CN114595601B - Optimization method and device of reinforcement structure in biplane envelope body, computer equipment and storage medium - Google Patents
Optimization method and device of reinforcement structure in biplane envelope body, computer equipment and storage medium Download PDFInfo
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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
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 double-plane enveloping body, a reinforcing rib structure needs to be added in the double-plane 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 (a reinforcing layer) where the reinforcing ribs are located is taken as an optimized design area, the structure is dispersed into a finite element grid, the unit density in the design area is taken as an optimized design variable, a simple simultaneous approximation (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 entity material distribution result (generally less clear, fuzzy boundaries and weak units exist) obtained by optimization, then, a rib model is re-established according to the size and characteristic parameters of the identified ribs, a new round of shape and size parameter optimization is carried out to obtain the optimal shape and size optimization result, and finally, the final optimal design result of the reinforcing rib in the double-plane envelope internal structure can be obtained through the two main optimization processes.
However, by using the implicit topological optimization method, the geometric description of the ribs depends on the pixel units or nodes of the implicit structure, no explicit geometric information exists, the internal through type reinforcement design scheme of the biplane enveloping body design domain which is common in the actual engineering cannot be rapidly modeled and optimized and solved, the effective control or constraint on the sizes of the ribs is difficult to realize, and the problems of more design variables and large calculation 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 realize the purpose, the technical scheme of the invention is as follows:
a method of optimizing a dual-plane envelope internal ribbing structure, 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 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.
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 internal reinforcement structure model of the biplane envelope according to the load and constraint conditions of the internal reinforcement structure of the biplane envelope, and performs finite element analysis to obtain mechanical indexes;
an optimized column module for forming an optimized column including 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 to a preset optimization solver, iteratively solving the updated design variable and the updated optimization column, and finishing optimization calculation when the objective function in the optimization column is converged to obtain an optimized inner reinforcement structure of the biplane envelope body; 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, and the computer program, when executed by the processor, causes the processor to execute the steps of the 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 above-mentioned method.
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 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.
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 embodiments or the prior art descriptions will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
Wherein:
FIG. 1 is a flow chart of a method for optimizing a reinforcement structure in a biplane envelope 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 enveloping internal ribbing model of the present invention matching that of FIG. 4;
FIG. 6 is a schematic view of a straight tendon member of the present invention;
FIG. 7 is a schematic diagram of the partitioning of adaptive grids according to rib member arrangement in the present invention;
FIG. 8 is a schematic diagram 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 view of an initial layout and assembly of rib members according to a numerical example 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 a graph of an optimization iteration performed in an example of a numerical calculation according to 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, and 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, where 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 rib 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:
correspondingly, the length of the rib member is:
wherein x, y are the coordinates of any point on the tendon members,
is a first end point p 1 Is determined by the coordinate of (a) in the space,
is the second end point p 2 U is an introduced parameter variable, u is an element of 0,1]。
Obviously, the shape of the flex-bar member can be expressed in more control points and preset curve patterns, as shown in fig. 3. The shape of the rib members is not limited to the shape of straight rib members as shown in fig. 2 or the shape of curved rib members as shown in fig. 3, but may also 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 effectively controlled or constrained 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 plate and the lower plate, the rib member is divided into an upper part and a lower part 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 plate, is assumed as:
C 1 :a 1 x+b 1 y+c 1 z+d 1 ＝0
and then the height of the rib component at any point of the rib component at the upper half part is solved:
similarly, assume the analytical equation for the downward slope plane:
C 2 :a 2 x+b 2 y+c 2 z+d 2 ＝0
and then derive the rib height of the arbitrary point of the rib component of the latter half:
in the above formula, a 1 ,b 1 ,c 1 Is the plane equation parameter of the upper plate, a 2 ,b 2 ,c 2 Is the plane equation parameter of the lower flat plate, the height of the rib component is
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 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 column, wherein the optimized column 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 determinant may be represented as:
Find D＝(P 1 ) T ,…,(P np ) T ,t 1 ,…,t ns ) T ,u(x)
Minimize I＝I(D)
s.t.
g j (D)≤0,j＝1,…,m,
wherein D is the total vector of the design variables,
i =1, \8230;, np denotes the end point coordinates of the rib member in the design variable, t i I =1, \ 8230;, ns denotes the thickness of the rib member in the design variable; i is an objective function, and the objective function in the embodiment is the structural flexibility of the internal reinforcement structure of the biplane envelope; u and v are respectively the real displacement and the virtual displacement of the biplane enveloping internal reinforcement structure, and f and t are respectively the physical force and the surface force boundary gamma of the biplane enveloping internal reinforcement structure t The upper part of the body is subjected to the surface force,
for structures at displacement boundaries t u The displacement of (a) is greater, epsilon is strain,
is the elasticity tensor, omega is the volume of the reinforcement structure in the biplane envelope,
for the space made up of all possible virtual shifts,
to design the design space made up of all possible solutions for the variable D,
at a given upper material volume fraction limit; constraint function g j (D),j＝1,…And m is constraint requirements that may exist in the optimization problem, such as stress, fundamental frequency, fatigue life, and the like, and these constraint functions may be obtained from the mechanical indexes 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:
when the optimization target is flexibility, f in the formula is the strain energy of the structure boundary; v. of n As evolution terms of the boundary, there are: v. of n And (= δ S · n), where δ S is the perturbation term of the boundary and n is the normal direction of the boundary.
Because in practical engineering, S 1 ，S 2 The 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:
S 1 the sensitivity expression of the face:
S 2 the sensitivity expression of the face:
the volume sensitivity of the rib member is
In the above formula, (x) 1 ,y 1 )，(x 2 ,y 2 ) Respectively, the coordinates of the two ends of the rib member, (P) x ,P y ) Is the coordinate of any point on the rib member, δ (, is the total variation of the variable, and the remaining symbols are defined as follows:
τ x ,τ y determined by the following equation
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.
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 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 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 member l ,t u ]And punishing by adopting a Heaviside function, wherein the punishment function can be specifically as follows:
t p ＝H(t-t l )t；
wherein the content of the first and second substances,
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, thereby completing 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 exponential increment of the structural flexibility caused by the excessively small penalty coefficient alpha at the beginning, the invention adopts a linear Heaviside function penalty strategy, namely alpha satisfies:
α＝1-0.01*Loop
α＝1e -3 When Loop
≥100
where Loop refers to the number of iteration steps.
And finally, importing the optimized reinforcement structure in the double-plane envelope body into a preset program for display.
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 is converged, optimization calculation is completed to obtain an optimized inner reinforcement structure of the biplane envelope; 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 inner reinforcement structure of the biplane envelope.
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 be specifically 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: 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;
s130: forming an optimized column, wherein the optimized column 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 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 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 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.
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 (Rambus) direct RAM (RDRAM), direct Rambus Dynamic RAM (DRDRAM), and Rambus Dynamic RAM (RDRAM), among others.
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, fixing entities C, and leading edge entities D. The objective of the reinforcement optimization is to realize the minimization of the structural flexibility based on the appearance requirement and the load requirement, complete the topological optimization of the reinforcement structure in the double-plane envelope body and output 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 describe the boundary profile of the envelope, with dimensions in the range of [5,10 ] respectively]The h1-h3 planes describe the height information of the envelope, the size range being [10,50, respectively]The upper and lower inclined planes are symmetrically arranged and have a thickness t Oblique 。
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 move freely in a design domain, the thickness variation range of all the reinforcing ribs is set as t _ s E [1.5,15], and the maximum available volume usage of the reinforcing rib is V.
The minimum rib thickness that can be produced in engineering is set to t _ l =4, taking into account the added manufacturing constraints in this example. 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
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 worth noting 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 method for optimizing the topology of the bi-slope plane enveloping body reinforcement can provide wider engineering application.
All possible combinations of the technical features in the above embodiments may not be described for the sake of brevity, but should be considered as being within the scope of the present disclosure 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 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 (9)
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; the geometrical parameters comprise the position, height, length and thickness of the rib members, the position of the rib members and the length of the rib members are represented by a first endpoint and a second endpoint which are positioned at two ends of the rib members, and the rib members are connected and closed through the first endpoint and the second endpoint;
the height of the tendon members is determined by the position of the tendon members, the upper plate, and the lower plate, including:
setting a horizontal plane phi as an imaginary plane between the upper flat plate and the lower flat plate, dividing the rib member into an upper part and a lower part along the horizontal plane phi, establishing an oxyz rectangular coordinate system by taking any point in the horizontal plane phi as a coordinate system origin, and assuming that an analytic equation of a plane formed by the upper surface of the rib member is as follows:
C 1 :a 1 x+b 1 y+c 1 z+d 1 ＝0
and then the height of the rib component at any point of the upper half part of the rib component is solved as follows:
assuming that the analytical equation of the surface formed by the lower surface of the rib member is:
C 2 :a 2 x+b 2 y+c 2 z+d 2 ＝0
and then solve the rib member height of any point of the lower half part of the rib member as follows:
in the above formula, a 1 ,b 1 ,c 1 ,d 1 Is the plane equation parameter of the upper plate, a 2 ,b 2 ,c 2 ,d 2 Is a plane equation parameter of the lower flat plate, and the height of the rib component is as follows:
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 rib 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.
2. The method according to claim 1, wherein said representing each said tendon member with said geometric 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 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.
3. The method of claim 1, wherein the objective function is the compliance of the bi-planar envelope internal ribbing; the constraint function includes a volume.
4. The method of claim 1, wherein the shape sensitivity comprises sensitivity information of six faces of the tendon members and volume sensitivity information of the tendon members.
5. The method according to claim 1, wherein the preset optimization solver is a gradient optimization solver using a gradient-based algorithm.
6. The method of claim 1, wherein the meshing of the bi-planar intra-envelope ribbing employs an adaptive meshing technique.
7. An apparatus for optimizing a dual planar envelope internal ribbing, the apparatus comprising:
the model building module is used for building a double-plane enveloping internal reinforced structure model, the double-plane enveloping internal reinforced 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 not parallel to the lower flat plate, the upper surface of each rib component is coincided with the lower surface of the upper flat plate, the lower surface of each rib component is coincided with the upper surface of the lower flat plate, and each rib component is represented by using geometric parameters; the geometrical parameters comprise the position, height, length and thickness of the rib members, the position of the rib members and the length of the rib members are represented by a first endpoint and a second endpoint which are positioned at two ends of the rib members, and the rib members are connected and closed through the first endpoint and the second endpoint;
the height of the rib member is determined by the position of the rib member, the upper plate and the lower plate, including:
setting a horizontal plane phi as an imaginary plane between the upper flat plate and the lower flat plate, dividing the rib member into an upper part and a lower part along the horizontal plane phi, establishing an oxyz rectangular coordinate system by taking any point in the horizontal plane phi as a coordinate system origin, and assuming that an analytic equation of a plane formed by the upper surface of the rib member is as follows:
C 1 :a 1 x+b 1 y+c 1 z+d 1 ＝0
and then the height of the rib component at any point of the upper half part of the rib component is solved as follows:
assuming that the analytical equation of the surface formed by the lower surface of the rib member is:
C 2 :a 2 x+b 2 y+c 2 z+d 2 ＝0
and then the height of the rib component at any point of the lower half part of the rib component is solved as follows:
in the above formula, a 1 ,b 1 ,c 1 Is the plane equation parameter of the upper plate, a 2 ,b 2 ,c 2 Is a plane equation parameter of the lower flat plate, and the height of the rib component is as follows:
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 including 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 rib 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 does not converge, representing each rib member with the geometric parameters in the updated design variables, forming an updated model of the bi-planar envelope in-body rib 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.
8. 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 6.
9. 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 6.
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