CN113886993A - Combined engine thin-wall structure reinforcement layout method based on topology optimization - Google Patents

Combined engine thin-wall structure reinforcement layout method based on topology optimization Download PDF

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CN113886993A
CN113886993A CN202111227136.2A CN202111227136A CN113886993A CN 113886993 A CN113886993 A CN 113886993A CN 202111227136 A CN202111227136 A CN 202111227136A CN 113886993 A CN113886993 A CN 113886993A
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严佳强
王能茂
张全林
张元文
彭勃
王占学
郭宝俊
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Shaanxi Aerospace Power Research Institute Co ltd
Beijing Power Machinery Institute
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Beijing Power Machinery Institute
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Abstract

The invention discloses a combined engine thin-wall structure reinforcement layout method based on topology optimization, which comprises the following steps: s1, establishing a reinforced area model; s2, establishing an analysis model; s3, partitioning the matrix structure to obtain a design domain and a non-design domain, and identifying a non-design point; and S4, establishing an optimization model, and obtaining a reinforcement layout result by utilizing finite element calculation according to the optimization model. The method solves the problems that the existing thin-wall part of the combined engine and the test piece thereof are complex in reinforcement layout design process, low in efficiency and difficult to consider the manufacturing cost under the action of thermal load or force-thermal coupling load.

Description

Combined engine thin-wall structure reinforcement layout method based on topology optimization
Technical Field
The invention belongs to the technical field of engine reinforcement layout, and particularly relates to a combined engine thin-wall structure reinforcement layout method based on topology optimization.
Background
The plate shell structure is widely applied to the fields of aviation, aerospace and the like, the rigidity, strength, buckling, vibration and other mechanical properties of the thin-wall structure are poor, a reinforced structure is generally adopted in practical application to reduce weight, and the shape, size and layout of the reinforced rib directly influence the weight and performance of the structure. The isolation section, the square-to-round section and the rocket section of the combined engine and the test piece thereof are structural members with different shapes, the isolation section is generally of a similar rectangular structure, the square-to-round section is of a transition structure from square to round, and the rocket section is cylindrical and bears high-temperature and high-pressure loads with different sizes in the working process. If the structural strength is insufficient or a certain part is deformed excessively in the working or testing process, gas leakage is possibly caused, and the test is distorted or cannot be carried out. In order to meet the requirement of the structure on the rigidity and the strength without increasing the manufacturing cost, a reinforcement design is usually carried out on the outer surface of the thin-wall part. The thin-wall part is subjected to reinforcement layout design, so that the structural weight can be obviously reduced, the assembly and the transportation are facilitated, and the method has guiding significance for improving the thermodynamic performance of the combined engine and the structure of a test part of the combined engine, reducing the material consumption cost and providing an innovative structural form.
In the thin-wall part reinforcement layout design, most of the reinforcement layout design is based on single load, such as pressure load, or only thermal load, and particularly, the reinforcement layout topology optimization design containing the thermal load mainly focuses on a simple flat plate structure under unidirectional temperature difference, and a complex thin-wall structure under the combined action of the fresh mechanical and thermal loads, such as the reinforcement layout design of a three-dimensional rectangular structure and a round-to-square structure on a combined engine. The traditional reinforcing rib layout method for the thin-wall structure of the combined engine is that a designer often strengthens ribs at weak positions or increases the wall thickness by combining the structural analysis result according to the design experience of the designer. Due to the complex structure and the coupling of force and heat loads of each section of the engine combustion chamber, the rib layout method needs repeated process iteration of structural analysis and redesign when controlling the structural stress and deformation, and the structural design efficiency is low. The design method does not give consideration to the influence of rib layout on the structure quality and the mechanical property at the beginning, does not fully exert the function of guiding the design by the topology optimization technology, and is not beneficial to the manufacturing economy. By adopting the topological optimization technology, the optimal reinforcement layout scheme can be obtained by removing materials to the maximum extent within given load, constraint conditions and design requirements, and a new thought can be provided for structural design.
Disclosure of Invention
The invention aims to provide a combined engine thin-wall structure reinforcement layout method based on topology optimization, and aims to solve the problems that the design process of reinforcement layout is complex, the efficiency is low and the manufacturing cost is difficult to consider under the action of thermal load or force-thermal coupling load of the existing combined engine thin-wall part and a test part thereof.
The invention adopts the following technical scheme: a combined engine thin-wall structure reinforcement layout method based on topology optimization comprises the following steps:
s1, establishing a reinforced area model:
establishing a three-dimensional geometric model of an initial structure according to the molded surface of an engine runner, wherein in the three-dimensional geometric model, a matrix structure and a reinforced area are divided and share topology, and the reinforced area is completely filled with solid materials;
s2, establishing an analysis model:
carrying out grid division on the three-dimensional geometric model, carrying out joint connection on a reinforced area and a matrix area, and defining the elastic modulus, Poisson ratio and density of materials used by the three-dimensional geometric model; then, defining the degree of freedom constraint, the temperature load and the pressure load of the three-dimensional geometric model;
s3, partitioning the matrix structure to obtain a design domain and a non-design domain, and identifying a non-design point;
and S4, establishing an optimization model, and obtaining a reinforcement layout result by utilizing finite element calculation according to the optimization model.
Further, the specific content of step S3 is:
defining the limited units of the matrix structure as non-design domains, and defining the limited units of the reinforcement region as design domains; partitioning the structural model of the design domain along different surface normals;
respectively applying surface normal direction constraint, rib minimum width constraint and material consumption constraint to each design domain, and respectively corresponding to the height direction, width size and volume ratio of rib areas of the optimized generated ribs;
and performing statics analysis on the finite element model, identifying stress concentration and stress singular units in the result, and establishing a set for the units needing to be optimized in the rest regions of the model.
Further, the specific content of the optimization model established in step S4 is as follows:
establishing design variable rho by adopting SIMP interpolation modeliEstablishing an optimization model according to boundary conditions and load conditions, performing topological optimization on a reinforced area, and performing statics analysis on the topological optimization result containing the ribs under the same load and boundary conditions according to a reinforced distribution form obtained by a topological optimization cloud picture result to obtain a strength and rigidity result of the reinforced area;
the optimal formula with the objective of minimum maximum stress is:
Figure BDA0003314548670000031
wherein σjThe equivalent stress of a finite element j in a non-design domain is represented, rho is a design variable vector, and F is a node equivalent load vector; u is a structure node displacement vector; k is a stiffness matrix; v (rho) is the optimized volume, ViIs the volume of cell i; v0The total volume for a given material dosage; u shapesC is a displacement limiting constant for node displacement in an s domain in a design domain omega; rhoiA design variable for a finite element i, which takes on a lower bound ρminAnd upper bound 1 represents the hole and solid element, respectively, typically taken as ρmin＝0.001。
Further, in step S2, when the material selected for the reinforced area is different from the structure of the base, the elastic modulus, poisson' S ratio and density of the reinforced area and the base are respectively defined.
Further, in step S2, the temperature load is a uniform temperature rise or includes a temperature gradient.
The invention has the beneficial effects that:
1. the invention considers the reinforcement topology optimization problem of the combined engine and the test piece thereof under the combined action of high pressure and high temperature load, and compared with the rib arrangement under the single load working condition, the rib arrangement is more reasonable, thereby being beneficial to improving the strength and the rigidity of the thin-wall structure.
2. According to the invention, through partition optimization of the complex structure, the ribs of the complex structure grow together along different height directions in a single optimization process, the problems of repeated optimization and unreasonable rib generation are avoided, the reinforcement layout design process is simplified, and the method can be suitable for reinforcement topology optimization of various structures of different types.
3. When the structure contains thermal load, the traditional structure optimization based on the minimization of the strain energy can reduce the strain energy, meanwhile, the structure is softened, and a continuous reinforcement structure is difficult to obtain.
4. According to the method, the screening process after the statics analysis of various schemes in the design stage is omitted, the design efficiency is improved, the optimized thin-wall structure reinforcement form is better, and the rib layout taking manufacturing cost into consideration can be obtained.
Drawings
FIG. 1 is a schematic diagram of an optimization model according to embodiment 1 of the present invention;
FIG. 2 is a diagram showing the optimization results of embodiment 1 of the present invention;
FIG. 3 is a schematic diagram of an optimization model according to embodiment 2 of the present invention;
FIG. 4 is a diagram illustrating an optimization result in embodiment 2 of the present invention;
FIG. 5 is a schematic diagram of an optimization model according to embodiment 3 of the present invention;
FIG. 6 is a diagram illustrating an optimization result according to embodiment 3 of the present invention;
FIG. 7 is a graph of an iteration of an optimization process according to embodiment 2 of the present invention;
fig. 8 is a graph of an iteration of the optimization process of embodiment 3 of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention provides a reinforced topology optimization method for a thin-wall part and a test part of a combined engine under the action of force-heat coupling load, which comprises the following steps:
s1, establishing a reinforced area model: establishing a three-dimensional geometric model of an initial structure according to the molded surface of the engine runner, wherein in the three-dimensional geometric model, a base structure and a reinforced area are divided and topology is shared, so that a design area and a non-design area are conveniently defined subsequently, and the reinforced area is completely filled with solid materials; the initial structure refers to a three-dimensional geometric model which is established before optimization and contains a design domain and a non-design domain;
s2, establishing an analysis model: carrying out grid division on the three-dimensional geometric model, carrying out joint connection on a reinforced area and a matrix area, and defining the elastic modulus, Poisson ratio and density of materials used by the three-dimensional geometric model; then, defining the degree of freedom constraint, the temperature load and the pressure load of the three-dimensional geometric model;
s3, partitioning the matrix structure to obtain a design domain and a non-design domain, and identifying a non-design point;
and S4, establishing an optimization model, and obtaining a reinforcement layout result by utilizing finite element calculation according to the optimization model.
In some embodiments, the specific content of step S3 is: defining the limited units of the matrix structure as non-design domains, and defining the limited units of the reinforcement region as design domains; partitioning the design domains, respectively naming each partition, and defining the partitions as different design domains; the partitioning principle is to partition the structural model of the design domain along different surface normal directions so as to control the growth direction of the ribs in the optimization of each region.
Respectively applying surface normal direction constraint, rib minimum width constraint and material consumption constraint to each design domain, and respectively corresponding to the height direction, width size and volume ratio of rib areas of the optimized generated ribs;
performing statics analysis on the finite element model, identifying stress concentration and stress singular units in the result, establishing a set for the units needing optimization in the rest areas of the model so as to select the units in the optimization target units of the topological optimization, judging the areas with stress concentration and stress singular in the result through the statics analysis, and if the areas exist, excluding the areas during optimization so as to be conveniently and stably executed in the optimization process instead of transition optimization at the position with excessive local stress. If there are no stress concentration and stress singularity elements, the step is skipped, only these two regions. The finite element model is a calculation model in which mesh division and load application are performed on the basis of a three-dimensional geometric model.
In some embodiments, the specific content of the optimization model established in step S4 is: establishing a design variable rho by adopting an SIMP (simple Isotropic Material with Penalification) interpolation modeliEstablishing an optimization model according to boundary conditions and load conditions, performing topological optimization on a reinforced area, and performing static scoring on the reinforced bar topological optimization results under the same load under the boundary conditions according to a reinforced distribution form obtained by topological optimization cloud picture resultsAnalyzing to obtain the strength and rigidity result;
the optimal formula with the objective of minimum maximum stress is:
Figure BDA0003314548670000061
wherein σjThe equivalent stress of a finite element j in a non-design domain is represented, rho is a design variable vector, and F is a node equivalent load vector; u is a structure node displacement vector; k is a stiffness matrix; v (rho) is the optimized volume, ViIs the volume of cell i; v0The total volume for a given material dosage; f is the proportion of volume parts; u shapesC is a displacement limiting constant for node displacement in an s domain in a design domain omega; rhoiA design variable for a finite element i, which takes on a lower bound ρminAnd upper bound 1 represents the hole and solid element, respectively, typically taken as ρmin＝0.001。
In some embodiments, in step S2, when the material selected for the reinforced region is different from the matrix structure, the elastic modulus, poisson' S ratio and density of the reinforced region and the matrix material are respectively defined.
In some embodiments, the temperature loading is a uniform temperature rise or comprises a temperature gradient in step S2.
Example 1:
the base structure is a flat structure. The length and width of the base plate are 500mm, the thickness is 5mm, the designed reinforcement height is 20mm, the base plate and the ribs are made of the same material, the elastic modulus E is 198Mpa, the Poisson ratio mu is 0.3, and the thermal expansion coefficient is 1.76 multiplied by 10-5. The reinforced area is designed to be normal to the surface of the substrate, and the material consumption of the designed area is 40%. Meanwhile, under the pressure load and the thermal load, the linear temperature distribution exists in the thickness direction, the temperature of the Z-direction surface is 100 ℃, the temperature of the Z-direction surface is 60 ℃, and the pressure load is 1MPa pressure applied to the bottom surface of the plate. UG is adopted as modeling software, and hypertorks is adopted as finite element calculation software.
1. Establishing a three-dimensional CAD model of a flat plate structure, determining that a 500mm multiplied by 5mm area is a non-design area, determining that a 500mm multiplied by 20mm area is a design area, segmenting a substrate and a reinforced area and sharing topology, and filling the reinforced area with solid materials;
2. dividing a model into grids, wherein the size of each grid is 5mm, and defining the elastic modulus, Poisson's ratio and thermal expansion coefficient of the model; the degree of freedom dof 1-dof 2-dof 3-0 and the degree of freedom dof 1-dof 2-0 for restricting two sides in the X direction on the substrate; applying a linear change temperature difference of 100-40 ℃ to the structure along the Z-axis direction;
3. according to the segmentation of the design domain in the step 1, the design domain limited unit domain non-design domain limited unit is partitioned according to different positions where the design domain limited unit is located, the design domain limited unit is classified into different sets, the substrate limited unit is defined as a non-design domain and named for distinguishing, the reinforcement domain limited unit is defined as a design domain and named for distinguishing, the minimum width of ribs formed by the design domain limited unit is 15mm, the reinforcement direction is a Z direction, and the volume fraction of the material consumption is 30%, as shown in figure 1.
4. According to the boundary conditions and the loads, the optimization with the minimum maximum stress as a target and the volume and displacement as constraints is established as an optimization formula, a rib layout result cloud chart obtained by topological optimization is shown in fig. 2, and a dark color area is obtained rib layout.
As seen from FIG. 2, the optimization method of the present invention can also be used for solving the problem of flat plate reinforcement design only under thermal load, and an effective reinforcement effect can be obtained.
Figure BDA0003314548670000081
Example 2:
the base structure is a quasi-rectangular structure. The thickness of the substrate is 15mm, the total length is 1340mm, the total width is 375mm, the structure is under the action of 0.25Mpa internal pressure, and the temperature difference between the inner surface and the outer surface is 720 ℃. The base body and the ribs are made of the same material, the elastic modulus E is 198Mpa, the Poisson ratio mu is 0.3, and the thermal expansion coefficient is 1.76 multiplied by 10 < -5 >. The design adds muscle layout form and makes structural stress minimum, and the deformation reduces, adds the muscle region normal direction at the base member surface, and design regional material consumption is 45%. UG is adopted as modeling software, and hypertorks is adopted as finite element calculation software.
1. Stretching the outer surface of the matrix structure by 50mm along different normal directions to form a design domain, rounding the corner transition position by 50mm, dividing the design domains with different normal directions by using the outer surface of the substrate, sharing topology in the matrix structure, and filling all the reinforcement design domains with solid materials;
2. taking a half of the model according to symmetry, dividing the model into grids with the size of 18mm, and defining the elastic modulus, Poisson's ratio and thermal expansion coefficient of the model; the axial displacement of the gas inlet is restrained to be 0, meanwhile, the freedom degrees along the surface expansion direction are released from the inlet side and the outlet side, and the symmetrical surface is restrained symmetrically; applying 0.22Mpa pressure to the inner surface unit of the model, wherein the temperature load is 750 ℃ on the inner surface, 30 ℃ on the outer edge surface, and the node temperature between the inner surface and the outer surface is in linear interpolation transition; performing statics analysis on the finite element model according to the requirement, and if the stress concentration or stress singular positions exist in the result, excluding the units existing in the positions from the topological optimization model;
3. partitioning the design domain limited unit and the non-design domain limited unit according to different positions of the design domain limited unit and the non-design domain limited unit according to the segmentation of the model in the step 1, and classifying the design domain limited unit and the non-design domain limited unit into different sets; defining the finite elements of the base structure as non-design domains and naming them for distinction; the limited units of the reinforced areas are defined as design areas, the design area units are divided into an X direction, a Y direction and a Z direction according to different normal directions of the surfaces, the design areas are named for distinguishing respectively, the minimum width of ribs formed by the limited design area units is 35mm, the reinforcement starting directions of the design areas are respectively the X direction, the Y direction and the Z direction, and the volume fraction of the material consumption is 45 percent, as shown in figure 3;
4. according to boundary conditions and loads, an optimization model is established by taking the minimum maximum stress as an optimization target and the volume and displacement as constraints, the optimization formula used in the problems is as follows, a fillet layout result cloud chart obtained by topological optimization is shown in fig. 4, the model after optimization is subjected to static analysis, the strength and rigidity results are shown in table 1, and an objective function iteration curve is shown in fig. 7.
Figure BDA0003314548670000091
TABLE 1 comparison of mechanical Property parameters before and after optimization of isolation segment
Figure BDA0003314548670000092
Example 3:
the square-to-round transition structure. The thickness of the substrate is 15mm, the total length is 502.5mm, the total width is 368mm, the outer diameter of the round end is 628mm, the structure is acted by 0.2Mpa internal pressure, and the temperature difference between the inner surface and the outer surface is 720 ℃. The base body and ribs are made of same material, elastic modulus E is 198MPa, Poisson ratio mu is 0.3, and thermal expansion coefficient is 1.76X 10-5. The design of the reinforcement layout mode enables the structural stress to be minimum, the deformation is reduced, the reinforcement area is normal to the outer surface of the base body, and the material consumption of the design area is 40%. UG is adopted as modeling software, and hypertorks is adopted as finite element calculation software.
1. Stretching the outer surface of the matrix structure by 50mm along different normal directions to form a design domain, wherein the design domain is divided by using the outer surface of the substrate and shares topology with the matrix structure, and all the reinforcement design domains are filled with solid materials;
2. dividing the model into grids according to one fourth of the symmetry, wherein the size of each grid is 10mm, and defining the elastic modulus, Poisson's ratio and thermal expansion coefficient of the model; the axial displacement of the gas inlet is restrained to be 0 when the rotary displacement is measured, meanwhile, the freedom degrees along the surface expansion direction are released from the inlet side and the outlet side, and the symmetrical restraint is applied to the symmetrical plane; applying 0.2Mpa pressure to the inner surface unit of the model, wherein the temperature load is 740 ℃ on the inner surface, 30 ℃ on the outer edge surface, and the node temperature between the inner surface and the outer surface is in linear interpolation transition; performing statics analysis on the finite element model according to the requirement, and if the stress concentration or stress singular positions exist in the result, excluding the units existing in the positions from the topological optimization model;
3. classifying the design domain limited units and the non-design domain limited units into two different sets according to different positions of the design domain limited units and the non-design domain limited units according to the segmentation of the model in the step 1; defining the finite elements of the base structure as non-design domains and naming them for distinction; the limited units of the reinforced areas are defined as design areas and named for distinguishing, the minimum width of ribs formed by the limited design area units is 25mm, the reinforcement starting direction is radial, the volume fraction of the material consumption is 45%, and the volume fraction is shown in figure 5;
4. according to boundary conditions and loads, an optimization model is established by taking the minimum maximum stress as an optimization target and the volume and displacement as constraints, the optimization formula used in the problems is as follows, a fillet layout result cloud chart obtained by topological optimization is shown in fig. 6, the model after optimization is subjected to static analysis, the strength and rigidity results are shown in table 2, and an objective function iteration curve is shown in fig. 8.
Figure BDA0003314548670000111
TABLE 2 comparison of mechanical properties of isolation sections before and after optimization of square to round
Equivalent stress/MPa x-direction (radial) displacement/mm Weight/kg
Non-reinforced model 112 3.0 26.8
Pre-optimization model 478 3.2 111.6
Optimized post-model 227 2.7 60.9
In conclusion, compared with the original mechanism, the combined engine thin-wall structure reinforcement layout method based on topology optimization effectively reduces structural deformation during reinforcement design, obviously reduces structural thermal stress relative to the design of increasing the thickness of an engine body, balances stress to deformation, and reduces manufacturing cost.
At present, the reinforcement design of the thin-wall structure of the combined engine mainly carries out reinforcement layout by analyzing the rigidity strength of the structure for many times and combining the experience of designers. The invention provides a different method for the reinforcement design of the thin-wall structure of the combined engine, and is rarely applied to the topology optimization technology, particularly to the reinforcement layout scheme research of the structure under the action of the force-heat coupling load.
The invention relates to a reinforced layout method of a thin-wall structure of a combined engine based on topology optimization, which considers the reinforced topology optimization problem of the combined engine and a test piece thereof under the combined action of high-pressure and high-temperature loads, is more reasonable in rib layout compared with the rib layout under the working condition of single load, and improves the strength and the rigidity of the thin-wall structure. The method has the advantages that the complex partition optimization of the complex structure is simplified, the reinforcement layout design process is simplified, and the method is suitable for the reinforcement topology optimization problem of various different types of structures. When the structure contains thermal load, the traditional structure optimization based on the minimization of the strain energy can reduce the strain energy, meanwhile, the structure is softened, and a continuous reinforcement structure is difficult to obtain. According to the method, the screening process after the statics analysis of various schemes in the design stage is omitted, the design efficiency is improved, the optimized thin-wall structure reinforcement form is better, and the rib layout with design performance and manufacturing economy can be obtained. The problems that the existing thin-wall part of the combined engine and a reinforced layout under the action of a thermal load or a force-heat coupling load of a test piece of the thin-wall part are complex in design process, low in efficiency and difficult to design and consider material cost are solved.

Claims (5)

1. A combined engine thin-wall structure reinforcement layout method based on topology optimization is characterized by comprising the following steps:
s1, establishing a reinforced area model:
establishing a three-dimensional geometric model of an initial structure according to the molded surface of an engine runner, wherein in the three-dimensional geometric model, a matrix structure and a reinforced area are divided and share topology, and the reinforced area is completely filled with solid materials;
s2, establishing an analysis model:
carrying out grid division on the three-dimensional geometric model, carrying out joint connection on a reinforced area and a matrix area, and defining the elastic modulus, Poisson ratio and density of materials used by the three-dimensional geometric model; then, defining the degree of freedom constraint, the temperature load and the pressure load of the three-dimensional geometric model;
s3, partitioning the matrix structure to obtain a design domain and a non-design domain, and identifying a non-design point;
and S4, establishing an optimization model, and obtaining a reinforcement layout result by utilizing finite element calculation according to the optimization model.
2. The topology optimization-based composite engine thin-wall structure reinforcement layout method according to claim 1, wherein the step S3 specifically comprises:
defining the limited units of the matrix structure as non-design domains, and defining the limited units of the reinforcement region as design domains; partitioning the structural model of the design domain along different surface normals;
respectively applying surface normal direction constraint, rib minimum width constraint and material consumption constraint to each design domain, and respectively corresponding to the height direction, width size and volume ratio of rib areas of the optimized generated ribs;
and performing statics analysis on the finite element model, identifying stress concentration and stress singular units in the result, and establishing a set for the units needing to be optimized in the rest regions of the model.
3. The topology optimization-based composite engine thin-wall structure reinforcement layout method according to claim 2, wherein the concrete contents of the step S4 for establishing the optimization model are as follows:
establishing design variable rho by adopting SIMP interpolation modeliEstablishing an optimization model according to boundary conditions and load conditions, performing topological optimization on a reinforced area, and performing statics analysis on the topological optimization result containing the ribs under the same load and boundary conditions according to a reinforced distribution form obtained by a topological optimization cloud picture result to obtain a strength and rigidity result of the reinforced area;
the optimal formula with the objective of minimum maximum stress is:
Figure FDA0003314548660000021
wherein σjThe equivalent stress of a finite element j in a non-design domain is represented, rho is a design variable vector, and F is a node equivalent load vector; u is a structure node displacement vector; k is a stiffness matrix; v (rho) is the optimized volume, ViIs the volume of cell i; v0The total volume for a given material dosage; u shapesC is a displacement limiting constant for node displacement in an s domain in a design domain omega; rhoiA design variable for a finite element i, which takes on a lower bound ρminAnd upper bound 1 represents the hole and solid element, respectively, typically taken as ρmin＝0.001。
4. The topologically-optimized combined engine thin-wall structure reinforcement layout method according to claim 1 or 2, wherein in step S2, when the material selected for the reinforcement region is different from the base structure, the elastic modulus, poisson' S ratio and density of the reinforcement region and the base material are respectively defined.
5. The topology optimization-based composite engine thin-wall structure reinforcement layout method according to claim 1 or 2, wherein in the step S2, the temperature load is a uniform temperature rise or contains a temperature gradient.
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CN116088170A (en) * 2023-02-14 2023-05-09 中国航天三江集团有限公司 Large-sized optical lens barrel structure and optimal design method thereof
CN116088170B (en) * 2023-02-14 2024-02-23 中国航天三江集团有限公司 Large-sized optical lens barrel structure and optimal design method thereof
CN117892599A (en) * 2024-03-14 2024-04-16 中南大学 Expansion method of ribbed cylinder piece and application thereof
CN117892599B (en) * 2024-03-14 2024-06-04 中南大学 Expansion method of ribbed cylinder piece and application thereof

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