CN114722655A - Structural topology optimization method based on local limited life fatigue constraint condition - Google Patents

Structural topology optimization method based on local limited life fatigue constraint condition Download PDF

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CN114722655A
CN114722655A CN202210243731.3A CN202210243731A CN114722655A CN 114722655 A CN114722655 A CN 114722655A CN 202210243731 A CN202210243731 A CN 202210243731A CN 114722655 A CN114722655 A CN 114722655A
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fatigue
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CN114722655B (en
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江旭东
孙成
熊志
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Harbin University of Science and Technology
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Abstract

The invention discloses a structural topology optimization method based on a local limited life fatigue constraint condition. According to the high cycle fatigue damage of the structure under the action of variable amplitude load, the average stress and the stress amplitude under the multi-axis stress state are determined by a rain flow counting method, the fatigue equivalent stress is evaluated by adopting the Sines criterion, and finally the fatigue failure of the structure is evaluated based on a Palmgren-Miner linear accumulated damage model. Compared with the optimization result of fatigue constraint coagulation, the fatigue damage and the material consumption of the design configuration obtained by the local fatigue constraint condition are obviously reduced. Compared with the existing topological optimization method for the fatigue problem based on the unit, the method adopts the unstructured polygon finite element method to complete the fatigue analysis and damage assessment of the continuum structure, and can realize the topological optimization design of the design domain structure with any curve boundary.

Description

Structure topology optimization method based on local limited life fatigue constraint condition
Technical Field
The invention relates to a topological optimization method, which provides an effective design strategy for improving the fatigue resistance of an engineering structure. In order to reduce the calculation cost caused by large-scale local fatigue constraint, a P norm method is often adopted to condense the local fatigue constraint into a global constraint, but the optimal solution meeting the weak constraint and the optimal solution of the original problem have gaps. In order to accurately satisfy local fatigue constraint and reduce the number of constraints, an augmented Lagrange method is adopted to process the original problem into an unconstrained problem, and a structural topology optimization method under the local limited life fatigue constraint condition is provided to obtain the optimal solution of the original optimization problem.
Background
The structural topology optimization technology oriented to additive manufacturing greatly enriches the design space of an engineering structure, gives consideration to the forming requirements of complex structures and high-performance components, and has wide application prospects and development spaces in the fields of aviation, aerospace, traffic, nuclear power and the like. At present, most of topological optimization research work is focused on solving the problem of structural rigidity maximization under volume constraint, an engineering structure is often used in a working environment with an alternating load effect, and the design with optimal rigidity generally cannot completely meet the anti-fatigue requirement, so that the reliability of the structure in operation within the whole life cycle is seriously influenced. Therefore, fatigue performance constraint is fully considered in the lightweight design of the structure, and the method has important scientific value and engineering significance for enriching the engineering structure strength design theory and improving service performance.
To suppress stress concentration and structural fracture caused by high stress values, a topological optimization problem under stress constraint has attracted a high degree of attention. The difficulty of the stress constrained topology optimization design is that a large number of local constraints increase the computational cost of sensitivity analysis. In order to reduce the number of stress constraints, a local stress constraint is generally converted into a global constraint by using a condensation method such as a P norm and a K-S function. For example, the fatigue constraints are condensed by a P-norm method, which, although it can greatly reduce the computational cost of the fatigue constraints and their sensitivity analysis, its approximate properties do not accurately control the fatigue constraints.
Disclosure of Invention
The invention provides a topological optimization framework of a local fatigue constraint problem based on an augmented Lagrange method. Considering the variable amplitude proportional load action condition, evaluating the fatigue damage of the structure by a Palmgren-Miner fatigue criterion, and providing a structure lightweight design method based on local fatigue constraint by taking the material consumption as an objective function and the fatigue performance as a constraint condition. Compared with the optimization result of the existing P norm method, the effectiveness of the proposed non-agglomeration method in processing the fatigue constraint topology optimization problem is verified.
The technical problem to be solved by the invention is as follows: the topological optimization method provides an effective design strategy for improving the fatigue resistance of the engineering structure, reduces the calculation cost caused by large-scale local fatigue constraint, accurately meets the local fatigue constraint and reduces the constraint quantity.
The technical scheme adopted by the invention is as follows: a structure topology optimization method based on a local limited life fatigue constraint condition is characterized by comprising the following implementation steps:
the method comprises the following steps: in the topology optimization framework provided by the invention, the non-condensed local fatigue constraint problem is respectively solved by taking the structure lightweight as the target (
Figure DEST_PATH_IMAGE001
) And P norm agglomeration global fatigue constraint problem (
Figure DEST_PATH_IMAGE002
) And comparing and analyzing the optimized solutions of the two problems, and verifying the effectiveness of the proposed method.
Figure DEST_PATH_IMAGE003
Figure DEST_PATH_IMAGE004
In the formula:
Figure DEST_PATH_IMAGE005
is a vector of the area of the cell,
Figure DEST_PATH_IMAGE006
is a sheetA bit-column vector of the bit-line,
Figure DEST_PATH_IMAGE007
the number of the units is the same as the number of the units,
Figure DEST_PATH_IMAGE008
、
Figure DEST_PATH_IMAGE009
respectively a cell density variable and a design variable,
Figure DEST_PATH_IMAGE010
in order to be a function of the volume interpolation,
Figure DEST_PATH_IMAGE011
operator for fatigue damage variable on cell j
Figure DEST_PATH_IMAGE012
Is the P-norm of the vector function,
Figure DEST_PATH_IMAGE013
is a node displacement vector.
Step two: in order to solve the topological optimization problem with a complex design domain structure, an unstructured polygonal mesh technology is utilized to disperse a spatial design domain, a modified qp relaxation technology is adopted to process unit stress, a rain flow counting method is adopted to extract peak values and valley values from a stress spectrum, stress cycles with different cycle characteristics are determined, stress amplitude scaling factors and average stress scaling factors are obtained, and the stress state of any stress cycle is estimated according to a formula. Respectively calculating the stress amplitude of the unit e in the ith cycle
Figure DEST_PATH_IMAGE014
And mean stress array
Figure DEST_PATH_IMAGE015
Amplitude of stress in the i-th cycle
Figure DEST_PATH_IMAGE016
And average stress scaling factor
Figure DEST_PATH_IMAGE017
。
Step three: fatigue failure analysis, in order to estimate the high cycle fatigue damage of the structure under the action of variable amplitude proportional load, the fatigue equivalent stress is estimated by adopting the Sines criterion, and finally the fatigue failure of the structure is estimated based on the Palmgren-Miner linear accumulated damage model, and the engineering structure needs to meet the following fatigue constraint so as to avoid the occurrence of fatigue fracture:
Figure DEST_PATH_IMAGE018
in the formula:
Figure DEST_PATH_IMAGE019
presentation uniteThe accumulated damage of the steel wire is reduced,
Figure DEST_PATH_IMAGE020
representing a scaling parameter (typically greater than 1),
Figure DEST_PATH_IMAGE021
for the number of alternating loads in a load spectrum block,
Figure DEST_PATH_IMAGE022
indicating load cyclesiThe number of cycles of (a) to (b),
Figure DEST_PATH_IMAGE023
the number of life cycles of unit e under the ith alternating load.
Step four: and (5) fatigue constraint. For optimization problems
Figure 737728DEST_PATH_IMAGE002
The P-norm fatigue constraint can be expressed as:
Figure DEST_PATH_IMAGE024
in the formula:Pis a P norm factor, high PThe norm factor is favorable for estimating the maximum value of the function, but also increases the nonlinearity of the optimization problem, is unfavorable for solving the problem and causes difficulty in convergence. In order to make the P-norm impairment approach the maximum value of the actual impairment, an adaptive constraint scaling technique is generally used to correct the P-norm impairment.
And (3) constructing polynomial local fatigue performance constraints one by one on a limited unit according to a mode of processing local stress constraints by GIRALDO-LONDONO, and avoiding fatigue failure at any material evaluation point. According to the local fatigue performance constraint formula, when the local fatigue constraint function satisfies
Figure DEST_PATH_IMAGE025
When the utility model is used, the water is discharged,
Figure DEST_PATH_IMAGE026
and
Figure DEST_PATH_IMAGE027
and the same order, so that the optimization algorithm is driven to iterate towards the direction of low damage. Also, when
Figure DEST_PATH_IMAGE028
When the temperature of the water is higher than the set temperature,
Figure 530235DEST_PATH_IMAGE026
and with
Figure DEST_PATH_IMAGE029
In the same order, thus
Figure 185338DEST_PATH_IMAGE026
The characteristics of the conventional linear constraint are preserved.
Figure DEST_PATH_IMAGE030
Step five: sensitivity analysis, the invention adopts global convergence Moving asymptote calculation (Global Convergent Method of Moving asymptots, GCMMA) to solve the problem of fatigue constraint topological optimization
Figure DEST_PATH_IMAGE031
。
Step six: the augmented Langerian method is taken as a typical non-agglomeration method, the optimal solution of the original optimization problem can be obtained by solving a series of unconstrained subproblems, and the topological optimization problem is solved by initializing and substituting a Lagrange multiplier and a square penalty factor into a gradient-based optimization algorithm GCMMA
Figure DEST_PATH_IMAGE032
The sub-problem of unconstrained standardization of the method is to update the design variables of the structural finite element model units;
step seven: and repeating the second step to the sixth step, and updating the design variables of the structural finite element model for multiple times until the obtained target value of the non-agglomeration method is more accurate than the target value of the P-norm agglomeration method, the optimized topology with the local constraint action has a more reasonable structural form near a load application area, and the transmission effect of weakening fatigue damage is also achieved.
Drawings
Fig. 1 is a flow chart of the augmented lagrangian optimization framework of the present invention.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
The method comprises the following steps:
the method comprises the following steps: in the topology optimization framework provided by the invention, the non-condensed local fatigue constraint problem is respectively solved by taking the structure lightweight as the target (
Figure 455914DEST_PATH_IMAGE032
) And P-norm cohesive global fatigue constraint problem: (
Figure 270286DEST_PATH_IMAGE002
) Comparing and analyzing the optimized solutions of the two problems, and verifying the existence of the proposed methodHigh effect.
Figure DEST_PATH_IMAGE033
Figure DEST_PATH_IMAGE034
(1)
In the formula:
Figure 968115DEST_PATH_IMAGE005
is a vector of the area of the cell,
Figure 235148DEST_PATH_IMAGE006
is a unit column vector of the column of the image,
Figure 434048DEST_PATH_IMAGE007
the number of the units is the same as the number of the units,
Figure 102927DEST_PATH_IMAGE008
、
Figure 971657DEST_PATH_IMAGE009
respectively a cell density variable and a design variable,
Figure 725986DEST_PATH_IMAGE010
in order to be a function of the volume interpolation,
Figure 462998DEST_PATH_IMAGE011
operator being a fatigue damage variable on cell j
Figure 986383DEST_PATH_IMAGE012
Is the P-norm of the vector function,
Figure 291594DEST_PATH_IMAGE013
is a node displacement vector.
Step two: in order to solve the topology optimization problem with a complex design domain structure, the unstructured polygon mesh technology is utilized to design a domain in a discrete space, and a modified qp relaxation technology is adoptedAnd (4) managing unit stress, extracting peak values and valley values from the stress spectrum by adopting a rain flow counting method, determining stress cycles with different cycle characteristics, thus obtaining a stress amplitude scaling factor and an average stress scaling factor, and estimating the stress state of any stress cycle according to a formula. Respectively calculating the stress amplitude of the unit e in the ith cycle
Figure 533219DEST_PATH_IMAGE014
And mean stress array
Figure 808343DEST_PATH_IMAGE015
Amplitude of stress in the i-th cycle
Figure 451814DEST_PATH_IMAGE016
And average stress scaling factor
Figure 662346DEST_PATH_IMAGE017
。
Step three: and (5) analyzing fatigue failure. In order to estimate the high-cycle fatigue damage of the structure under the action of variable-amplitude proportional load, the invention determines the average stress and the stress amplitude under the multi-axial stress state by a rain flow counting method, evaluates the fatigue equivalent stress by adopting a Sines criterion, and finally evaluates the fatigue failure of the structure based on a Palmgren-Miner linear accumulated damage model.
According to the Sines finite life fatigue criterion, the equivalent uniaxial stress of finite life in the plane stress state can be obtained from alternating octahedral shear stress and hydrostatic mean stress according to the formula:
Figure DEST_PATH_IMAGE035
in the formula:
Figure DEST_PATH_IMAGE036
、
Figure DEST_PATH_IMAGE037
the stress amplitude and average stress array of the unit e at the ith cycle respectively,
Figure DEST_PATH_IMAGE038
is a uniteIn stress cycleiThe uniaxial equivalent stress of (a) a (b),
Figure DEST_PATH_IMAGE039
the material parameter (typically taken to be 0.5).
The Basquin equation describes the relationship between uniaxial equivalent stress and fatigue life, and is expressed as:
Figure DEST_PATH_IMAGE040
in the formula:
Figure DEST_PATH_IMAGE041
is the coefficient of the fatigue strength of the steel,
Figure DEST_PATH_IMAGE042
is the fatigue life of the structure under stress cycle i, and b is the fatigue strength index.
The fatigue damage of any unit under the action of the whole load spectrum can be evaluated by adopting a Palmgren-Miner linear accumulated damage model, and the engineering structure needs to meet the following fatigue constraint so as to avoid the occurrence of fatigue fracture.
Figure DEST_PATH_IMAGE043
In the formula:
Figure 118563DEST_PATH_IMAGE019
presentation uniteThe accumulated damage of the steel wire is reduced,
Figure 197377DEST_PATH_IMAGE020
representing a scaling parameter (typically greater than 1),
Figure DEST_PATH_IMAGE044
indicating the unit under the ith alternating loadeThe accumulated damage of the steel wire is reduced,
Figure 570721DEST_PATH_IMAGE021
for the number of alternating loads in a load spectrum block,
Figure 342368DEST_PATH_IMAGE022
representing the number of cycles of the load cycle i.
Step four: and (5) fatigue constraint. For optimization problems
Figure 293006DEST_PATH_IMAGE002
The P-norm fatigue constraint can be expressed as:
Figure 50878DEST_PATH_IMAGE024
in the formula:Pfor the P-norm factor, a high P-norm factor is favorable for estimating the maximum value of the function, but also increases the nonlinearity of the optimization problem, which is unfavorable for solving the problem and causes difficulty in convergence. In order to make the P-norm impairment approach the maximum value of the actual impairment, an adaptive constraint scaling technique is generally used to correct the P-norm impairment.
And (3) constructing polynomial local fatigue performance constraints one by one on a limited unit according to a mode of processing local stress constraints by GIRALDO-LONDONO, and avoiding fatigue failure at any material evaluation point. According to the local fatigue performance constraint formula, when the local fatigue constraint function satisfies
Figure 403362DEST_PATH_IMAGE025
When the utility model is used, the water is discharged,
Figure 345910DEST_PATH_IMAGE026
and with
Figure 783845DEST_PATH_IMAGE027
And the same order, so that the optimization algorithm is driven to iterate towards the direction of low damage. Also, when
Figure 79828DEST_PATH_IMAGE028
When the temperature of the water is higher than the set temperature,
Figure 552398DEST_PATH_IMAGE026
and with
Figure 665847DEST_PATH_IMAGE029
In the same order, thus
Figure 591078DEST_PATH_IMAGE026
The features of the conventional linear constraint are preserved.
Figure DEST_PATH_IMAGE045
Step five: sensitivity analysis, the invention adopts global convergence Moving asymptote calculation (Global Convergent Method of Moving asymptots, GCMMA) to solve the fatigue constraint topological optimization problem
Figure 690752DEST_PATH_IMAGE031
。
Step six: a topological optimization framework of a local fatigue constraint problem is provided based on an augmented Lagrange method, the augmented Lagrange method is used as a typical non-agglomeration method, the optimal solution of the original optimization problem can be obtained by solving a series of unconstrained subproblems, and if the convergence condition is met:
Figure DEST_PATH_IMAGE046
the algorithm flow is shown in figure 1
Wherein,
Figure 752249DEST_PATH_IMAGE007
the number of the units is the number of the units,
Figure DEST_PATH_IMAGE047
to design variables, Tol is an absolute error limit, and when the number of cells is large enough, the penalty term may be much larger than the objective function, causing the algorithm to fail. Thus, introducing a normalized penalty term avoids singularity of the optimization problem, and the normalized lagrangian subproblem is expressed as:
Figure DEST_PATH_IMAGE048
Figure DEST_PATH_IMAGE049
Figure DEST_PATH_IMAGE050
in the formula:
Figure DEST_PATH_IMAGE051
is a function of the lagrange multiplier and,
Figure DEST_PATH_IMAGE052
is a square penalty factor that is a function of,
Figure DEST_PATH_IMAGE053
and converting the inequality constraint of the local fatigue performance into an equality constraint.
Figure DEST_PATH_IMAGE054
In the formula:
Figure DEST_PATH_IMAGE055
updating parameters, supremum limits, for penalty factors
Figure DEST_PATH_IMAGE056
The method is used for suppressing numerical instability of the algorithm. The lagrange multiplier is updated as follows:
Figure DEST_PATH_IMAGE057
method for solving topological optimization problem by adopting gradient-based optimization algorithm GCMMA
Figure DEST_PATH_IMAGE058
Unconstrained normalization sub-problems. Normalization of lagrange mesh according to the chain-type derivation ruleThe sensitivity of the calibration function is:
Figure DEST_PATH_IMAGE059
Figure DEST_PATH_IMAGE060
to volume fraction
Figure DEST_PATH_IMAGE061
Not directly related, but constrained by local fatigue properties
Figure 538065DEST_PATH_IMAGE026
And a stiffness parameter
Figure DEST_PATH_IMAGE062
The correlation, its partial derivative for the above parameters, is:
Figure DEST_PATH_IMAGE063
Figure DEST_PATH_IMAGE064
for the multi-working condition problem of variable amplitude load action, the sensitivity of the optimization problem can be effectively solved by the accompanying method. Introducing a balance equation under the action of a reference load in a residual form to form an augmented penalty term sensitivity analysis equation, wherein the method comprises the following steps:
Figure DEST_PATH_IMAGE065
Figure DEST_PATH_IMAGE066
in the formula:
Figure 701324DEST_PATH_IMAGE067
、
Figure DEST_PATH_IMAGE068
are respectively residual expressions of the stress amplitude and the average stress balance equation,
Figure DEST_PATH_IMAGE069
、
Figure DEST_PATH_IMAGE070
are the corresponding companion vectors.
The partial derivative of the stiffness parameter of the material is obtained by the following formula:
Figure DEST_PATH_IMAGE071
looking at the above equation, the calculation of the accompanying vector will take a significant amount of time as the number of stress cycles increases. Therefore, the displacement under the action of the reference load is scaled by the following formula to represent the amplitude displacement and the average displacement under the action of any cyclic load, so that the resolving scale of the accompanying vector can be effectively reduced.
Figure DEST_PATH_IMAGE072
Thus, the companion term is represented as:
Figure DEST_PATH_IMAGE073
in addition, to avoid direct solutions
Figure DEST_PATH_IMAGE074
If the accompanying vector is reasonably selected to disappear in the above formula, the following vectors are:
Figure DEST_PATH_IMAGE075
Figure DEST_PATH_IMAGE076
thus, after all scaled companion vectors are determined, the partial derivatives of the penalty term for the stiffness parameter can be obtained.
If it is satisfied with
Figure DEST_PATH_IMAGE077
Then there is
Figure DEST_PATH_IMAGE078
Otherwise:
Figure DEST_PATH_IMAGE079
Figure DEST_PATH_IMAGE080
finally, the process is carried out in a batch,
Figure DEST_PATH_IMAGE081
and
Figure DEST_PATH_IMAGE082
the following can be obtained explicitly:
Figure DEST_PATH_IMAGE083
step seven: and repeating the second step to the sixth step, and updating the design variables of the structural finite element model for multiple times until the obtained target value of the non-agglomeration method is more accurate than the target value of the P-norm agglomeration method, the optimized topology with the local constraint action has a more reasonable structural form near a load application area, and the transmission effect of weakening fatigue damage is also achieved.
The above are only the specific steps of the present invention, and the protection scope of the present invention is not limited in any way; the method can be expanded and applied to the field of design of a metal structure topology optimization method under the constraint of fatigue stress, and all technical schemes formed by adopting equivalent transformation or equivalent replacement fall within the protection scope of the invention.
The invention has not been described in detail and is part of the common general knowledge of a person skilled in the art.

Claims (1)

1. A structure topology optimization method based on a local limited life fatigue constraint condition is characterized by comprising the following implementation steps:
the method comprises the following steps: in the topology optimization framework provided by the invention, the non-condensed local fatigue constraint problem (is solved respectively by taking the structure lightweight as the target: (
Figure 245893DEST_PATH_IMAGE001
) And P norm agglomeration global fatigue constraint problem (
Figure 641102DEST_PATH_IMAGE002
) Comparing and analyzing the optimized solutions of the two problems, and verifying the effectiveness of the proposed method;
Figure 658737DEST_PATH_IMAGE003
Figure 340254DEST_PATH_IMAGE004
in the formula:
Figure 607287DEST_PATH_IMAGE005
is a vector of the area of the cell,
Figure 540608DEST_PATH_IMAGE006
is a vector of a unit column, and,
Figure 678328DEST_PATH_IMAGE007
the number of the units is the same as the number of the units,
Figure 937271DEST_PATH_IMAGE008
、
Figure 426021DEST_PATH_IMAGE009
respectively a cell density variable and a design variable,
Figure 22088DEST_PATH_IMAGE010
in order to be a function of the volume interpolation,
Figure 545473DEST_PATH_IMAGE011
operator being a fatigue damage variable on cell j
Figure 709738DEST_PATH_IMAGE012
Is the P-norm of the vector function,
Figure 420205DEST_PATH_IMAGE013
is a node displacement vector;
step two: in order to solve the topological optimization problem with a complex design domain structure, an unstructured polygonal mesh technology is utilized to disperse a spatial design domain, a modified qp relaxation technology is adopted to process unit stress, a rain flow counting method is adopted to extract peak values and valley values from a stress spectrum, stress cycles with different cycle characteristics are determined, stress amplitude scaling factors and average stress scaling factors are obtained, the stress state of any stress cycle is estimated according to a formula, and the stress amplitude of a unit e in the ith cycle is respectively solved
Figure 960908DEST_PATH_IMAGE014
And mean stress array
Figure 338800DEST_PATH_IMAGE015
Amplitude of stress in the i-th cycle
Figure 939545DEST_PATH_IMAGE016
And average stress scaling factor
Figure 996363DEST_PATH_IMAGE017
;
Step three: fatigue failure analysis, in order to estimate the high-cycle fatigue damage of the structure under the action of variable amplitude proportional load, a Sines criterion is adopted to estimate the fatigue equivalent stress, and finally the fatigue failure of the structure is estimated based on a Palmgren-Miner linear accumulated damage model, wherein the engineering structure needs to meet the following fatigue constraint so as to avoid the occurrence of fatigue fracture:
Figure 340757DEST_PATH_IMAGE018
in the formula:
Figure 838734DEST_PATH_IMAGE019
presentation uniteThe accumulated damage of the steel wire is reduced,
Figure 813643DEST_PATH_IMAGE020
representing a scaling parameter (typically greater than 1),
Figure 29861DEST_PATH_IMAGE021
for the number of alternating loads in a load spectrum block,
Figure 912366DEST_PATH_IMAGE022
indicating load cyclesiThe number of cycles of (a) to (b),
Figure 858326DEST_PATH_IMAGE023
the number of life cycles of unit e under the ith alternating load;
step four: the fatigue of the patient is restrained by the fatigue,
for optimization problems
Figure 535295DEST_PATH_IMAGE002
The P-norm fatigue constraint can be expressed as:
Figure 973229DEST_PATH_IMAGE024
in the formula:Pthe method is characterized in that a P norm factor is adopted, a high P norm factor is beneficial to estimating the maximum value of a function, however, nonlinearity of an optimization problem is increased, problem solving is not facilitated, and convergence is difficult to cause
Figure 128267DEST_PATH_IMAGE025
When the temperature of the water is higher than the set temperature,
Figure 335257DEST_PATH_IMAGE026
and
Figure 448707DEST_PATH_IMAGE027
same order, thus driving the optimization algorithm to iterate in the direction of low damage, and the same way
Figure 967413DEST_PATH_IMAGE028
When the temperature of the water is higher than the set temperature,
Figure 191721DEST_PATH_IMAGE026
and
Figure 518797DEST_PATH_IMAGE029
in the same order, thus
Figure 271989DEST_PATH_IMAGE026
The characteristics of the traditional linear constraint are retained:
Figure 418937DEST_PATH_IMAGE030
step five: sensitivity analysis, the invention adopts global convergence Moving asymptote calculation (Global Convergent Method of Moving asymptots, GCMMA) to solve the fatigue constraint topological optimization problem
Figure 446936DEST_PATH_IMAGE031
Step six: the augmented Langerian method is taken as a typical non-agglomeration method, the optimal solution of the original optimization problem can be obtained by solving a series of unconstrained subproblems, and the topological optimization problem is solved by initializing and substituting a Lagrange multiplier and a square penalty factor into a gradient-based optimization algorithm GCMMA
Figure 221994DEST_PATH_IMAGE032
The sub-problem of unconstrained standardization of the method is to update the design variables of the structural finite element model units;
step seven: and repeating the second step to the sixth step, and updating the design variables of the structural finite element model for multiple times until the obtained target value of the non-agglomeration method is more accurate than the target value of the P-norm agglomeration method, the optimized topology with the local constraint action has a more reasonable structural form near a load application area, and the transmission effect of weakening fatigue damage is also achieved.
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CN116484667A (en) * 2023-03-13 2023-07-25 北京交通大学 Topology optimization and stability assessment method for support connector structure
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