium to the fluid is; u is a fluid velocity field, q is a penalty parameter, and gamma is a material density;
(2) constructing a CFD topological optimization model based on a compressible fluid control equation:
Min:J(u,p,T,γ)；
Figure RE-FDA0003369283070000021
Figure RE-FDA0003369283070000022
Figure RE-FDA0003369283070000023
wherein:
Figure RE-FDA0003369283070000024
Figure RE-FDA0003369283070000025
0≤γ≤1
wherein E is the energy density and ρ isMass density, u is the fluid velocity field, p is the fluid pressure field, T is the fluid temperature field, k is the thermal conductivity,
Figure RE-FDA0003369283070000026
is the viscosity tensor, μ is the kinetic viscosity, μTSolving the resulting turbulence viscosity, V, for the turbulence modelθThe volume fraction upper limit.
4. The compressible turbulent fluid topology optimization method based on automatic differentiation according to claim 1, wherein in step 3, the specific steps of constructing the objective function and constructing the nonlinear programming problem are as follows: converting optimization objective and fluid control equation into weak form according to basic parameters
Figure RE-FDA0003369283070000027
And construct an objective function
Figure RE-FDA0003369283070000028
Converting volume fraction limits to constraints
Figure RE-FDA0003369283070000029
Where x represents the design variable γ, then constitutes the following nonlinear programming problem:
Minimize f0(x)
Subject to fi(x)≤0，i＝1,…,m。
5. the method for optimizing the topology of the compressible turbulent fluid based on automatic differentiation according to claim 1, wherein in step 4, the sensitivity equation is derived based on the adjoint method as follows:
Figure RE-FDA00033692830700000210
Figure RE-FDA0003369283070000031
Figure RE-FDA0003369283070000032
wherein, U is an intermediate variable comprising U, p and T;
let adjoint equation
Figure RE-FDA0003369283070000033
Obtaining a sensitivity equation:
Figure RE-FDA0003369283070000034
6. the compressible turbulent fluid topology optimization method based on automatic differentiation according to claim 1, wherein in step 6, the specific method for constructing the jacobian matrix and the gradient vector by using the automatic differentiation technology is as follows:
(1) assembling a jacobian matrix with a highly sparse structure by an automatic differential method:
Figure RE-FDA0003369283070000035
the expansion form is as follows:
Figure RE-FDA0003369283070000036
wherein: m is the number of intermediate variables, and n is the dimension of a design variable;
(2) assembling a gradient vector L by an automatic differential method, wherein the value of the gradient vector L is the partial derivative of the target function to the intermediate variable:
Figure RE-FDA0003369283070000037
7. the method for optimizing the topology of the compressible turbulent fluid based on automatic differentiation as claimed in claim 1, wherein in step 7, the accompanying equation in the form of a matrix is as follows:
Figure RE-FDA0003369283070000038
and solving the equation to obtain a value of the adjoint multiplier, and outputting the adjoint multiplier lambda.
8. The compressible turbulent fluid topology optimization method based on automatic differentiation according to claim 1, wherein in step 8, the solution sensitivity is as follows;
Figure RE-FDA0003369283070000039
9. the method for optimizing the topology of the compressible turbulent fluid based on automatic differentiation according to claim 1, wherein in step 9, the key parameters of the mathematical model comprise flow field results u, p, T, sensitivity with multiplier λ
Figure RE-FDA0003369283070000041
And first-order and second-order differential expressions of the objective function and the constraint condition.
10. The method for optimizing the topology of the compressible turbulent fluid based on automatic differentiation according to claim 1, wherein in step 10, the iteration is converged, and the maximum relative design variable change value of each grid cell before and after the updating is compared with the set iteration termination condition as a convergence criterion.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114896747A (en) * 2022-05-30 2022-08-12 四川启睿克科技有限公司 Sensitivity calculation-based micro-channel structure optimization design method

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112231900A (en) * 2020-10-09 2021-01-15 中国科学院力学研究所 Variable physical property topology optimization method
AU2020103808A4 (en) * 2020-01-17 2021-02-11 Beijing University Of Technology A design method of the fail-safe topology optimization of continuum structures with the frequency and displacement constraints
CN113094944A (en) * 2021-03-22 2021-07-09 华中科技大学 Micro-channel radiator and microscopic scale topology optimization design method thereof

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
AU2020103808A4 (en) * 2020-01-17 2021-02-11 Beijing University Of Technology A design method of the fail-safe topology optimization of continuum structures with the frequency and displacement constraints
CN112231900A (en) * 2020-10-09 2021-01-15 中国科学院力学研究所 Variable physical property topology optimization method
CN113094944A (en) * 2021-03-22 2021-07-09 华中科技大学 Micro-channel radiator and microscopic scale topology optimization design method thereof

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
CHENYUE XIE: "Artificial neural network mixed model for large eddy simulation of compressible isotropic turbulence", PHYSICS OF FLUIDS, 20 August 2019 (2019-08-20) *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114896747A (en) * 2022-05-30 2022-08-12 四川启睿克科技有限公司 Sensitivity calculation-based micro-channel structure optimization design method
CN114896747B (en) * 2022-05-30 2024-05-14 四川启睿克科技有限公司 Microchannel structure optimization design method based on sensitivity calculation

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