CN114741782A - Conical shell reinforcement structure optimization method and device, computer and storage medium - Google Patents
Conical shell reinforcement structure optimization method and device, computer and storage medium Download PDFInfo
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Abstract
The embodiment of the invention discloses a method and a device for optimizing a conical shell reinforcement structure, a computer and a storage medium. The method comprises the steps of mapping a conical shell to a mapping flat plate, mapping real rib components on the conical shell to mapping rib components, taking end coordinates of the mapping rib components and the thickness of the real rib components as design variables, using a shape sensitivity-based gradient optimization solver, and solving an optimization column under volume constraint and other constraints to obtain the optimized distribution of the real rib components and the optimized structure of a reinforced structure of the conical shell, wherein the optimization process does not depend on a background grid, the number of the 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 real 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 conical shell reinforcement structure optimization method and device, a computer and a storage medium.
Background
The conical shell structure has the characteristics of high bearing efficiency and light weight, and is widely applied to the fields of automobiles, ships, aerospace and the like. In order to improve the load-bearing properties of the conical shell structure, during the last decades, numerous expert scholars have developed several methods to analyze and enhance its strength, stiffness, stability, etc. Among these methods, the design of the reinforcement structure is one of the most effective and least costly methods to improve the performance, and the strength, rigidity, dynamic performance and the like of the reinforcement structure of the conical shell depend on the size, shape and layout of the reinforcement rib to a great extent, so how to reasonably lay the reinforcement rib on the conical shell becomes an important problem.
Topological optimization methods are commonly used in engineering and academia to determine the position, orientation and shape of reinforcing bars on a conical shell. In the prior art, an implicit topological optimization method based on units or nodes is mainly adopted to optimize reinforcing ribs; in the method, firstly, the area (the reinforcement layer) where the reinforcing ribs are positioned is taken as an optimized design area, the structures of the conical shell and the reinforcement layer are dispersed into a finite element grid, the unit density in the design domain is taken as an optimization design variable, the reinforced layer is subjected to topology optimization design by adopting an SIMP (variable density process) method to obtain the optimal material distribution of the reinforcing rib, then the result of primary optimization is manually identified, namely, according to the distribution result of the entity material (usually less clear, fuzzy boundary and weak unit) obtained by optimization, the main rib path and geometric characteristic parameters are extracted manually, and then, re-establishing a rib model according to the identified size and characteristic parameters of the ribs, performing a new round of parameter optimization of the shape and size to obtain an optimal shape and size optimization result, and finally obtaining a final optimal design result of the conical shell reinforcement structure 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, rapid modeling and optimization solution cannot be achieved, and effective control or constraint on the sizes of the ribs is difficult to achieve, so that the problems of large design variables and large calculation amount are caused.
Disclosure of Invention
Based on this, it is necessary to provide a method, an apparatus, a computer and a storage medium for optimizing a conical shell rib structure, which adopt an explicit topology optimization method to directly control and output the explicit geometric parameter size of a rib member and significantly reduce the calculation amount.
A method for optimizing a conical shell reinforcement structure comprises the following steps:
constructing a real model and a mapping model of a conical shell reinforced structure, wherein the real model comprises a conical shell and a plurality of real rib components arranged on the conical shell, and the mapping model comprises a mapping flat plate and a plurality of mapping rib components arranged on the mapping flat plate; the conical shell and the mapping flat plate are in a single-full mapping relation, each real rib component corresponds to each mapping rib component one by one, real geometric parameters are used for representing each real rib component, mapping geometric parameters are used for representing each mapping rib component, and the real geometric parameters and the mapping geometric parameters meet the single-full mapping relation;
dividing a mapping finite element grid into the mapping model, converting the mapping finite element grid into a real finite element grid through inverse mapping of the single-full mapping relation, applying load and constraint conditions to the real finite element grid, and performing finite element analysis on the real finite element grid 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 mapping geometry parameters of each of the mapping 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 objective function in the optimized formula is converged, completing optimization calculation to obtain the optimized mapping model, and obtaining the optimized real model through inverse mapping of the single-full mapping relation; when the target function in the optimized array is not converged, forming an updated mapping model by using the mapping geometric parameters in the updated design variables, forming an updated real model by using the single-full mapping relation, performing the finite element analysis again, forming the optimized array again, and performing the optimization calculation again until the target function in the optimized array is converged.
The invention also discloses an optimization device of the conical shell reinforcement structure, which comprises the following components:
the model construction module is used for constructing a real model and a mapping model of the conical shell reinforced structure, the real model comprises a conical shell and a plurality of real rib components arranged on the conical shell, and the mapping model comprises a mapping flat plate and a plurality of mapping rib components arranged on the mapping flat plate; the conical shell and the mapping flat plate are in a single-full mapping relation, each real rib component corresponds to each mapping rib component one by one, real geometric parameters are used for representing each real rib component, mapping geometric parameters are used for representing each mapping rib component, and the real geometric parameters and the mapping geometric parameters meet the single-full mapping relation; (ii) a
The finite element analysis module is used for dividing a mapping finite element grid for the mapping model, converting the mapping finite element grid into a real finite element grid through inverse mapping of the single-full mapping relation, applying load and constraint conditions to the real finite element grid, and performing finite element analysis on the real finite element grid to obtain a mechanical index;
an optimized columnar module for forming an optimized columnar and calculating shape sensitivity, the optimized columnar comprising 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 mapping geometry parameters of each of the mapping 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 iteratively solving the updated design variables and the updated optimization column, finishing optimization calculation when the objective function in the optimization column is converged to obtain the optimized mapping model, and obtaining the optimized real model through inverse mapping of the single-full mapping relation; when the target function in the optimized array is not converged, forming an updated mapping model by using the mapping geometric parameters in the updated design variables, forming an updated real model by using the single-full mapping relation, performing the finite element analysis again, forming the optimized array again, and performing the optimization calculation again until the target function in the optimized array is converged.
The invention also discloses a computer comprising a memory and a processor, wherein the memory stores a computer program, and the computer program is executed by the processor to enable the processor to execute the steps of the method.
The invention also discloses a computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of the above method.
The embodiment of the invention has the following beneficial effects:
according to the embodiment of the invention, the conical shell is mapped into the mapping flat plate, the real rib components on the conical shell are mapped into the mapping rib components, the mapping geometric parameters of the mapping 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 optimal distribution of the real rib components and the optimal structure of the conical shell reinforced structure represented by the explicit real geometric parameters 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 real 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 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 an optimization method of a conical shell reinforcement structure according to the present invention;
FIG. 2 is a schematic diagram of a mapping model and a real model according to the present invention;
FIG. 3 is a schematic view of the geometry of the conical shell of the present invention;
FIG. 4 is a schematic diagram of a coordinate system of a mapping model and a real model according to the present invention;
FIG. 5 is a view of a mapping tendon member in the mapping model of the present invention;
FIG. 6 is a schematic diagram of the sensitivity analysis of the tendon in the present invention;
FIG. 7 is another schematic of a sensitivity assay of the tendon of the present invention;
FIG. 8 is another schematic of the present invention for sensitivity analysis of a tendon;
fig. 9 is a structural block diagram of an optimization device of a conical shell reinforcement structure according to the present invention;
FIG. 10 is a block diagram of a computer with a conical shell reinforcement structure according to the present invention;
FIG. 11 is a diagram illustrating the dimensions and forces exerted on a conical shell according to an exemplary numerical calculation of the present invention;
FIG. 12 is a schematic diagram of the layout of initial rib members for the mapping plate and the conical shell in an example of numerical calculations according to the present invention;
FIG. 13 shows the result of the optimization of the actual rib structure according to an embodiment of the present invention;
FIG. 14 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 of a conical shell reinforcement structure. The method can be applied to both the terminal and the server, and this embodiment is exemplified by being applied to the terminal. The optimization method of the conical shell structure specifically comprises the following steps:
s110: constructing a real model and a mapping model of the conical shell reinforcement structure, wherein the real model comprises a conical shell and a plurality of real rib components arranged on the conical shell, and the mapping model comprises a mapping flat plate and a plurality of mapping rib components arranged on the mapping flat plate; the conical shell and the mapping flat plate are in a single-full mapping relation, each real rib component corresponds to each mapping rib component one by one, each real rib component is represented by using real geometric parameters, each mapping rib component is represented by using mapping geometric parameters, and the real geometric parameters and the mapping geometric parameters meet the single-full mapping relation.
As shown in fig. 2, in the present invention, the real model includes a conical shell 101 and a plurality of real rib members 102 disposed on the conical shell 101, and the mapping model includes a mapping flat 201 and a plurality of mapping rib members 202 disposed on the mapping flat 201. A one-to-one correspondence single-full mapping relationship exists between the conical shell 101 and the mapping flat plate 201, each real rib member 102 corresponds to each mapping rib member 202, each real rib member 102 is represented by a real geometric parameter, each mapping rib member 202 is represented by a mapping geometric parameter, and the real geometric parameter and the mapping geometric parameter satisfy the single-full mapping relationship.
The geometric dimensions of the conical shell structure are shown in fig. 3, and for the conical shell curved surface and the corresponding mapping flat plate shown in fig. 4, the single-full mapping relation formula can be expressed as
x＝R cosθ，
y＝R sinθ，
z＝u
Wherein
The geometry of the conical shell is given in FIG. 3, where R0Is the radius of the conical base, R1Is the radius of the top surface of the cone, L is the length of the parameter domain, and is also the height of the cone. The center o of the coordinate system oxyz is positioned at the bottom of the conical shellAt the intersection of the plane and the axis, the z-axis is superposed with the axis of the conical shell, and the coordinate system meets the right-hand rule; the uv plane in the coordinate system Ouvw coincides with the upper surface of the mapping plate (i.e., the surface on which the mapping rib members 202 are laid). Therefore, (u, v) is the parameter coordinate corresponding to the coordinate (x, y, z). The single-full mapping relation corresponding to the expression can be understood as that the conical curved surface is flattened along the circumferential direction to obtain a corresponding parameter plane.
For the ribs on the conical shell, the mapping rib components on the mapping flat plate can be mapped onto the conical shell through the single-full mapping relation, and then the conical shell is stretched along the normal direction of the conical shell to obtain the single-full mapping relation formula
x＝(R+w cosβ)cosθ，
y＝(R+w cosβ)sinθ，
z＝u+w sinβ
Wherein β is the angle of inclination of the conical surface, and
w is the parametric coordinate in the third direction introduced, i.e. the height of the mapping rib member. The mapping relation can be used for establishing a geometric model of the curved surface rib and can be subsequently applied to generating a finite element grid of the curved surface reinforced shell.
The thickness of each real tendon member 102 may be different from each other, but equal for a given real tendon member 102.
Each real tendon member 102 is represented using real geometric parameters including the position, height, length, and thickness of the real tendon member 102. Likewise, each mapping rib member 202 is represented using mapping geometry parameters, as shown in fig. 5, which in particular include the position, height, length and thickness of the mapping rib member 202.
The position and length of the mapping tendon member 202 may be represented by a first mapping endpoint and a second mapping endpoint at both ends of the mapping tendon member 202, and if the mapping tendon member 202 is preset as a straight tendon, the position coordinates of any point on the mapping tendon member are:
correspondingly, the length of the mapping rib member is:
wherein u, v are coordinates of any point of the mapping rib member in the mapping plate,
is the first mapping endpoint p1Is determined by the coordinate of (a) in the space,
is the second mapping endpoint p2With μ being an introduced parameter variable, μ ∈ [0,1 ]]. The uv plane in the coordinate system Ouvw coincides with the upper surface of the mapping plate (i.e. the surface on which the mapping rib members are arranged), and the origin is arbitrarily selected.
Obviously, more control points and preset curve patterns can be used to express the shape of the mapping curved-rib member.
Therefore, by adopting a preset representation method, the explicit geometric information of each mapping rib component can be obtained, and further the explicit geometric information of each real rib component can be obtained through the single-full mapping, so that the size of the real rib component can be effectively controlled or constrained in the subsequent optimization process, and meanwhile, the calculated amount is greatly reduced.
S120: and dividing a mapping finite element grid for the mapping model, converting the mapping finite element grid into a real finite element grid through inverse mapping of a single-full mapping relation, and performing finite element analysis according to load and constraint conditions to obtain mechanical indexes.
A finite element mesh model of the mapping model is divided by adopting a self-adaptive mesh technology, the mapping flat plate and the mapping rib components are simulated by adopting shell units, and the mesh of the mapping flat plate and the mesh of the mapping rib components share nodes, so that the displacement coordination is ensured. And updating the positions of the mapping rib components according to the result of each optimization iteration step, and dividing grids according to the updated conical shell reinforcement structure model by adopting a free grid technology. Regarding the technical idea of adaptive mesh division, the method proposed by zhanghou, guan zheng crowd and the like is adopted, and the following documents can be specifically referred:
【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.
And through the inverse mapping of the single-full mapping relation, the mapping finite element mesh can be converted into a real finite element mesh, then the load and constraint conditions are applied to the real finite element mesh, and the finite element analysis of the real finite element mesh is carried out to obtain the mechanical index.
And calculating mechanical indexes including but not limited to stress, frequency, buckling characteristic value, displacement and the like of the conical shell reinforced structure model according to requirements in an optimization column in the next step S3.
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 mapping tendon member.
In one particular embodiment, the optimized determinant may be represented as:
Minimize I＝I(D)
s.t.
gj(D)≤0，j＝1，...，m，
wherein D is the total vector of the design variables,
i 1.. np denotes the end point coordinates of the mapping rib member in the design variable, tiN represents the thickness of the real rib member in the design variables; i is an objective function, in this embodiment, the structural flexibility of the conical shell reinforcement structure; u and v are respectively the real displacement and the virtual displacement of the conical shell reinforced structure, and f and t are respectively the physical force and surface force boundary gamma of the conical shell reinforced structuretThe upper part of the body is subjected to the surface force,
for structures at displacement boundaries tuThe displacement of (a) is greater, epsilon is strain,
is elasticity tensor, omega is the volume of the conical shell reinforced structure,
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 gj(D) J is 1, …, and 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.
Shape sensitivity is calculated from the objective function and the design variables. Specifically, for the rib sensitivity analysis diagrams shown in fig. 6 to 8, each straight rib has five boundary surfaces, and therefore, the evolution term of the boundary is composed of five parts, and the shape sensitivity expression of the surface can be written as:
when the optimization goal is compliance, f in the equation is the strain energy of the boundary of the real tendon member. v. ofnIs an evolution term of the boundary. As in the actual engineering, S'1，S′2The area of the face is larger than the remaining three faces, and in order to improve the calculation efficiency, in the present embodiment, only the shape sensitivity of the two faces is taken, and only S 'is given'1Is calculated as formula S'2Can be analogized. S'1The sensitivity expression for a face is:
wherein
Is S 'of a real tendon member'1Strain energy of face, v'n,1Is S'1Evolution terms of the surface boundary, expressed as
Wherein δ (, is a variation of a variable, e.g.
Is a variable quantity
The variation of (a) is that,
and
representing mapping Rib Member in a mapping Flat Panel
The coordinates of the two end points of (2) in the coordinate system Ouvw,
mu is an introduced parameter variable
And is
In the calculation of the objective function, the constraint function, and the shape sensitivity, information required is derived from mechanical indexes and constraint conditions.
S140: 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 target function in the optimization column converges, completing optimization calculation to obtain an optimized mapping model, and obtaining an optimized real model through inverse mapping of a single-full mapping relation; and when the target function in the optimization column is not converged, forming an updated mapping model by using the mapping geometric parameters in the updated design variables, forming an updated real model by a single-full mapping relation, performing finite element analysis again, forming the optimization column again, and performing optimization calculation again until the target function in the optimization 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 real geometric parameters of the real rib members include the thickness of the real rib members, and the thickness of the real rib members needs to be constrained to meet the optimization requirements of users. Specifically, after the thickness of each real rib component is obtained, a penalty function of the thickness of the real rib component is constructed by referring to fig. 5, and the thickness t e [ t ] of the real rib componentl,tu]A Heaviside function penalty is adopted, and the penalty function may specifically be:
tp＝H(t-tl)t；
wherein,
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 the corrected thickness according to the thickness of the real rib component and the penalty function, and taking the corrected thickness as a real geometric parameter of the real rib component, thus finishing the size constraint of the thickness of the real 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
a＝1e-3When Loop≥100
where Loop refers to the number of iteration steps.
S150: and guiding the optimized conical shell reinforcement structure into a preset program for display.
The invention also provides an optimization device of the conical shell reinforcement structure, the optimization device of the conical shell reinforcement structure provided by the embodiment can execute the optimization method of the conical shell reinforcement structure provided by any embodiment of the invention, and the optimization device has corresponding functional modules and beneficial effects of the execution method. The optimization device for the conical shell reinforcement structure 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, as shown in fig. 9. In particular, the method comprises the following steps of,
the model construction module 100 is configured to construct a real model and a mapping model of the conical shell reinforcement structure, where the real model includes a conical shell and a plurality of real rib members disposed on the conical shell, and the mapping model includes a mapping flat plate and a plurality of mapping rib members disposed on the mapping flat plate; the conical shell and the mapping flat plate are in a single-full mapping relation, each real rib component corresponds to each mapping rib component one by one, each real rib component is represented by using real geometric parameters, each mapping rib component is represented by using mapping geometric parameters, and the real geometric parameters and the mapping geometric parameters meet the single-full mapping relation.
The finite element analysis module 200 divides the mapping finite element mesh into mapping finite element meshes for the mapping model, converts the mapping finite element meshes into real finite element meshes through inverse mapping of the single-full mapping relation, applies the load and constraint conditions to the real finite element meshes, and performs finite element analysis on the real finite element meshes to obtain mechanical indexes.
The optimized column module 300 is used for forming an optimized column including an objective function, a constraint function and a design variable and calculating shape sensitivity; calculating shape sensitivity according to the objective function and the design variable; the design variables include mapping geometry parameters for each mapping rib member; in the calculation of the objective function, constraint function, and 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, when an objective function in the optimization column is converged, optimization calculation is completed to obtain an optimized mapping model, and an optimized real model is obtained through inverse mapping of a single-full mapping relation; and when the target function in the optimization column is not converged, forming an updated parameter model by using the mapping geometric parameters in the updated design variables, forming an updated real model by a single-full mapping relation, performing finite element analysis again, forming the optimization column again, and performing optimization calculation again until the target function in the optimization column is converged.
The optimization output module 500 is configured to construct a mapping model according to the design variables, and convert the mapping model into a real model through single-full mapping, thereby obtaining an optimized conical shell reinforcement structure.
In one embodiment, optimization iteration module 400 is also used to construct a penalty function for the thickness of a real tendon member; and obtaining a corrected thickness according to the thickness of the real rib component and the penalty function, and taking the corrected thickness as a geometric parameter of the real rib component.
The invention also provides a computer with a conical shell reinforced structure, and referring to fig. 10, an internal structure diagram of the computer in one embodiment is shown. The computer may be a terminal or a server. As shown in fig. 10, the computer 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 stores an operating system and also stores a computer program, and when the computer program is executed by a processor, the computer program can enable the processor to realize the optimization method of the conical shell reinforcement structure. The internal memory may also store a computer program, which when executed by the processor, causes the processor to perform a method of optimizing a conical shell stiffened 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 computers to which the disclosed aspects may be applied, and that a particular computer 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 is proposed, comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to carry out the steps of: in one embodiment, a computer is proposed, comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to carry out the steps of:
s110: constructing a real model and a mapping model of the conical shell reinforcement structure, wherein the real model comprises a conical shell and a plurality of real rib components arranged on the conical shell, and the mapping model comprises a mapping flat plate and a plurality of mapping rib components arranged on the mapping flat plate; the conical shell and the mapping flat plate are in a single-full mapping relation, each real rib component corresponds to each mapping rib component one by one, each real rib component is represented by using real geometric parameters, each mapping rib component is represented by using mapping geometric parameters, and the real geometric parameters and the mapping geometric parameters meet the single-full mapping relation;
s120: dividing a mapping finite element mesh into mapping models, converting the mapping models into real finite element meshes through inverse mapping of a single-full mapping relation, applying load and constraint conditions to the real finite element meshes, and performing finite element analysis on the real finite element meshes to obtain mechanical indexes;
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 mapping geometry parameters for each mapping 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 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 formula is converged, completing optimization calculation to obtain an optimized mapping model, and obtaining an optimized real model through inverse mapping of a single-full mapping relation; and when the target function in the optimization column is not converged, forming an updated mapping model by using the mapping geometric parameters in the updated design variables, forming an updated real model by a single-full mapping relation, performing finite element analysis again, forming the optimization column again, and performing optimization calculation again until the target function in the optimization column is converged.
The invention also provides a readable storage medium of the conical shell reinforcement structure, which stores a computer program, and when the computer program is executed by a processor, the processor is caused to execute the following steps:
s110: constructing a real model and a mapping model of the conical shell reinforced structure, wherein the real model comprises a conical shell and a plurality of real rib components arranged on the conical shell, and the mapping model comprises a mapping flat plate and a plurality of mapping rib components arranged on the mapping flat plate; the conical shell and the mapping flat plate are in a single-full mapping relation, each real rib component corresponds to each mapping rib component one by one, each real rib component is represented by using a real geometric parameter, each mapping rib component is represented by using a mapping geometric parameter, and the real geometric parameter and the mapping geometric parameter meet the single-full mapping relation;
s120: dividing a mapping finite element mesh into mapping models, converting the mapping models into real finite element meshes through inverse mapping of a single-full mapping relation, applying load and constraint conditions to the real finite element meshes, and performing finite element analysis on the real finite element meshes to obtain mechanical indexes;
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 mapping geometry parameters for each mapping 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 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 formula is converged, completing optimization calculation to obtain an optimized mapping model, and obtaining an optimized real model through inverse mapping of a single-full mapping relation; and when the target function in the optimization column is not converged, forming an updated mapping model by using the mapping geometric parameters in the updated design variables, forming an updated real model by a single-full mapping relation, performing finite element analysis again, forming the optimization column again, and performing optimization calculation again until the target function in the optimization column is converged.
S150: and guiding the optimized conical shell reinforcement structure into a preset program for display.
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 (Synchlink) DRAM (SLDRAM), Rambus (Rambus) direct RAM (RDRAM), direct bused dynamic RAM (DRDRAM), and bused dynamic RAM (RDRAM).
A numerical example
Referring to fig. 11, the objective of the reinforcement optimization is to minimize the structural flexibility based on the appearance requirement and the load requirement, complete the topology optimization of the conical shell reinforcement structure, 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.
In the figure, the upper radius of the conical shell is 40, the lower radius is 100, the thickness is 1, the height is 80, the uniform force q at the top of the cone is 100, and the bottom is fixedly restrained. The height of all rib members was set to 6, and the thickness variation range of all rib members was set to ts∈[1.0e-3,4.0]. The thickness punishment is applied to carry out characteristic dimension constraint on the real rib component, and the lower thickness limit of the real rib component is set as tl1.5. The maximum usable volume of all real rib members is
Taking advantage of the symmetry of the structure, only half of the structure is actually analyzed and optimized. Fig. 12 shows the initial tendon member distribution, respectively the initial layout of the mapping tendon members in the mapping model and the initial layout of the real tendon members in the real model. There are a total of 450 initial mapping rib members and 736 design variables.
The optimization method provided by the invention is adopted for optimization, the optimization result is shown in fig. 13 (ribs with the thickness less than the threshold value of 0.1 are deleted), and the corresponding structural flexibility value (objective function value) is 9.132e7. FIG. 14 plots the convergence history of the structural compliance and volume constraint values during the optimization of this example. From the optimization results, it is clear that the real rib components form several effective force transmission paths from the upper load bearing area to the bottom constraint, which also reflects the rationality of the method. At the same time, the layout of the real tendon members in the vicinity of the load region does not vary much from the initial layout,this also reflects a certain dependency of the method on the initial layout of the real tendon members. The result of the optimization can be used to derive a CAD drawing conveniently thanks to the explicit geometric description of the method.
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 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, and these are all 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 conical shell reinforcement structure is characterized by comprising the following steps:
constructing a real model and a mapping model of a conical shell reinforced structure, wherein the real model comprises a conical shell and a plurality of real rib components arranged on the conical shell, and the mapping model comprises a mapping flat plate and a plurality of mapping rib components arranged on the mapping flat plate; the conical shell and the mapping flat plate are in a single-full mapping relation, each real rib component corresponds to each mapping rib component one by one, real geometric parameters are used for representing each real rib component, mapping geometric parameters are used for representing each mapping rib component, and the real geometric parameters and the mapping geometric parameters meet the single-full mapping relation;
dividing a mapping finite element mesh for the mapping model, converting the mapping finite element mesh into a real finite element mesh through inverse mapping of the single-full mapping relation, applying load and constraint conditions to the real finite element mesh, 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 comprise the mapping geometry parameters of each of the mapping 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 to a preset optimization solver to obtain the updated design variable and the updated optimized column; when the objective function in the optimized formula is converged, completing optimization calculation to obtain the optimized mapping model, and obtaining the optimized real model through inverse mapping of the single-full mapping relation; when the target function in the optimized array is not converged, forming an updated mapping model by using the mapping geometric parameters in the updated design variables, forming an updated real model by using the single-full mapping relation, performing the finite element analysis again, forming the optimized array again, and performing the optimization calculation again until the target function in the optimized array is converged.
2. The method according to claim 1, wherein the real geometric parameters comprise a position, a height, a length and a thickness of the real tendon members, the position of the real tendon members and the length of the real tendon members being represented by a first real end point and a second real end point at both ends of the real tendon members, the real tendon members being connected closed by the first real end point and the second real end point; the mapping geometrical parameters comprise the position, height, length and thickness of the mapping rib members, the position of the mapping rib members and the length of the mapping rib members are represented by a first mapping end point and a second mapping end point which are positioned at two ends of the mapping rib members, and the mapping rib members are connected and closed through the first mapping end point and the second mapping end point.
3. The method according to claim 2, wherein the step of forming the updated mapping model by using the mapping geometric parameters in the updated design variables and forming the updated real model by the single-full mapping relationship when the objective function in the optimized equation does not converge further comprises the following steps:
converting the mapping geometric parameters into the real geometric parameters of the real rib members through the single-full mapping relation;
constructing a penalty function of the thickness of the real rib component;
and obtaining the corrected thickness of the real rib member according to the thickness of the real rib member and the penalty function, and taking the corrected thickness as the thickness in the real geometric parameters of the real rib member.
4. The method of claim 1, wherein the objective function is a compliance of a real model and the constraint function comprises a volume of the real model.
5. The method of claim 1, wherein said shape sensitivity comprises sensitivity information of five faces of said real tendon members and volume sensitivity information of said real tendon members.
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 of claim 1, wherein said meshing said mapping model employs an adaptive meshing technique.
8. An optimization device of a conical shell reinforced structure is characterized by comprising:
the model construction module is used for constructing a real model and a mapping model of the conical shell reinforced structure, the real model comprises a conical shell and a plurality of real rib components arranged on the conical shell, and the mapping model comprises a mapping flat plate and a plurality of mapping rib components arranged on the mapping flat plate; the conical shell and the mapping flat plate are in a single-full mapping relation, each real rib component corresponds to each mapping rib component one by one, real geometric parameters are used for representing each real rib component, mapping geometric parameters are used for representing each mapping rib component, and the real geometric parameters and the mapping geometric parameters meet the single-full mapping relation;
the finite element analysis module is used for dividing a mapping finite element grid for the mapping model, converting the mapping finite element grid into a real finite element grid through inverse mapping of the single-full mapping relation, applying load and constraint conditions to the real finite element grid, and performing finite element analysis to obtain a mechanical index;
an optimized columnar module for forming an optimized columnar and calculating shape sensitivity, the optimized columnar comprising 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 mapping geometry parameters of each of the mapping 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 iteratively solving the updated design variables and the updated optimization column, finishing optimization calculation when the objective function in the optimization column is converged to obtain the optimized mapping model, and obtaining the optimized real model through inverse mapping of the single-full mapping relation; when the target function in the optimized array is not converged, forming an updated mapping model by using the mapping geometric parameters in the updated design variables, forming an updated real model by using the single-full mapping relation, performing the finite element analysis again, forming the optimized array again, and performing the optimization calculation again until the target function in the optimized array is converged.
9. A computer 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 of 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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| CN115510600A (en) * | 2022-11-10 | 2022-12-23 | 创辉达设计股份有限公司 | Urban drainage network optimization design method |
| CN117610180A (en) * | 2023-11-16 | 2024-02-27 | 苏州科技大学 | Board shell reinforcing rib generation type design method |
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| CN115510600A (en) * | 2022-11-10 | 2022-12-23 | 创辉达设计股份有限公司 | Urban drainage network optimization design method |
| CN117610180A (en) * | 2023-11-16 | 2024-02-27 | 苏州科技大学 | Board shell reinforcing rib generation type design method |
| CN117610180B (en) * | 2023-11-16 | 2024-05-14 | 苏州科技大学 | Board shell reinforcing rib generation type design method |
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