CN114595601A - Optimization method and device of reinforcement structure in biplane enveloping body, computer equipment and storage medium - Google Patents

Optimization method and device of reinforcement structure in biplane enveloping body, computer equipment and storage medium Download PDF

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CN114595601A
CN114595601A CN202210176149.XA CN202210176149A CN114595601A CN 114595601 A CN114595601 A CN 114595601A CN 202210176149 A CN202210176149 A CN 202210176149A CN 114595601 A CN114595601 A CN 114595601A
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biplane
flat plate
optimization
rib
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CN114595601B (en
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郭旭
杜宗亮
贾宜播
孟文
葛志福
刘畅
蒋旭东
张维声
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Beijing Mechanical And Electrical Engineering General Design Department
Dalian University of Technology
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Abstract

The embodiment of the invention discloses a method and a device for optimizing a reinforcement structure in a biplane envelope body, computer equipment and a storage medium. The method comprises the steps that ribs between an upper plane and a lower plane are processed into rib components, end coordinates and thicknesses of the rib components are used as design variables, a gradient optimization solver based on shape sensitivity is used, an optimization column with volume constraint and other constraints is solved, the optimized distribution of the rib components and an optimized structure of a biplane enveloping internal reinforcement structure are obtained, the optimization process does not depend on background grids, the number of design variables is greatly reduced, and the calculation efficiency is improved; and the optimized structure contains the definite size and shape parameter information of the rib component, can be directly guided into a CAD/CAE system without complex manual identification and post-processing processes, is convenient to derive an engineering strength analysis report to solve the engineering problem, and improves the optimization and working efficiency on the whole.

Description

Optimization method and device of reinforcement structure in biplane enveloping body, computer equipment and storage medium
Technical Field
The invention relates to the technical field of mechanical structures, in particular to a method and a device for optimizing a reinforcement structure in a biplane enveloping body, computer equipment and a storage medium.
Background
Biplane enveloping structures are widely used in important structural components in the fields of civil engineering, automotive manufacturing, aerospace industry and the like. In order to enhance the bearing capacity of the biplane enveloping body, a reinforcing rib structure needs to be added in the biplane enveloping body, and how to reasonably plan the layout of the reinforcing ribs is a very important problem in the structure optimization design.
In the prior art, a topological optimization method based on units or nodes is mainly adopted to optimize reinforcing ribs, firstly, the area (reinforced layer) where the reinforcing ribs are located is used as an optimized design area, a structure is dispersed into a finite element grid, the unit density in the design area is used as an optimized design variable, a simple simultaneous localization and mapping (SIMP) method is adopted to carry out topological optimization design on a reinforcing layer to obtain the optimal material distribution of the reinforcing ribs, then, a manual identification process is carried out on the result of primary optimization, namely, main rib paths and geometric characteristic parameters are manually extracted according to the solid material distribution result (usually not clear, fuzzy boundaries and weak units exist) obtained by optimization, and then, the size, the direction and the shape of the reinforcing ribs are determined according to the size and the shape of the identified ribs, And (3) reestablishing a rib model by using the characteristic parameters, carrying out a new round of parameter optimization of the shape and the size to obtain an optimal shape and size optimization result, and finally obtaining a final optimization design result of the reinforcing structure in the biplane enveloping body through the two main optimization processes.
However, by using the implicit topological optimization method, the geometric description of the rib depends on the pixel unit or node of the implicit structure, no explicit geometric information exists, the internal through type reinforcement design scheme of the biplane envelope design domain common in the actual engineering cannot be rapidly modeled and optimized, the effective control or constraint on the dimension of the rib is difficult to realize, and the problems of more design variables and large calculated amount are caused.
Disclosure of Invention
Based on this, it is necessary to provide an optimization method, an apparatus, a computer device and a storage medium for a biplane enveloping internal reinforcement structure, which adopt an explicit topology optimization method to directly control and output the explicit geometric parameter size of the rib member and significantly reduce the calculation amount.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a method of optimizing a bi-planar envelope internal ribbing, the method comprising:
constructing a biplane enveloping internal reinforcement structure model, wherein the biplane enveloping internal reinforcement structure model comprises an upper flat plate, a lower flat plate and a plurality of rib components arranged between the upper flat plate and the lower flat plate, the upper flat plate is parallel or nonparallel to the lower flat plate, the surfaces formed by the upper surfaces of the plurality of rib components are coincided with the lower surface of the upper flat plate, the surfaces formed by the lower surfaces of the plurality of rib components are coincided with the upper surface of the lower flat plate, and each rib component is represented by using geometric parameters;
dividing grids for the reinforced structure model in the biplane enveloping body according to the load and constraint conditions of the reinforced structure model in the biplane enveloping body, and performing finite element analysis to obtain a mechanical index;
forming an optimized array, wherein the optimized array comprises an objective function, a constraint function and a design variable; calculating shape sensitivity according to the objective function and the design variable; the design variables include the geometric parameters of each of the tendon members; in the calculation of the objective function, the constraint function and the shape sensitivity, the required information comes from the mechanical index and the constraint condition;
optimizing calculation, namely inputting the optimized column and the shape sensitivity into a preset optimization solver to obtain the updated design variables and the updated optimized column; when the target function in the optimized column converges, completing optimization calculation to obtain an optimized biplane envelope internal reinforcement structure; when the objective function in the optimized column is not converged, representing each rib member by the geometric parameters in the updated design variables, forming an updated model of the bi-planar envelope in-body rib-added structure, performing the finite element analysis again, forming the optimized column again, and performing the optimization calculation again until the objective function in the optimized column is converged.
The invention also discloses an optimization device of the reinforcement structure in the biplane enveloping body, which comprises the following components:
the model building module is used for building a biplane enveloping internal reinforcement structure model, the biplane enveloping internal reinforcement structure model comprises an upper flat plate, a lower flat plate and a plurality of rib components arranged between the upper flat plate and the lower flat plate, the upper flat plate is parallel or nonparallel to the lower flat plate, the upper surface of each rib component is superposed with the lower surface of the upper flat plate, the lower surface of each rib component is superposed with the upper surface of the lower flat plate, and each rib component is represented by using geometric parameters;
the finite element analysis module divides grids for the reinforced structure model in the biplane enveloping body according to the load and constraint conditions of the reinforced structure in the biplane enveloping body, and performs finite element analysis to obtain mechanical indexes;
an optimized column module for forming an optimized column comprising an objective function, a constraint function and a design variable and calculating shape sensitivity according to the objective function and the design variable; the design variables include the geometric parameters of each of the tendon members; in the calculation of the objective function, the constraint function and the shape sensitivity, the required information comes from the mechanical index and the constraint condition;
the optimization iteration module is used for inputting the optimization column and the shape sensitivity into a preset optimization solver, iteratively solving the updated design variables and the updated optimization column, and finishing optimization calculation when the objective function in the optimization column is converged to obtain an optimized internal reinforcement structure of the biplane envelope; when the objective function in the optimized column is not converged, representing each rib component by the geometric parameters in the updated design variables, forming an updated model of the bi-planar envelope internal stiffened structure, performing the finite element analysis again by the finite element analysis module, forming the optimized column again by the optimized column module, and performing the optimization calculation again by the optimization iteration module until the objective function in the optimized column converges.
The invention also discloses a computer device comprising a memory and a processor, wherein the memory stores a computer program which, when executed by the processor, causes the processor to execute the steps of the above method.
The invention also discloses a computer-readable storage medium, in which a computer program is stored, which, when executed by a processor, causes the processor to carry out the steps of the method as described above.
The embodiment of the invention has the following beneficial effects:
according to the embodiment of the invention, the reinforcing rib structure between the upper plane and the lower plane is processed into the rib members, the explicit geometric parameters of the rib members are directly used as design variables, an optimization solver based on shape sensitivity is used for solving the optimization column with volume constraint and other constraints, the optimal distribution of the rib members represented by the explicit geometric parameters and the optimal structure of the reinforcing rib structure in the biplane envelope body are obtained, the optimization process does not depend on a background grid, the number of design variables is greatly reduced, and the calculation efficiency is improved; and the optimized structure contains the clear size and shape parameter information of the rib component, can be directly guided into a CAD/CAE system, does not need complicated manual identification and post-processing processes, is convenient to derive an engineering strength analysis report to solve engineering problems, and improves the optimization and working efficiency on the whole.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Wherein:
fig. 1 is a flow chart of a method for optimizing a reinforcement structure in a biplane envelope body according to the present invention;
FIG. 2 is a schematic view of a tendon member of the present invention;
FIG. 3 is a schematic top view of the rib member of the present invention as a curved rib;
FIG. 4 is a schematic diagram of an upper flat plate and a lower flat plate in a biplane enveloping internal reinforcement structure model according to the present invention;
FIG. 5 is a schematic diagram of rib members in a biplane envelope internal ribbing model of the present invention matching that of FIG. 4;
FIG. 6 is a schematic view of a straight rib member of the present invention;
FIG. 7 is a schematic diagram of the partitioning of adaptive grids according to the arrangement of rib members in the present invention;
FIG. 8 is a schematic view of the sensitivity analysis of the tendon in the present invention;
fig. 9 is a structural block diagram of an apparatus for optimizing a bi-plane enveloping internal ribbing model according to the present invention;
FIG. 10 is a block diagram of a computer apparatus for optimizing a reinforcement structure in a biplane envelope;
FIG. 11 is a diagram illustrating design domains in an exemplary numerical algorithm of the present invention;
FIG. 12 is a diagram of design field size parameters in an example of numerical calculations in the present invention;
FIG. 13 is a schematic diagram illustrating the application of load and displacement constraints in an exemplary numerical algorithm of the present invention;
FIG. 14 is a schematic diagram of an initial layout and assembly of rib members according to an exemplary numerical algorithm of the present invention;
FIG. 15 shows the optimization results of rib members according to an example of numerical calculations in the present invention;
FIG. 16 is an optimization iteration curve according to an example of numerical calculations in the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the present invention provides an optimization method for a bi-plane envelope internal reinforcement structure, which can be applied to a terminal or a server, and this embodiment is exemplified by being applied to a terminal. The optimization method of the reinforcement structure in the double-plane envelope specifically comprises the following steps:
s110: referring to fig. 2, a biplane enveloping internal reinforcement structure model is constructed, where the biplane enveloping internal reinforcement structure model includes an upper flat plate (not shown in fig. 2), a lower flat plate 10, and a plurality of rib members 20 disposed between the upper flat plate and the lower flat plate 10, and the rib members are connected end to end, that is, the rib members 20 are connected and closed through a first end of one rib member and a second end of an adjacent rib member, so as to avoid the crossing of the adjacent rib members and avoid the irregularity of the obtained optimized structure. The upper and lower plates 10 are parallel or non-parallel, the upper surface of each rib member 20 forms a plane coincident with the lower surface of the upper plate, and the lower surface of each rib member forms a plane coincident with the upper surface of the lower plate 10, each rib member 20 being represented using geometric parameters.
As shown in fig. 4 and 5, in the present invention, the biplane enveloping internal reinforcement structure model is composed of three parts, i.e., an upper flat plate, a lower flat plate 10, and a rib member 20 located between the upper and lower flat plates, the rib member 20 is connected to the upper and lower flat plates, respectively, and the thickness of each rib member 20 may be different from each other, but is equal for the initially given rib member.
Each rib member is represented using geometric parameters, as shown in fig. 6. In particular, the geometric parameters include the position, height, length and thickness of the tendon members.
Referring to fig. 2, the position and length of the tendon member 20 may be represented by a first end point and a second end point at both ends of the tendon member, and if the tendon member is preset as a straight tendon, the position coordinates of any point on the tendon member are:
Figure BDA0003519111160000061
correspondingly, the length of the rib member is:
Figure BDA0003519111160000062
wherein x, y are the coordinates of any point on the tendon members,
Figure BDA0003519111160000063
is a first end point p1Is determined by the coordinate of (a) in the space,
Figure BDA0003519111160000064
is the second endpoint p2U is an introduced parameter variable, u belongs to [0,1 ]]。
Obviously, more control points and preset curve patterns can be used to express the shape of the curved tendon members, as shown in fig. 3. The shape of the tendon members is not limited to the shape of straight tendon members shown in fig. 2 or the shape of curved tendon members shown in fig. 3, but may be any other regular or irregular shape.
Therefore, by adopting a preset representation method, the explicit geometric information of each rib member can be obtained, the size of the rib member can be conveniently and effectively controlled or restrained in the subsequent optimization process, and the calculated amount is greatly reduced.
The height of the tendon members is determined by the position of the tendon members and the upper and lower plates.
Because the size of the design domain is limited by the upper inclined plane and the lower inclined plane, the rib component is in a ladder-shaped structure. For convenience of analysis, referring to fig. 6, a plane Φ is an imaginary plane located between the upper flat plate and the lower flat plate, the rib member is divided into an upper portion and a lower portion along the horizontal plane Φ, any point in the horizontal plane Φ is taken as an origin of a coordinate system, an xyz rectangular coordinate system is established, and an analytic equation of an upper inclined plane of the rib member, that is, a plane coincident with the lower surface of the upper flat plate, is assumed as follows:
C1:a1x+b1y+c1z+d1＝0
and then the height of the rib component at any point of the rib component at the upper half part is solved:
Figure BDA0003519111160000071
similarly, assume the analytical equation for the downward slope plane:
C2:a2x+b2y+c2z+d2＝0
and then derive the rib height of the arbitrary point of the rib component of the latter half:
Figure BDA0003519111160000072
in the above formula, a1,b1,c1Is the plane equation parameter of the upper plate, a2,b2,c2Is the plane equation parameter of the lower flat plate, the height of the rib component is
Figure BDA0003519111160000073
S120: and dividing grids for the internal reinforcement structure model of the biplane envelope according to the load and constraint conditions of the internal reinforcement structure model of the biplane envelope, and performing finite element analysis to obtain mechanical indexes.
A finite element grid model of the structure is divided by adopting a self-adaptive grid technology, the upper flat plate, the lower flat plate and the rib components are simulated by adopting shell units, and the grids of the upper flat plate and the lower flat plate and the grids of the rib components share nodes, so that the displacement coordination of the structure is ensured. And updating the positions of the rib components according to the result of each optimization iteration step, and dividing grids according to the updated biplane envelope internal reinforcement structure model by adopting a free grid technology, as shown in fig. 7. Regarding the technical idea of adaptive mesh division, the method proposed by zhanghou, guan zheng group and the like is adopted, and the following references can be specifically made:
【1】 Single jerusalem, research and application of adaptive finite element mesh generation algorithm [ D ], university of college, 2007.
【2】 Liu rock, efficient and reliable three-dimensional constraint Delaunay tetrahedron finite element grid generation algorithm [ D ], university of great courseware, 2010.
Different from the prior fixed grid analysis technology, the invention adopts the variable free grid division technology, does not need to adopt a projection operator or a proxy model method during analysis, and has more accurate analysis and more approximate to a real result.
The mechanical indexes are calculated according to the requirements in the optimization column in the next step S130, including but not limited to stress, frequency, buckling eigenvalue and displacement of the biplane envelope internal reinforcement structure model.
S130: forming an optimized array, wherein the optimized array comprises an objective function, a constraint function and a design variable; calculating shape sensitivity according to the objective function and the design variable; the design variables include the geometric parameters of each rib member.
In one particular embodiment, the optimized formula may be expressed as:
Find D＝(P1)T,…,(Pnp)T,t1,…,tns)T,u(x)
Minimize I＝I(D)
s.t.
Figure BDA0003519111160000081
Figure BDA0003519111160000082
gj(D)≤0,j＝1,…,m,
Figure BDA0003519111160000083
wherein D is the total vector of the design variables,
Figure BDA0003519111160000084
i is 1, …, np denotes the end point coordinates of the rib member in the design variable, tiI-1, …, ns denotes the thickness of the rib member in the design variable; i is an objective function, which in this embodiment is the structural flexibility of the biplane enveloping internal reinforcement structure; u and v are respectively the real displacement and the virtual displacement of the double-plane enveloping internal reinforced structure, and f and t are respectively the physical force and surface force boundary gamma of the double-plane enveloping internal reinforced structuretThe upper part of the body is subjected to the surface force,
Figure BDA0003519111160000085
for structures at displacement boundaries tuThe displacement of (a) is greater, epsilon is strain,
Figure BDA0003519111160000086
is the elasticity tensor, omega is the volume of the reinforcement structure in the biplane envelope,
Figure BDA0003519111160000087
for the space made up of all possible virtual shifts,
Figure BDA0003519111160000088
to design the design space made up of all possible solutions for the variable D,
Figure BDA0003519111160000089
an upper limit for a given volume fraction of material; constraint function gj(D) J — 1, …, m is a constraint requirement that may exist in the optimization problem, such as stress, fundamental frequency, fatigue life, etc., and these constraint functions can be obtained from the mechanical index obtained in the previous step S120.
Shape sensitivity is calculated from the objective function and the design variables. Specifically, for the rib sensitivity analysis diagram shown in fig. 8, the shape of the rib sensitivity analysis diagram is determined by the design domain defined by the upper and lower inclined planes, each straight rib has six boundary surfaces, therefore, the evolution term of the boundary is composed of six parts, and the shape sensitivity expression of the surface can be written as:
Figure BDA00035191111600000810
when the optimization target is flexibility, f in the formula is the strain energy of the structure boundary; v. ofnAs evolution terms of the boundary, there are: v. ofnδ S · n, where δ S is the perturbation term of the boundary and n is the normal direction of the boundary.
Since in actual engineering, S1，S2The area of the surface is larger than that of the rest four surfaces, and in order to improve the calculation efficiency, the shape sensitivities of the two surfaces are only taken in the embodiment and are respectively:
S1the sensitivity expression of the face:
Figure BDA0003519111160000091
S2the sensitivity expression of the face:
Figure BDA0003519111160000092
the volume sensitivity of the rib member is
Figure BDA0003519111160000093
In the above formula, (x)1,y1)，(x2,y2) Respectively, the coordinates of the two ends of the rib member, (P)x,Py) Is the coordinate of any point on the rib member, delta is the total variation of the variable, and the other symbols are defined as follows:
Figure BDA0003519111160000094
Figure BDA0003519111160000095
Figure BDA0003519111160000096
Figure BDA0003519111160000097
τx,τyis determined by
Figure BDA0003519111160000098
In the calculation of the objective function, the constraint function, and the shape sensitivity, information required is derived from mechanical indexes and constraint conditions.
S130: optimizing calculation, namely inputting the optimized array and the shape sensitivity into a preset optimization solver to obtain an updated design variable and an updated optimized array; when the objective function in the optimized column converges, completing optimization calculation to obtain an optimized biplane envelope internal reinforcement structure; and when the target function in the optimized column is not converged, representing each rib component by using the geometric parameters in the updated design variables, forming an updated biplane envelope internal reinforcement structure model, performing finite element analysis again, forming the optimized column again, and performing optimization calculation again until the target function in the optimized column is converged.
The preset optimization solver is a gradient optimization algorithm solver, such as MMA (moving asymptote algorithm), SLP (sequence linear programming algorithm), SQP (sequence quadratic programming algorithm), and the like.
The geometric parameters of the rib members comprise the thicknesses of the rib members, and the thicknesses of the rib members are used as design variables of the objective function, so that the thicknesses of the rib members also need to be restrained to meet the optimization requirements of users. Specifically, after obtaining the geometric parameters of each rib member, namely the thickness of each rib member, a penalty function of the thickness of the rib member is constructed by referring to fig. 5, wherein the thickness t e [ t ] of the rib memberl,tu]And punishing by adopting a Heaviside function, wherein the punishment function can be specifically as follows:
tp＝H(t-tl)t；
wherein the content of the first and second substances,
Figure BDA0003519111160000101
wherein epsilon is a parameter for controlling the regularization degree of the expression; α is a small positive number to ensure non-singularity of the finite element global stiffness matrix. And then obtaining a corrected thickness according to the thickness of the rib component and the penalty function, and taking the corrected thickness as a geometric parameter of the rib component, thus finishing the size constraint on the thickness of the rib component.
In order to avoid the problem that the efficiency of subsequent iterative computation is reduced due to the fact that the structure flexibility exponential increase is caused by the fact that the penalty coefficient alpha is too small at the beginning, the invention adopts a linear Heaviside function penalty strategy, namely, alpha meets the following conditions:
α＝1-0.01*Loop
α＝1e-3When Loop
≥100
where Loop refers to the number of iteration steps.
And finally, importing the optimized reinforcement structure in the biplane enveloping body into a preset program for displaying.
Referring to fig. 9, the present invention further provides an apparatus for optimizing a biplane enveloping internal reinforcement structure, where the apparatus for optimizing a biplane enveloping internal reinforcement structure provided in this embodiment may perform the method for optimizing a biplane enveloping internal reinforcement structure provided in any embodiment of the present invention, and has corresponding functional modules and beneficial effects of the method. The optimization device of the internal reinforcement structure of the biplane envelope comprises a model building module 100, a finite element analysis module 200, an optimization column module 300, an optimization iteration module 400 and an optimization output module 500.
Specifically, the model building module 100 is used for building a double-plane enveloping body internal reinforced structure model, the double-plane enveloping body internal reinforced structure model comprises an upper flat plate, a lower flat plate and a plurality of rib members arranged between the upper flat plate and the lower flat plate, the upper flat plate is parallel or not parallel to the lower flat plate, the upper surface of each rib member coincides with the lower surface of the upper flat plate, the lower surface of each rib member coincides with the upper surface of the lower flat plate, and each rib member is represented by using geometric parameters.
The finite element analysis module 200 divides the model of the internal reinforcement structure of the biplane enveloping body into grids according to the load and constraint conditions of the internal reinforcement structure of the biplane enveloping body, and performs finite element analysis to obtain mechanical indexes.
The optimization column module 300 is used for forming an optimization column and calculating shape sensitivity, wherein the optimization column comprises an objective function, a constraint function and a design variable, and the shape sensitivity is calculated according to the objective function and the design variable; the design variables include geometric parameters of each rib member; in the calculation of the objective function, the constraint function, and the shape sensitivity, information required is derived from mechanical indexes and constraint conditions.
The optimization iteration module 400 iteratively solves the updated design variables and the updated optimization column, and when an objective function in the optimization column converges, completes optimization calculation to obtain an optimized biplane enveloping body internal reinforcement structure; when the target function in the optimized array is not converged, representing each rib component by using the geometric parameters in the updated design variables to form an updated biplane envelope internal reinforcement structure model, performing finite element analysis again by the finite element analysis module, forming the optimized array again by the optimized array module, and performing optimization calculation again by the optimized iteration module until the target function in the optimized array is converged.
The optimization output module 500 is configured to construct a target rib model according to the target geometric parameters, and obtain an optimized biplane enveloping internal reinforcement structure.
In one embodiment, model building module 100 is further configured to build a penalty function for the thickness of the tendon members; and obtaining a corrected thickness according to the thickness of the rib component and the penalty function, and taking the corrected thickness as a geometric parameter of the rib component.
The invention also provides computer equipment with a double-plane envelope internal reinforcement structure, and referring to fig. 10, an internal structure diagram of the computer equipment in one embodiment is shown. The computer device may specifically be a terminal, and may also be a server. As shown in fig. 10, the computer device includes a processor, a memory, and a network interface connected by a system bus. Wherein the memory includes a non-volatile storage medium and an internal memory. The non-volatile storage medium of the computer device stores an operating system and may further store a computer program, which when executed by the processor, causes the processor to implement the method for optimizing a bi-plane envelope intra ribbing structure. The internal memory may also have stored therein a computer program that, when executed by the processor, causes the processor to perform a method of optimizing a bi-planar envelope internal ribbing structure. Those skilled in the art will appreciate that the architecture shown in fig. 10 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
In one embodiment, a computer device is proposed, comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps of:
s110: constructing a biplane enveloping internal reinforcement structure model, wherein the biplane enveloping internal reinforcement structure model comprises an upper flat plate, a lower flat plate and a plurality of rib components arranged between the upper flat plate and the lower flat plate, the upper flat plate is parallel or nonparallel to the lower flat plate, the upper surface of each rib component is superposed with the lower surface of the upper flat plate, the lower surface of each rib component is superposed with the upper surface of the lower flat plate, and each rib component is represented by using geometric parameters;
s120: dividing grids for the reinforced structure model in the biplane enveloping body according to the load and constraint conditions of the reinforced structure model in the biplane enveloping body, and performing finite element analysis to obtain a mechanical index;
s130: forming an optimized array, wherein the optimized array comprises an objective function, a constraint function and a design variable; calculating shape sensitivity according to the objective function and the design variable; the design variables include geometric parameters of each rib member; in the calculation of the objective function, the constraint function and the shape sensitivity, the required information comes from mechanical indexes and constraint conditions;
s140: optimizing calculation, namely inputting the optimized formula into a preset optimization solver to obtain an updated design variable and an updated optimized formula; when the objective function in the optimization column converges, completing optimization calculation to obtain an optimized internal reinforcement structure of the biplane envelope; and when the target function in the optimized column is not converged, representing each rib component by using the geometric parameters in the updated design variables, forming an updated biplane envelope internal reinforcement structure model, performing finite element analysis again, forming the optimized column again, and performing optimization calculation again until the target function in the optimized column is converged.
The invention also provides a readable storage medium for a biplane enveloping in-vivo stiffened structure, storing a computer program which, when executed by a processor, causes the processor to perform the steps of:
s110: constructing a biplane enveloping internal reinforcement structure model, wherein the biplane enveloping internal reinforcement structure model comprises an upper flat plate, a lower flat plate and a plurality of rib components arranged between the upper flat plate and the lower flat plate, the upper flat plate is parallel or nonparallel to the lower flat plate, the upper surface of each rib component is superposed with the lower surface of the upper flat plate, the lower surface of each rib component is superposed with the upper surface of the lower flat plate, and each rib component is represented by using geometric parameters;
s120: dividing grids for the reinforced structure model in the biplane enveloping body according to the load and constraint conditions of the reinforced structure model in the biplane enveloping body, and performing finite element analysis to obtain a mechanical index;
s130: forming an optimized array, wherein the optimized array comprises an objective function, a constraint function and a design variable; calculating shape sensitivity according to the objective function and the design variable; the design variables include geometric parameters of each rib member; in the calculation of the objective function, the constraint function and the shape sensitivity, the required information comes from mechanical indexes and constraint conditions;
s140: optimizing calculation, namely inputting the optimization column to a preset optimization solver to obtain an updated design variable and an updated optimization column; when the objective function in the optimized column converges, completing optimization calculation to obtain an optimized biplane envelope internal reinforcement structure; and when the target function in the optimized column is not converged, representing each rib component by using the geometric parameters in the updated design variables, forming an updated biplane envelope internal reinforcement structure model, performing finite element analysis again, forming the optimized column again, and performing optimization calculation again until the target function in the optimized column is converged.
S150: and importing the optimized reinforcement structure in the biplane enveloping body into a preset program for displaying.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware related to instructions of a computer program, and the program can be stored in a non-volatile computer readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the embodiments provided herein may include non-volatile and/or volatile memory, among others. Non-volatile memory can include read-only memory (ROM), Programmable ROM (PROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus Direct RAM (RDRAM), direct bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
A numerical example
Referring to fig. 11, the design field Ω of the present example is formed by a combination of internal ribs a, upper and lower plates B, a fixed entity C, and a leading edge entity D. The reinforcement optimization aims at realizing the minimization of the structural flexibility based on the appearance requirement and the load requirement, finishing the topological optimization of the reinforcement structure in the biplane enveloping body and outputting a geometric model. To verify the numerical performance of the proposed method, the material properties, loading conditions and geometrical parameters involved in the calculation were all considered as non-dimensionalization.
The elastic modulus of the materials adopted by the internal ribs A, the upper flat plate and the lower flat plate B, the fixed entity C and the front edge entity D are all E, the Poisson ratio is all v, and the main size parameters are shown in figure 12, wherein a-C determine the main shape of the enveloping body, and the size ranges are respectively (300,400,400)]D-f describe the dimensions and positional relationships of the other components that make up the envelope, the dimensions being in the respective ranges [10,250 ]]A1-c1 describes the boundary contour and size of the envelopeIn the range of [5,10 respectively]The h1-h3 planes describe the height information of the envelope, and the size ranges are [10,50 ] respectively]The upper and lower inclined planes are symmetrically arranged and have a thickness tOblique。
The considered loading condition is that the upper surface of the enveloping body bears uniform load, the uniform load is as shown in fig. 13(a), the fixed entity b is completely restrained, and the restrained position is as shown in fig. 13 (b). The control point of the reinforcing rib under the working condition can freely move in a design domain, the thickness variation range of all the reinforcing ribs is set to t _ s E [1.5,15], and the maximum available volume consumption of the reinforcing rib is V.
In this example, taking into account the additive manufacturing constraints, the minimum rib thickness that can be produced in engineering terms is set to t _ l-4. As shown in fig. 14(a), the initial rib layout is composed of 315 initial rib members, and a complete envelope model is generated after cutting and assembling each solid part of the envelope, and the internal rib layout (cross-sectional view) is shown in fig. 14 (b).
FIG. 15 shows the final design of the envelope structure after the optimization result and the materialized geometric reconstruction, and the compliance value of the finally output materialized structure is obviously reduced compared with that before the optimization, and the total volume of the ribs meets the volume constraint requirement
Figure BDA0003519111160000151
FIG. 16 plots the convergence history of the structure compliance, volume constraint ratio and invalid volume level throughout the structure. By analyzing the three curves we can get the following information: (1) the curve representing the target function has numerical sudden increase after iteration for a certain number of steps, because a linear Heaviside function punishment strategy about the elastic modulus of the ribs is added in the iterative calculation, alpha is reduced to the minimum value in the 100 th iteration step, the structural flexibility is suddenly increased, but the alpha is reduced to the normal level after a certain number of iteration steps. (2) The curve representing the volume constraint (ratio) oscillates around the value of 1 at all times, indicating that the structure satisfies the volume constraint. (3) The invalid volume is the sum of all the volumes with the thickness smaller than the manufacturing constraint part ribs, and the elastic modulus of the volume is punished by the Heaviside function in the iterative process and should not exist in the final structure design. Therefore, the lower the level of the part of invalid volume ribs is, the smaller the influence of the part of ribs on the whole structure is finally eliminated, and the more stable the whole structure is. Due to the fact that the penalty effect is added, the curve representing the invalid volume level is at a lower level after certain iteration, the ribs do not exist in the final design of materialized geometric reconstruction any more, and the final structure meets the requirement of minimizing the volume constraint flexibility. It is noted that based on different models, we can further improve the penalty effect by adjusting the parameters α, ε in the penalty function.
In order to evaluate the strength of the final design, the generated materialized model can be conveniently re-analyzed to derive a stress cloud picture and a displacement cloud picture, and the final design is confirmed to meet the design requirements. Due to the explicit geometric description of the method, the optimization result can be conveniently imported into CAD software, so that the bi-slope plane envelope reinforcement topology optimization method can provide wider engineering application.
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present application. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (10)

1. A method for optimizing a reinforcement structure in a biplane enveloping body is characterized by comprising the following steps:
constructing a biplane enveloping internal reinforcement structure model, wherein the biplane enveloping internal reinforcement structure model comprises an upper flat plate, a lower flat plate and a plurality of rib components arranged between the upper flat plate and the lower flat plate, the upper flat plate is parallel or nonparallel to the lower flat plate, the surfaces formed by the upper surfaces of the plurality of rib components are coincided with the lower surface of the upper flat plate, the surfaces formed by the lower surfaces of the plurality of rib components are coincided with the upper surface of the lower flat plate, and each rib component is represented by using geometric parameters;
according to the load and constraint conditions of the reinforced structure model in the biplane enveloping body, dividing grids for the reinforced structure model in the biplane enveloping body, and performing finite element analysis to obtain a mechanical index;
forming an optimized array, wherein the optimized array comprises an objective function, a constraint function and a design variable; calculating shape sensitivity according to the objective function and the design variable; the design variables include the geometric parameters of each of the tendon members; in the calculation of the objective function, the constraint function and the shape sensitivity, the required information comes from the mechanical index and the constraint condition;
optimizing calculation, namely inputting the optimized column and the shape sensitivity into a preset optimization solver to obtain the updated design variables and the updated optimized column; when the target function in the optimized column converges, completing optimization calculation to obtain an optimized biplane envelope internal reinforcement structure; when the objective function in the optimized column is not converged, representing each rib component by the geometric parameters in the updated design variables, forming an updated model of the bi-planar enveloping in-vivo stiffened structure, performing the finite element analysis again, forming the optimized column again, and performing the optimization calculation again until the objective function in the optimized column is converged.
2. The method of claim 1, wherein the geometric parameters include a position, a height, a length, and a thickness of the tendon members, the position of the tendon members and the length of the tendon members being represented by a first end and a second end at both ends of the tendon members, the tendon members being closed by the first end and the second end, the height of the tendon members being determined by the position of the tendon members, the upper plate, and the lower plate.
3. The method according to claim 2, wherein said representing each rib member with said geometry parameters in said updated design variables when said objective function in said optimized equation does not converge, forming an updated bi-planar envelope intra-body reinforcement structure model, further comprising the steps of:
constructing a penalty function of the thickness of the rib member;
and obtaining the corrected thickness of the rib component according to the thickness of the rib component and the penalty function, taking the corrected thickness as the geometric parameter of the rib component, and updating the geometric parameter in the design variable again.
4. The method of claim 1, wherein the objective function is a compliance of a biplane envelope internal ribbing; the constraint function includes a volume.
5. The method of claim 1, wherein the shape sensitivity comprises sensitivity information for six faces of the tendon member and volume sensitivity information for the tendon member.
6. The method according to claim 1, wherein the preset optimization solver is a gradient optimization solver using a gradient-based algorithm.
7. The method according to claim 1, wherein the ribbing the bi-planar envelope internal volume employs an adaptive meshing technique.
8. An apparatus for optimizing a dual planar envelope internal ribbing, the apparatus comprising:
the model building module is used for building a biplane enveloping internal reinforcement structure model, the biplane enveloping internal reinforcement structure model comprises an upper flat plate, a lower flat plate and a plurality of rib components arranged between the upper flat plate and the lower flat plate, the upper flat plate is parallel or nonparallel to the lower flat plate, the upper surface of each rib component is superposed with the lower surface of the upper flat plate, the lower surface of each rib component is superposed with the upper surface of the lower flat plate, and each rib component is represented by using geometric parameters;
the finite element analysis module divides grids for the reinforced structure model in the biplane enveloping body according to the load and constraint conditions of the reinforced structure in the biplane enveloping body, and performs finite element analysis to obtain mechanical indexes;
an optimized column module for forming an optimized column comprising an objective function, a constraint function and a design variable and calculating shape sensitivity according to the objective function and the design variable; the design variables include the geometric parameters of each of the tendon members; in the calculation of the objective function, the constraint function and the shape sensitivity, the required information comes from the mechanical index and the constraint condition;
the optimization iteration module is used for inputting the optimization column and the shape sensitivity into a preset optimization solver, iteratively solving the updated design variables and the updated optimization column, and finishing optimization calculation when the objective function in the optimization column is converged to obtain an optimized internal reinforcement structure of the biplane envelope; when the objective function in the optimized column is not converged, representing each rib component by the geometric parameters in the updated design variables, forming an updated model of the bi-planar envelope internal stiffened structure, performing the finite element analysis again by the finite element analysis module, forming the optimized column again by the optimized column module, and performing the optimization calculation again by the optimization iteration module until the objective function in the optimized column converges.
9. A computer device comprising a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the method according to any one of claims 1 to 7.
10. A computer-readable storage medium, storing a computer program which, when executed by a processor, causes the processor to carry out the steps of the method according to any one of claims 1 to 7.
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