CN112507592A - Strain energy regionalized continuum structure topology optimization method - Google Patents

Strain energy regionalized continuum structure topology optimization method Download PDF

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CN112507592A
CN112507592A CN202011477701.6A CN202011477701A CN112507592A CN 112507592 A CN112507592 A CN 112507592A CN 202011477701 A CN202011477701 A CN 202011477701A CN 112507592 A CN112507592 A CN 112507592A
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energy
strain
constraint
stress
specific energy
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余杨
崔宇朋
余建星
孙若飞
成司元
李振眠
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Tianjin University
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Abstract

The invention provides a strain energy regionalization continuum structure topology optimization method, which comprises the steps of firstly converting stress constraint of a structure finite element unit into distortion specific energy constraint based on the equivalent effect of the distortion energy constraint and the stress constraint; based on the fact that the unit strain specific energy is the sum of the distortion specific energy and the volume change specific energy, the unit strain specific energy is used for replacing the unit distortion specific energy, the unit strain specific energies of finite elements of the structure are summed, the strain specific energy constraint of the whole layer of the structure is obtained, and then the strain specific energy constraint is converted into the strain energy constraint: the design area is divided into a high stress area and a low stress area, the strain energy of the low stress area is minimized, and the allowable strain energy is independently arranged in the high stress area, so that the optimization result of reducing the structural stress and solving the problem of strain energy concentration is obtained. The structure is divided into a high stress area and a low stress area, and the structure stress is reduced and the stress concentration phenomenon is relieved by minimizing the strain energy of the low stress area and independently setting the allowable strain energy of the high stress area.

Description

Strain energy regionalized continuum structure topology optimization method
Technical Field
The invention relates to the field of structure optimization, in particular to a continuum structure topology optimization method capable of relieving stress concentration phenomenon in strain energy regionalization.
Background
At present, the structure optimization of a continuum is divided into three levels, namely size optimization, shape optimization and topology optimization. Compared with size optimization and shape optimization, structural topology optimization is in a higher level, more parameters to be determined are needed, influence of variables on optimization targets is larger, and generated economic benefits are larger.
The topological optimization is to realize the optimal distribution of materials under the condition of meeting an objective function and a constraint function so as to obtain an optimal force transmission path, and the essence is whether a structural unit has a problem or not. By means of the topology optimization technology, designers can get rid of the limitation of an initial design scheme and seek an optimal design scheme meeting target conditions and constraint conditions according to boundary and load conditions.
In recent years, a structure topology optimization technology is rapidly developed and widely applied to the fields of ships, automobiles, machinery and the like, at present, numerical algorithms are mainly adopted for solving, and effective solving algorithms mainly comprise a homogenization Method based on a microstructure idea, a Solid Isotropic Material Punishment (SIMP) Method for directly carrying out rigidity interpolation by means of material density, an evolutionary algorithm (ESO Method) for gradually seeking improved design by utilizing a heuristic means, a Level Set Method (Level Set Method) and the like.
In an actual engineering structure, the structural strength is one of important conditions to be considered, and topological optimization under stress constraint aims to improve the structural strength, but the traditional topological optimization considering von mises stress has the following problems:
(1) a stress concentration phenomenon;
(2) stress singularity (i.e., low density cells have high stress);
(3) stress locality.
Disclosure of Invention
The invention aims to provide a topological optimization method of a continuum structure, which can relieve the stress concentration phenomenon in the strain energy regionalization.
Specifically, the invention provides a strain energy regionalized continuum structure topology optimization method, which comprises the following steps,
step 100, converting stress constraint of the structural finite element unit into distortion specific energy constraint based on the equivalent effect of the distortion energy constraint and the stress constraint;
step 200, based on the sum of the specific energy of unit strain and the specific energy of volume change, the specific energy of unit strain is used to replace the specific energy of unit strain, the specific energy of unit strain of the finite element of the structure is summed to obtain the specific energy constraint of the whole layer of the structure, and then the specific energy constraint is converted into the strain energy constraint:
and 300, dividing the design area into a high stress area and a low stress area, minimizing the strain energy of the low stress area, and independently setting allowable strain energy in the high stress area to obtain an optimization result of reducing structural stress and solving strain energy concentration.
The stress singularity phenomenon is eliminated and the stress locality problem is solved by replacing stress constraint with strain energy constraint; the structure is partitioned into a high stress area and a low stress area, and the structure stress is reduced and the stress concentration phenomenon is relieved by minimizing the strain energy of the low stress area and independently setting the allowable strain energy of the high stress area.
Drawings
FIG. 1 is a schematic diagram of the optimization method steps of one embodiment of the present invention;
FIG. 2 is a schematic flow diagram of an optimization method according to an embodiment of the invention;
FIG. 3 is a schematic diagram of the dimension, partition, load and boundary conditions of an L-shaped cantilever structure optimally designed by an optimization method;
FIG. 4 is a finite element model of an L-shaped cantilever beam structure optimally designed by an optimization method;
FIG. 5 is a schematic diagram of the design configuration and stress distribution of the L-shaped cantilever of FIG. 3 optimized by conventional methods;
FIG. 6 is a schematic diagram of the design configuration of the L-shaped cantilever of FIG. 3 and the stress distribution at an allowable strain energy of 2 in the high stress region;
FIG. 7 is a schematic diagram of the design configuration of the L-shaped cantilever beam of FIG. 3 and the stress distribution at an allowable strain energy of 1 in the high stress region;
FIG. 8 is a schematic diagram of the design configuration of the L-shaped cantilever of FIG. 3 and the stress distribution at an allowable strain energy of 0.9 in the high stress region;
FIG. 9 is a schematic diagram of the design configuration of the L-shaped cantilever of FIG. 3 and the stress distribution at 0.8 allowable strain energy in the high stress zone;
fig. 10 is a schematic diagram of the design configuration of the L-shaped cantilever beam in fig. 3 and the stress distribution at the allowable strain energy of 0.7 in the high stress area.
Detailed Description
The detailed structure and implementation process of the present solution are described in detail below with reference to specific embodiments and the accompanying drawings.
In one embodiment of the present invention, as shown in fig. 1, a strain energy regionalized continuum structure topology optimization method is disclosed, comprising the steps of,
step 100, converting stress constraint of the structural finite element unit into distortion specific energy constraint based on the equivalent effect of the distortion energy constraint and the stress constraint;
the proof of equivalent effect of distortion energy constraint and stress constraint is as follows:
according to the fourth strength theory-distortion energy theory, the failure criterion of material yield is
Figure BDA0002836135470000041
Figure BDA0002836135470000042
Figure BDA0002836135470000043
Wherein u isdIn order to be able to distort the structure specifically,
Figure BDA0002836135470000044
is the allowable distortion ratio energy of the structure; ν is the poisson ratio; e is the modulus of elasticity; sigma1,σ2,σ3The first, second and third principal stresses; sigmasIs the yield point of the material;
the formula (3) is expressed as von Mises stress:
σeq＝σs (4)
Figure BDA0002836135470000045
wherein σeqIs von Mises stress, and thus the distortion energy constraint and the stress constraint have the same effect.
The process of converting the stress constraint to the distortion specific energy constraint is as follows:
Figure BDA0002836135470000046
wherein,
Figure BDA0002836135470000047
is the specific energy of distortion for unit i.
Step 200, based on the sum of the specific energy of unit strain and the specific energy of volume change, the specific energy of unit strain is used to replace the specific energy of unit strain, the specific energy of unit strain of the finite element of the structure is summed to obtain the specific energy constraint of the whole layer of the structure, and then the specific energy constraint is converted into the strain energy constraint:
the proof based on the specific energy in unit strain as the sum of the specific energy in distortion and the specific energy in volume change is as follows:
Figure BDA0002836135470000048
wherein e isiIs the strain energy of unit i; viIs the volume of cell i;
Figure BDA0002836135470000049
the specific energy of change in volume for unit i.
From (6) to (7), it can be seen that, for structural failure, replacing the specific cell strain energy with the specific cell distortion energy is a safer strategy, i.e. equation (6) is transformed into:
Figure BDA0002836135470000051
wherein e isiIs the strain energy of unit i; viIs the volume of cell i.
The strain specific energy of the finite element units of the structure is summed to obtain the strain specific energy constraint of the whole layer of the structure, and then the process of converting the strain specific energy constraint into the strain energy constraint is as follows:
Figure BDA0002836135470000052
Figure BDA0002836135470000053
wherein,
Figure BDA0002836135470000054
referred to as allowable strain energy.
However, the structure may have a strain energy concentration phenomenon, and the strain energy of part of the units is too large, so that the formula (9) is a necessary condition rather than a sufficient condition of the formula (8), but although the structural units cannot be guaranteed to completely meet stress constraint, the number of stress constraint can be greatly reduced, and further, the stress constraint condition of the units can be accurately met in subsequent size and shape optimization.
And 300, dividing the design area into a high stress area and a low stress area, minimizing the strain energy of the low stress area, and independently setting allowable strain energy in the high stress area to obtain an optimization result of reducing structural stress and solving strain energy concentration.
In the embodiment, stress constraint is replaced by strain energy constraint to eliminate the singular phenomenon of stress and solve the problem of stress locality; the structure is partitioned into a high stress area and a low stress area, and the structure stress is reduced and the stress concentration phenomenon is relieved by minimizing the strain energy of the low stress area and independently setting the allowable strain energy of the high stress area. The method is realized by means of commercial software Hyperworks, has robustness and high efficiency, is easy to implement and has strong adaptability.
The method is further described in the following with reference to the accompanying drawings in specific embodiments, as shown in fig. 2, the optimization process is as follows:
1. an L-shaped cantilever beam geometric model is established through a Rhino modeling software, and is divided into a design area and a non-design area (stress singularity prevention) through segmentation operation, wherein the design area is divided into a high stress area and a low stress area, as shown in FIG. 3;
2. introducing the L-shaped cantilever beam geometric model into a Hyperworks-Hypermesh module in an IGES format, creating components named high _ region, low _ region and nodesign, and moving the surface elements in the high stress region, the low stress region and the non-design region into the components named high _ region, low _ region and nodesign;
3. creating a material named steel, wherein the attribute of the material is E1.0, ν 0.3, and card image is MAT 1;
4. creating attributes named high _ region, low _ region and nondesign and distributing the attributes to corresponding components, wherein the three attributes are all shell units, the material is the steel created in the step (3), and the thickness is 1;
5. grid division, namely adopting a first-order quadrilateral unit, wherein the grid size is 1 multiplied by 1;
6. creating load sets named as spc and force, selecting the spc load set and fixing the upper end of the L-shaped cantilever beam, selecting the force load set and applying a load which is vertically downward in the direction of 3 at the vertex of the right end of the L-shaped cantilever beam; as shown in fig. 4;
7. creating a load step named as linear and selecting spc and force load sets;
8. design variables are created. Creating a design variable named design and selecting attributes named high _ region and low _ region, wherein the type is PSHELL, and the minimum member size is 10;
9. a response function is created. Creating a response named com _ high and selecting a compliance and an attribute named high _ region; creating a response named com _ low and selecting the compliance and an attribute named high _ low; creating a response named volume and selecting the volume and the total;
10. a constraint function is created. Creating a constraint named com _ high, selecting a response named com _ high, wherein the upper limit value is 0.7,0.8,0.9,1 and 2, and the loadstep selects a load step named linear; creating a constraint named volume and selecting a response named volume, wherein the upper limit value is set to be 7680;
11. an objective function is created. Minimizing the response named com _ low, and selecting the load step named linear by loadstep;
12. performing topological structure analysis, judging whether the structure is converged, if so, stopping calculation, and if not, executing the steps (13) - (16);
13. the design response carries out sensitivity analysis on the deviation of the optimization design variable;
14. unfolding the design response by using the sensitivity information to obtain a display approximate model;
the Hyperworks-Optistruct module automatically selects a proper mathematical programming method for optimizing so that the optimization problem meets the Kuhn-Tucker condition at the optimal point;
16. the design variables are updated in such a way that,
17. and (5) repeating the steps (12) to (17).
As can be seen from fig. 5, the L-shaped cantilever beam adopts a traditional topological optimization method based on strain energy, the maximum stress of the configuration diagram obtained by design optimization is 2.008, and stress concentration occurs at corners, which is very likely to cause structural failure. As can be seen from fig. 6 to 10, after the topology optimization method of the present invention is adopted for the L-shaped cantilever beam, the allowable strain energies with the sizes of 2, 1, 0.9, 0.8, and 0.7 are respectively set for the high stress regions, and the maximum stresses of the configuration diagram obtained by design optimization are 1.390, 1.361, 1.336, 1.289, and 1.268.
Table 1 is the maximum stress statistics in the stress distribution diagrams of fig. 6-10 and the percentage stress reduction statistics relative to the maximum stress in fig. 5.
Figure BDA0002836135470000071
Figure BDA0002836135470000081
Compared with the traditional method, the maximum stress is greatly reduced, the reduction amplitude is increased along with the reduction of the allowable strain energy of a high-stress area, the maximum reduction amplitude reaches 57.14%, in addition, the stress concentration phenomenon at corners disappears, and the failure resistance of the structure is greatly improved.
Compared with the traditional topological optimization method based on the strain energy, the topological optimization method of the strain energy regionalized continuum structure provided by the invention replaces stress constraint with strain energy constraint, eliminates the stress singularity phenomenon and solves the problem of stress locality. In addition, the stress level of the design configuration is greatly reduced and the stress concentration phenomenon is solved by minimizing the strain energy of the low stress region and independently setting the allowable strain energy of the high stress region. The method has the advantages of short iteration time, robustness, high efficiency, easy implementation and strong adaptability.
Thus, it should be appreciated by those skilled in the art that while a number of exemplary embodiments of the invention have been illustrated and described in detail herein, many other variations or modifications consistent with the principles of the invention may be directly determined or derived from the disclosure of the present invention without departing from the spirit and scope of the invention. Accordingly, the scope of the invention should be understood and interpreted to cover all such other variations or modifications.

Claims (6)

1. A strain energy regionalized continuum structure topology optimization method is characterized by comprising the following steps,
step 100, converting stress constraint of the structural finite element unit into distortion specific energy constraint based on the equivalent effect of the distortion energy constraint and the stress constraint;
step 200, based on the sum of the specific energy of unit strain and the specific energy of volume change, the specific energy of unit strain is used to replace the specific energy of unit strain, the specific energy of unit strain of the finite element of the structure is summed to obtain the specific energy constraint of the whole layer of the structure, and then the specific energy constraint is converted into the strain energy constraint:
and 300, dividing the design area into a high stress area and a low stress area, minimizing the strain energy of the low stress area, and independently setting allowable strain energy in the high stress area to obtain an optimization result of reducing structural stress and solving strain energy concentration.
2. The continuum structure topology optimization method of claim 1,
in step 100, the proof of the equivalent effect of the distortion energy constraint and the stress constraint is as follows:
the failure criterion of material yield is
Figure FDA0002836135460000011
Figure FDA0002836135460000012
Figure FDA0002836135460000013
Wherein u isdIn order to be able to distort the structure specifically,
Figure FDA0002836135460000014
is the allowable distortion ratio energy of the structure; ν is the poisson ratio; e is the modulus of elasticity; sigma1,σ2,σ3The first, second and third principal stresses; sigmasIs the yield point of the material;
the formula (3) is expressed as von Mises stress:
σeq＝σs (4)
Figure FDA0002836135460000015
wherein σeqIs von Mises stress, and thus the distortion energy constraint and the stress constraint have the same effect.
3. The continuum structure topology optimization method of claim 2,
in step 100, the process of converting the stress constraint into the specific energy of distortion constraint is as follows:
Figure FDA0002836135460000021
wherein,
Figure FDA0002836135460000022
is the specific energy of distortion for unit i.
4. The continuum structure topology optimization method of claim 3,
the proof based on the specific energy per unit strain as the sum of the specific energy to distortion and the specific energy to volume change in said step 200 is as follows:
Figure FDA0002836135460000023
wherein e isiIs the strain energy of unit i; viIs the volume of cell i;
Figure FDA0002836135460000024
the specific energy of change in volume for unit i.
5. The continuum structure topology optimization method of claim 4,
in the step 200, the process of replacing the specific energy of unit strain with the specific energy of unit strain is as follows:
according to (6), the following conversion is carried out:
Figure FDA0002836135460000025
wherein e isiIs the strain energy of unit i; viIs the volume of cell i.
6. The continuum structure topology optimization method of claim 5,
in the step 200, the strain specific energy of the finite element units of the structure is summed to obtain the strain specific energy constraint of the whole layer of the structure, and then the process of converting the strain specific energy constraint into the strain energy constraint is as follows:
Figure FDA0002836135460000026
Figure FDA0002836135460000027
wherein,
Figure FDA0002836135460000031
referred to as allowable strain energy.
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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109359321A (en) * 2018-08-24 2019-02-19 南京理工大学 A kind of lightweight connecting hinge optimization method of topological optimization in conjunction with lattice structure

Patent Citations (1)

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Publication number Priority date Publication date Assignee Title
CN109359321A (en) * 2018-08-24 2019-02-19 南京理工大学 A kind of lightweight connecting hinge optimization method of topological optimization in conjunction with lattice structure

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