CN117973065A

CN117973065A - Iso-geometric topology optimization method and system for complex design domain

Info

Publication number: CN117973065A
Application number: CN202410249286.0A
Authority: CN
Inventors: 高亮; 张潇; 高杰; 肖蜜
Original assignee: Huazhong University of Science and Technology
Current assignee: Huazhong University of Science and Technology
Priority date: 2024-03-05
Filing date: 2024-03-05
Publication date: 2024-05-03

Abstract

The invention belongs to the technical field of material structure optimization, and discloses an isogeometric topology optimization method and system for complex design domains, wherein the isogeometric topology optimization method comprises the following steps: building a complex geometric model based on T spline; building a finite element data structure based on T spline and Bezier extraction; implicit description of topology based on T-splines; a rigidity maximizing topological optimization model of the complex design domain; stiffness maximization sensitivity analysis of complex design domain; and updating design variables of the complex design domain and solving problems. The method provided by the invention constructs a topological description model based on T spline and Bezier extraction to present the distribution of materials, realizes the optimal design of structural materials with complex design domains, is applied to the design of a plate-shell structure with complex geometric shapes, effectively eliminates the tensor product limitation of NURBS and a plurality of numerical limitations in complex geometric analysis and optimization, and shows superiority and necessity on a plurality of complex shell structures in actual engineering.

Description

Iso-geometric topology optimization method and system for complex design domain

Technical Field

The invention belongs to the technical field of material structure optimization, and particularly relates to an isogeometric topology optimization method and system for a complex design domain.

Background

In recent years, topological optimization has been considered as a powerful design tool for engineering structural designs that can effectively seek a reasonable material layout in the domain under a number of constraints to achieve the desired structural performance. However, most of the previous researches focus on tensor spline (such as B-spline and NURBS), and NURBS has excellent mathematical and algorithm characteristics such as uniformity, non-negativity, linear independence and the like, so that the related method is greatly benefited. The tensor product topology of NURBS severely limits its application to complex structural designs where multiple pieces of divide or clip features are required to represent complex engineering models in a way that is difficult to understand. In addition, the multi-sheet division scheme can cause problems such as gaps and gaps, and the trimmed surface generally does not have independent representation capability and cannot be used for numerical analysis. The above limitations result in many excellent optimization methods that can only deal with the optimization problem defined in the simple regular design domain.

In order to overcome the defects of NURBS, surface description methods such as T-splines, PHT-splines and the like are provided, wherein the T-splines are used as extension splines of NURBS, and have flexible topological structures by introducing T nodes and abnormal points. The T spline is similar to NURBS in expression form and theoretical derivation, the cut NURBS curved surface can be converted into an unclamped T spline curved surface, and a plurality of NURBS sheets can be combined into a single gapless T spline sheet, so that the structural model can be reconstructed according to the optimized configuration for analysis after optimization. Meanwhile, IGA is introduced to overcome the defects of low numerical accuracy, low analysis efficiency and the like of the classical finite element method. The introduction of T-splines into isogeometric topological optimization is therefore a superior method of handling complex design domains, but also introduces some numerical limitations: 1) Defining a discrete distribution of density over T-spline control points in topology optimization, rather than a continuous Density Distribution Function (DDF), to represent the structure topology results in "zig-zag" features in the optimized topology. However, T-spline curves do not have tensor product characteristics of NURBS, and therefore DDFs with continuity and smoothness cannot be constructed directly using T-spline curves. 2) The implementation of the values of the T-splines in the structural geometric model and the IGA based on the T-splines are complex without Bezier extraction, and cannot be directly extended to other or more complex design examples, namely the effectiveness is weak. 3) The design problem of topology optimization only considers classical compliance minimization of two-dimensional planar structures, and does not involve three-dimensional complex spatial shell structures. In fact, the topological optimization of the plate-and-shell structure is also a difficult problem in the field of structural design research and is not a simple extension of the planar structure.

Through the above analysis, the problems and defects existing in the prior art are as follows:

(1) Defining a discrete distribution of density over T-spline control points in topology optimization, rather than a continuous Density Distribution Function (DDF), to represent the structure topology results in "zig-zag" features in the optimized topology. However, T-spline curves do not have tensor product characteristics of NURBS, and therefore DDFs with continuity and smoothness cannot be constructed directly using T-spline curves.

(2) The implementation of the values of the T-splines in the structural geometric model and the IGA based on the T-splines are complex without Bezier extraction, and cannot be directly extended to other or more complex design examples, namely the effectiveness is weak.

(3) The design problem of topology optimization only considers classical compliance minimization of two-dimensional planar structures, and does not involve three-dimensional complex spatial shell structures.

Disclosure of Invention

Aiming at the problems existing in the prior art, the invention provides an isogeometric topology optimization method and system for a complex design domain, which aims to eliminate the limitation of NURBS tensor product and a plurality of numerical limitations generated by introducing T spline and improve the numerical precision and analysis efficiency of structural design of the complex design domain.

The invention is realized in such a way that an isogeometric topology optimization method facing to a complex design domain is characterized by comprising the following steps:

S1, modeling a geometric model with a complex design domain in CAD software (Rhinoceros 3D) based on T spline, dividing grids, and deriving a model file;

S2, reading a model file, converting the model file into a data model suitable for analysis, establishing a finite element data structure based on Bezier extraction, and using the finite element data structure in IGA analysis of complex geometry;

S3, constructing a corresponding local Density Distribution Function (DDF) in each Bezier unit, ensuring the smoothness and continuity of the local DDF by tensor product characteristics of the Bezier curved surface in each unit, and assembling all the local DDFs to obtain a structural topology global DDF for presenting continuity and smoothness;

S4, solving all the equigeometric unit stiffness matrixes by utilizing a Gaussian integration method and based on IGA analysis of complex geometry and the elastic performance of each point in a design domain, assembling the stiffness matrixes into a global stiffness matrix, solving a displacement field of the design domain, and constructing a stiffness maximization topology optimization mathematical model aiming at the complex design domain by taking structural stiffness maximization as a target;

s5, carrying out iterative updating on design variables in the topology optimization model by calculating an objective function and sensitivity to obtain an optimized topology optimization configuration.

Further, the implementation manner of the step S1 includes:

S101, creating, editing and converting a T-spline-based surface model by combining with the Rhinoceros3D and AutodeskT-splines plug-ins, wherein the visual process of the geometric modeling step can be realized, and the realization of the current T-spline geometric model is only limited to untrimmed bicubic surfaces. In the invention, the construction of the curved surface model with complex geometry mainly comprises two modes: (1) Drawing NURBS curved surfaces, dividing grids to obtain grid models, converting the grid models into T spline models through T-splines plug-ins, and performing smoothing and other operations according to specific conditions of the models; (2) Direct modeling is performed through a T-splines plug-in, but different modeling methods can generate different Bezier grids, so that the grid distribution of the geometric model needs to be carefully considered before modeling to obtain a proper grid is one of the keys of modeling; when the structure topology changes, the positions of the Bezier grid and the configuration points are automatically updated, for example, the features in the design domain are locally refined;

S102, after the T spline model is completed and a proper selection set is determined, the T spline model can be automatically stored as an analysis model containing unit and control point information without a grid generation or geometric cleaning step; the analytical model may be exported as iga an analytical model file containing global grid data, including the following fields:

(1) type-type of derived surface. The plate model type is displayed as a plane, and the three-dimensional curved surface model is displayed as a curved surface;

(2) nodeN-total number of spline control points;

(3) elemN-defining the total number of Bezier units of the T spline surface;

(4) Data of control points: the designated format of each T spline control point is nodexyzw;

(5) Bezier unit data: the Bezier unit data is block data comprising Bernstein polynomials and unit extraction operators; the first row of data is the global data of the cell, including the base function support number and the order of the two directions, denoted by belemnp _ξp_η; the global index of each non-zero T-spline basis function in the second row is a ₁A₂…A_n. In the next n rows, the extraction operator is specified as:

further, the implementation manner of step S2 includes:

Since the IGA method using T-splines needs to be combined with the Rhino and analysis procedure, after the IGA file is imported into the analysis procedure, the imported model data needs to be read and converted into data suitable for structural analysis. The T-spline mixing function based on the Bezier extraction method can be expressed as:

N^e(ξ,η)＝C^eB(ξ,η)；

in the method, in the process of the invention, Is a vector of T-spline mixing functions containing a support unit e, a represents the relevant local index of the control points, n is the total number of control points; /(I)Is the unit extraction operator for unit e, assuming the polynomial order is the same in each direction, the dimension is nx (p+1) ². /(I)Is a vector defining the Bernstein polynomial. Let/>Is a vector of T-spline blending functions of element e, and T-spline blending functions of element e can be expressed as:

And (3) with

In the method, in the process of the invention,And w ^e are two expressions of the weights of the n control points corresponding to the unit e. The first order and second order differential of the T spline mixing function are:

in the method, in the process of the invention, And the T spline basis function form based on Bezier extraction can be further applied to the unknown field of the IGA analysis solving design domain.

Further, as known from S2, the same curved surface can be constructed by using the T-spline control point and the corresponding Bezier control point, each Bezier unit has the same equally divided Bezier control point, and adjacent boundaries of two Bezier units share p+1 control points with the same weight value; the two refined units share p+1 control points with the adjacent units, wherein the two refined units contain p-1 control points in the shared control points, so that the same coordinates of the control points on the boundaries of the two adjacent units are ensured, the densities of the control points used for constructing the DDF are also the same, and the continuity of combining the local DDFs into the global DDF is ensured. Thus, building a topology description model based on Bezier extraction mainly comprises the following parts:

s301, constructing a local DDF in each Bezier unit by using a corresponding Bernstein basis function, wherein the method mainly comprises the following steps:

(1) Defining an initial density of Bezier control points, namely the Bezier control density phi _i{i＝1,...,(p+1)², which is in the range of [0,1];

(2) A smoothing mechanism is constructed based on a Shebard function, and the corresponding mathematical formula is as follows:

where ψ (φ _i) is the shepherd function value at control point Q _i, calculated as:

in the method, in the process of the invention, Is the weight function of control point Q _i, which is built up from Radial Basis Functions (RBFs) with C4 continuity, n is the total number of control densities affecting the current control density,/>Representing a smoothed Bezier control density;

(3) A local Density Distribution Function (DDF) is constructed using a linear combination of all Bernstein polynomials and smoothed control design variables in the corresponding Bezier units, the corresponding formulas being as follows:

Where Φ _l is the local DDF, which can also be regarded as the density response surface of the Bezier units, Is a vector of smooth control density,/>Is a vector of Bernstein polynomials of the corresponding Bezier unit;

(4) An implicit description mechanism of the structure boundary is constructed, and the equivalent contour of the local DDF represents the structure boundary of the corresponding topology, and the value of the equivalent contour is:

Where phi _ISO represents the iso-contour value of the local DDF, Is the structural topology of the corresponding Bezier unit;

S302, combining all local DDFs into a global DDF for representing the structure topology, and if the number of Bezier units in a given domain is N _b, the corresponding global DDF can be expressed as:

in the method, in the process of the invention, Local DDF, Φ _g, representing the ith Bezier unit, represents global DDF of the entire structure topology, the corresponding structure topology can be expressed as:

in the method, in the process of the invention, Representing the structural topology of the entire design domain; perfect and natural connection between adjacent Bezier units can keep gapless of the global DDF, so that the global DDF and the global structure topology have enough smoothness and continuity; the structural topology is deduced by optimizing the DDF until the expected structural performance is reached, and the optimized topological structure is trimmed into a single watertight T-spline surface along the contour line, and the single watertight T-spline surface can be used as a new analysis input surface.

Further, the two-dimensional numerical equation of the isogeometric unit stiffness matrix K _e calculated based on the gaussian orthogonal method is as follows:

Wherein E _min is the solid material stiffness, E ₀ is the minimum material stiffness, γ is the penalty factor, J is the jacobian of the mapping from parent cell space to physical space, B is the cell strain-displacement matrix, N _g is the total number of Gaussian orthogonal points, ω _g is the weight of the corresponding Gaussian point;

in step S4, the stiffness maximization topology optimization model of the complex design domain is expressed as:

Where φ _i denotes the initial density of Bezier control points, the range of variation of the design variables during the optimization is [ φ _min,1].φ_min is the minimum value of the design variables, usually equal to 1e-6 in order to avoid singular points during the optimization. J represents an objective function, i.e. a structural mean compliance for describing the load capacity, u represents the displacement field of the design domain Ω calculated by T-spline based IGA. V represents a material volume constraint, where V ₀ is the solid volume fraction and V ₀ is the maximum material consumption; a is the bilinear energy, δu is the virtual displacement field belonging to the kinematically tolerable space H ¹ (Ω), g provides the specified displacement vector on the Dirichlet boundary Γ _D, l is the linear load function, expressed as:

Where f _Ω is the physical strength of the design domain and f _N is the boundary traction applied by Neumann boundary Γ _N.

Further, step S5 includes:

S501, initializing design variables;

s502, substituting the design variable into an isogeometric analysis model based on a T spline, and calculating a displacement field by KU=F, so as to calculate an objective function and sensitivity;

s503, updating the control density phi _i, namely the design variable by adopting an OC method, repeatedly executing until reaching the iteration termination condition, and obtaining an optimized structure topology optimization configuration according to the objective function and the sensitivity calculated in the last iteration step S502;

The sensitivity is obtained by the derivatives of the objective function and the constraint condition on the design variable respectively, wherein the partial derivatives of the objective function and the constraint condition on the design variable respectively are expressed as follows:

in the formula, the calculation points (ζ, η) correspond to Gaussian intersection points in the design domain, and are different from the control points.

Another object of the present invention is to provide a complex design domain oriented isogeometric topology optimization system for implementing the complex design domain oriented isogeometric topology optimization method, including:

The geometric model modeling and grid dividing module is used for modeling a geometric model with a complex design domain in CAD software (Rhinoceros 3D) based on T-splines, dividing grids and deriving a model file;

The finite element data structure building module reads the model file and converts the model file into a data model suitable for analysis, builds a finite element data structure based on Bezier extraction, and uses the finite element data structure in IGA analysis of complex geometry;

The density distribution function construction module is used for constructing a corresponding local Density Distribution Function (DDF) in each Bezier unit, the tensor product characteristic of the Bezier curved surface in each unit ensures the smoothness and continuity of the local DDF, and all the local DDFs are assembled to obtain a structural topology global DDF for presenting continuity and smoothness; firstly constructing a local density distribution function, and then assembling the local density distribution function into a global density distribution function;

The rigidity maximizing topological optimization mathematical model construction module is used for solving all the rigidity matrixes of the geometric units and assembling the rigidity matrixes into a global rigidity matrix by utilizing a Gaussian integration method based on IGA analysis of complex geometry and the elasticity performance of each point in a design domain, solving a displacement field of the design domain, and constructing a rigidity maximizing topological optimization mathematical model aiming at the complex design domain by taking structural rigidity maximization as a target;

and the design variable iteration updating module is used for carrying out iteration updating on the design variables in the topology optimization model by calculating the objective function and the sensitivity to obtain an optimized topology optimization configuration.

It is a further object of the present invention to provide a computer device 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 the complex design domain oriented isogeometric topology optimization method.

It is a further object of the present invention to provide a computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of the complex design domain oriented isogeometric topology optimization method.

The invention further aims to provide an information data processing terminal which is used for realizing the isogeometric topology optimization system facing the complex design domain.

In combination with the technical scheme and the technical problems to be solved, the technical scheme to be protected has the following advantages and positive effects:

Firstly, the isogeometric topological optimization method for the complex design domain provided by the invention is developed for solving the unknown response of the complex structural design domain based on the T spline aiming at the problem that the conventional NURBS-based complex structural domain design method is not available. T-splines with local refinement characteristics can effectively describe complex geometries, eliminate key defects of NURBS due to tensor product limitation, and realize optimal design and analysis of complex geometries. In addition, a solution space is still constructed by using a T spline mixing function in a Bezier expression form in analysis, so that the problems of low numerical precision, low analysis efficiency and the like caused in the optimization process of the traditional classical method are solved, and the effectiveness and the efficiency of the method are improved;

According to the isogeometric topology optimization method of the complex design domain, the topology description model based on the T spline and the Bezier extraction method is constructed to present the optimized structure topology, wherein a large number of local DDFs are constructed in all the Bezier units, and tensor product characteristics of the Bezier curved surfaces in each unit can effectively ensure smoothness and continuity of each local DDF. Combining all local DDFs to construct a global DDF to present a structural topology with continuity and smoothness, and the high unification of the basis functions effectively keeps clearly and smoothly describing the structural boundaries;

The isogeometric topology optimization method for the complex structure design domain has strong applicability and can be applied to the optimization design and analysis of the complex plate-shell structure. Based on the method, an isogeometric shell unit based on T-spline and Bezier extraction can be developed according to Kirchhoff-Love theory, and an isogeometric topological optimization mathematical model based on T-spline with maximized rigidity is established for a plate-shell structure with any geometric shape so as to improve the load capacity, and the same numerical scheme and optimization algorithm are adopted to solve the related problems, so that the method has stronger applicability and effectiveness.

Secondly, the technical scheme of the invention is established based on the T spline, the T spline overcomes various defects of NURBS modeling complex structure, the local refinement property of the T spline ensures that the T spline can model a single watertight model with any shape, and the T spline extracted based on Bezier provides a unified expression form for any control point in the complex model, so that the invention can optimize the complex engineering structure with any design domain, and the optimization result obtained by the optimization of the invention can be directly exported and utilized and subjected to subsequent re-analysis and the like due to the special property of the T spline, thereby improving the practicability and convenience of the optimized engineering.

The technical scheme of the invention is established based on an isogeometric analysis method, and the structural response is solved by utilizing the basis function used for representing the geometric model in CAD, so that the uniformity of engineering design and analysis is truly realized, the complicated model conversion operation in the optimization process is eliminated, the numerical precision of the topology optimization process is greatly improved, meanwhile, the possibility of searching a proper optimization result in the optimization process is ensured due to the high-order continuity of the isogeometric analysis, the numerical analysis efficiency of structural optimization is improved, and the accuracy of the optimization result is ensured;

The technical scheme of the invention comprises the establishment of a density distribution function, and the global density distribution function with a smoothing mechanism cannot be established by utilizing tensor product property due to the local refinement characteristic of a T spline. Converting the T spline into a series of Bezier units based on Bezier extraction, establishing a local density distribution function based on the Bezier units, applying a smoothing mechanism in the local density distribution function, and finally assembling all the local distribution functions into a global density distribution function to represent the structure topology. Considering the local density distribution function of the smoothing mechanism ensures the smoothness and continuity of the topology result, while the consistency of the medium control points and the basis functions of the adjacent Bezier units ensures the perfect connection of the local density distribution function. The T spline based on Bezier extraction can perfectly accord with the later development of a topology description model, so that the difficulty of directly using the T spline to construct DDF can be effectively avoided, the smooth use of a direct smoothing mechanism can be ensured, and the smooth and clear boundary of an optimization result is ensured;

thirdly, the expected benefits and commercial value after the technical scheme of the invention is converted are as follows:

(1) Meet the high-end equipment requirement: aiming at complex geometric description of high-end equipment structural members in the fields of aerospace and the like, the geometric topology optimization method can provide an effective solution and meet the requirements of the high-end equipment field on high-performance structural members.

(2) Integrating design and analysis flow: the invention aims at incorporating CAD and CAE into a unified mathematical expression framework, which is helpful for realizing seamless docking from design to analysis and improving the efficiency of the whole product development flow.

(3) The design efficiency is improved: the technical scheme of the invention provides an efficient topology optimization method for processing complex geometric shapes, which is a challenge in the traditional topology optimization method, and the design process of complex structures is simplified by optimizing after modeling in CAD software;

(4) Enhancing the product performance: the geometric topological optimization is beneficial to realizing lighter structural design, which is particularly important to the aerospace field, and the structural design directly influences the performance and the fuel efficiency of the product;

(5) The cost is reduced: the invention improves the optimization efficiency, integrates the initial model modeling and the optimization result process which can be visualized, can reduce the use of materials and the times of iterative design and test through the optimization design of the invention, and further saves the production and development cost;

(6) And the reliability of the product is improved: the optimized structural member can keep or improve the strength and durability of the structure while meeting the light weight requirement, thereby improving the reliability and service life of the product.

(7) Cross-industry application potential: although the isogeometric topology optimization method has remarkable application prospect in the aerospace field, the principle and the technology are also suitable for other industries, such as automobiles, ships, buildings and the like, and have wide cross-industry application potential.

In summary, the transformation of the isogeometric topology optimization method for the design domain of the complex structure is expected to bring about improvement of design efficiency, reduction of cost and enhancement of product performance and reliability for related industries, and meanwhile, the method is helpful to promote technical innovation and industry development, and has remarkable commercial value and wide application prospect.

Fourth, the technical proposal of the invention fills the blank field of topology optimization of complex design field, and is based on the present domestic and foreign fields

(1) Topology optimization of complex structures: the invention models a single watertight model with complex geometry based on the local refinement property of the T spline, and provides a unified expression form for any control point in the complex model based on Bezier extraction, so the invention fills the blank field of the optimization design of a complex engineering structure with any design field, and the optimization result obtained by the optimization of the invention can be directly exported and utilized and subjected to subsequent re-analysis and the like due to the special property of the T spline, thereby improving the engineering practicability and convenience of the optimization.

(2) Compatibility with CAD modeling systems: the isogeometric topology optimization method uses T-splines to describe geometry, which enables it to be compatible with existing CAD modeling systems, providing a familiar working environment for designers, allowing them to take advantage of isogeometric topology optimization without changing existing design tools.

(3) Improvement of calculation efficiency: the isogeometric topological optimization method realizes the unification of a geometric model, an analysis model and an optimization model by using the same mathematical description to calculate domain, structural response and an objective function. This approach increases computational efficiency, especially when dealing with complex design domains, and can more quickly yield optimized results.

(4) Improvement of numerical solution technology: the development of the isogeometric topology optimization method also promotes the progress of the design analysis integrated high-efficiency numerical solution technology. The research and application of the technology further improve the precision and efficiency of topology optimization, and have remarkable significance for optimizing the design domain of the complex structure.

In summary, the isogeometric topology optimization method facing the complex structure design domain has remarkable progress in the aspects of compatibility, calculation efficiency, complex engineering structure design, numerical solution technology and the like, and the progress not only fills the technical blank, but also lays a solid foundation for innovation and development of future engineering design.

Fifth, when the isogeometric topology optimization method is used for processing complex structure design, the limitations of some traditional methods are overcome, and the technical breakthroughs of the following aspects are realized:

(1) The calculation efficiency is improved: by using the T spline mathematical description compatible with the CAD system, the isogeometric topological optimization method improves the calculation efficiency, and particularly when complex design domains are processed, the optimization result can be obtained quickly and accurately.

(2) The optimization method facing the complex engineering structure is enhanced: the invention makes great progress in the aspect of complex structural design, is particularly important for the optimal design of complex engineering structures, especially plate-shell structures, and is beneficial to promoting the lightweight development in the aerospace field.

(3) Optimizing a numerical solution technology: the development of the geometric topological optimization method promotes the progress of design analysis integrated high-efficiency numerical solution technology, and improves the precision and efficiency of topological optimization.

(4) The design and analysis flow is unified: geometric analysis such as structure and the like aims at incorporating CAD and CAE into a unified mathematical expression frame, which is helpful for realizing seamless butt joint of design and analysis and improving the efficiency of the whole product development flow.

The technical breakthroughs not only improve the quality and efficiency of engineering design, but also provide powerful technical support for the innovative development of high-end equipment. By the optimization method, a structure with lighter weight and better performance can be designed, and the requirements of the aerospace field on the high-performance structure can be met. In addition, the research and application of the method bring new research directions and commercialization opportunities for the related fields, and have important economic and social values.

Sixth, the technical solution of the present invention overcomes the technical prejudice and limitations of traditional topology optimization by:

(1) Application of complex engineering structure: by realizing the isogeometric analysis of the irregular model in the regular embedded domain, the method breaks through the limitation of the traditional topological optimization on the irregular geometric shape, and meets the optimization design of the plate-shell structure with any shape.

(2) Unified mathematical expression framework: geometric analysis such as structure and the like aims at incorporating CAD and CAE into a unified mathematical expression frame, the method is closely related with geometric information, and the geometric precise modeling, structural analysis and design process are combined by adopting the same mathematical expression, so that new possibility is provided for structural optimization design.

(3) Improvement of numerical calculation stability: the method is also focused on solving the problem of unstable numerical calculation such as unit dependence, singularity, checkerboard and the like which are commonly existed in the numerical method for topological optimization of the continuum structure, thereby improving the stability of calculation.

In summary, the isogeometric topology optimization method facing the complex structure design domain effectively overcomes the limitations and prejudices of some traditional topology optimization technologies by introducing new technologies and strategies, and brings new development opportunities for the structural design field.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments of the present invention will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a flow chart of an isogeometric topology optimization method for a complex design domain provided by an embodiment of the invention;

FIG. 2 is a schematic diagram of two main modeling methods based on T-spline modeling provided by an embodiment of the present invention;

FIG. 3 is a schematic diagram of a local density distribution function and a global density distribution function according to an embodiment of the present invention, where (a) is a schematic diagram of the construction of the local density distribution function, and (b) is a schematic diagram of the construction of the global density distribution function;

FIG. 4 is a schematic diagram of an optimized structural design of a vehicle shell with a quarter saddle surface thin shell structure according to the preferred embodiment of the present invention, wherein (a) is an initial geometric model and a grid model of the quarter saddle surface, (b) is a schematic diagram of an optimized topology, (c) is a schematic diagram of a reconstructed model, and (d) is a schematic diagram of a displacement structure of a re-analysis of an optimized structure;

FIG. 5 is a diagram of an isogeometric topology optimization system for a complex design domain provided by an embodiment of the present invention.

FIG. 6 is a schematic diagram of an optimized structural design of a complex thin-shell structural hull of an embodiment of the present invention, where (a) is an initial geometric model and a mesh model of the hull structure, (b) is a schematic diagram of an optimized topology, (c) is a schematic diagram of a reconstructed model, and (d) is a schematic diagram of a displacement structure for re-analysis of the optimized structure;

Detailed Description

The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.

Aiming at the problems existing in the prior art, the invention provides an isogeometric topology optimization method and an isogeometric topology optimization system for complex design domains, and the invention is described in detail below with reference to the accompanying drawings.

The invention provides an isogeometric topology optimization method facing to complex design domain, the flow of which is shown in figure 1, comprising the following steps:

(1) Modeling a geometric model with a complex shape in Rhino by using a T spline, wherein a specific modeling mode is shown in FIG. 2, and mainly comprises two modeling methods: ① Drawing NURBS curved surfaces, dividing grids to obtain grid models, converting the grid models into T spline models through T-splines plug-ins, and performing smoothing and other operations according to specific conditions of the models; ② Direct modeling is performed by the T-splines plug-in. After meshing, a model file containing unit and control point information is derived, and the analysis model file contains global mesh data and comprises the following fields:

① type-type of derived surface. The plate model type is shown as a plane and the three-dimensional curved surface model is shown as a curved surface.

② NodeN-total number of T spline control points.

③ ElemN-define the total number of Bezier units for the T-spline surface.

④ Data of control points: the designated format for each T-splines control point is nodexyzw.

⑤ Bezier unit data: bezier unit data is block data containing Bernstein polynomials and unit extraction operators. The first row of data is the global data of the cell, including the base function support number and the order of both directions, denoted by belemnp _ξp_η. The global index of each non-zero T-spline basis function in the second row is a ₁A₂…A_n. In the next n rows, the extraction operator is designated as

And establishes the corresponding load and boundary conditions of the complex thin-shell vehicle shell structure.

(2) Reading the imported model file and converting the T spline object into a data structure suitable for analysis; and establishing a finite element data structure based on the Bezier extraction, and pre-calculating the base functions and derivatives of the Bezier element extraction operators and the Bezier elements. Wherein the T-spline mixing function based on Bezier extraction method can be expressed as

N^e(ξ,η)＝C^eB(ξ,η)

In the method, in the process of the invention,Is a vector of T-spline mixing functions containing a support unit e, a represents the relevant local index of the control point, and n is the total number of control points. /(I)Is the unit extraction operator for unit e, assuming the polynomial order is the same in each direction, the dimension is nx (p+1) ². /(I)Is a vector defining the Bernstein polynomial. Let/>Is a vector of T-spline blending functions of element e, and T-spline blending functions of element e can be expressed as

And (3) with

In the method, in the process of the invention,And w ^e are two expressions of the weights of the n control points corresponding to the unit e. The first order and second order differential of the T spline mixing function is

In the method, in the process of the invention,

(3) According to the Bezier expression form of the T spline in the step (2), the same curved surface can be constructed by utilizing the T spline control points and the corresponding Bezier control points, and the same coordinates of the control points on the boundaries of two adjacent units are ensured, so that the densities of the control points for constructing the DDF are also the same, and the continuity of combining the local DDFs into the global DDF is ensured. The local DDF is built at each Bezier unit using the corresponding Bernstein basis functions, the main steps being as shown in FIG. 3 (a), including:

① Defining an initial density of Bezier control points, namely the Bezier control density phi _i{i＝1,...,(p+1)², which is in the range of [0,1];

② A smoothing mechanism is constructed based on a Shebard function, and the corresponding mathematical formula is as follows

in the method, in the process of the invention, Is the weight function of control point Q _i, which is constructed from Radial Basis Functions (RBFs) with C4 continuity. n is the total number of control densities affecting the current control density,/>Representing a smoothed Bezier control density.

③ A local Density Distribution Function (DDF) is constructed using a linear combination of all Bernstein polynomials and smoothed control design variables in the corresponding Bezier units, the corresponding formulas being as follows:

Where Φ _l is the local DDF, which can also be regarded as the density response surface of the Bezier units. Is a vector of smooth control density,/>Is a vector of Bernstein polynomials of the corresponding Bezier unit.

④ Implicit description mechanism for constructing structure boundary, equivalent contour of local DDF represents structure boundary of corresponding topology, its value is

Where phi _ISO represents the iso-contour value of the local DDF,Is the structural topology of the corresponding Bezier unit.

And combines all local DDFs into a global DDF for representing the topology of the structure, as shown in FIG. 3 (B), the corresponding global DDF can be represented as

In the method, in the process of the invention,The local DDF, Φ _g, representing the ith Bezier unit, represents the global DDF of the entire domain structure topology. The corresponding structure topology can be expressed as

In the method, in the process of the invention,Representing the structural topology of the entire design domain. Perfect and natural connection between adjacent Bezier units can keep no gap of global DDF, so that the global DDF and the global structure topology have enough smoothness and continuity. The structural topology is deduced by optimizing the DDF until the expected structural performance is reached, and the optimized topological structure is trimmed into a single watertight T-spline surface along the contour line, and the single watertight T-spline surface can be used as a new analysis input surface.

(4) The unknown response of the structure is solved by adopting a Gaussian product method on the model established in the steps, in order to effectively solve the integral stiffness matrix K, firstly, an IGA unit stiffness matrix K _e needs to be calculated, and a specific two-dimensional mathematical equation is as follows:

Where E _min is the solid material stiffness, E ₀ is the minimum material stiffness, γ is the penalty factor, J is the jacobian of the mapping from parent cell space to physical space, B is the cell strain-displacement matrix, N _g is the total number of Gaussian orthogonal points, and ω _g is the weight of the corresponding Gaussian point.

After solving the displacement field, calculating the structural flexibility minimization objective function and constraint condition of the composite material of the structure, and expressing the rigidity maximization topology optimization model of the corresponding complex design domain as follows:

Where φ _i denotes the initial density of Bezier control points, the range of variation of the design variables during the optimization is [ φ _min,1].φ_min is the minimum value of the design variables, usually equal to 1e-6 in order to avoid singular points during the optimization. J represents an objective function, i.e. the structural mean compliance used to describe the load capacity. u represents the displacement field of the design domain Ω calculated by T-spline based IGA. V represents the material volume constraint, where V ₀ is the solid volume fraction and V ₀ is the maximum material consumption. a is the bilinear energy and δu is the virtual displacement field belonging to the kinematically tolerable space H ¹ (Ω). g provides a specified displacement vector on Dirichlet boundary Γ _D, l is a linear load function, expressed as:

(5) The sensitivity is obtained by calculating the derivatives of the objective function and the constraint condition on the design variables respectively, wherein the partial derivatives of the objective function and the constraint condition on the design variables respectively are expressed as:

(6) And updating the control density phi _i, namely the design variable by using an OC method, substituting the updated design variable into a topology description model for updating the design domain representing the complex structure, updating a displacement field by using the updated model, thereby updating and calculating the objective function and the sensitivity calculation to obtain a new control variable, judging whether a convergence condition is met (the node density difference between two continuous iterations is smaller than a certain value), and continuing the iteration process if the convergence condition is not met, so that the topology optimization configuration of the optimized composite material is obtained.

The results of the above steps of the present invention are described in detail below in conjunction with one embodiment shown in fig. 4:

(1) Modeling an initial geometric model of a saddle surface in Rhino, performing model construction by adopting a modeling mode of FIG. 2 (a), and locally refining at a position where a curvature structure changes, wherein one fourth of the structure is selected as an initial optimization model because the structure has symmetry, as shown in FIG. 4 (a);

(2) Importing a model file and converting the model file into data suitable for analysis, wherein the related data of the quarter saddle surface structure in the T spline parameterization and the IGA are shown in a table 1, and the related data comprise polynomial orders of a T spline basis function, the number of control points and the number of isogeometric analysis units, and constructing a geometric design model by utilizing the T spline according to the parameters; the penalty factor is 3, the maximum value of the volume fraction is set to 40%;

table 1 data relating quarter saddle surface structure in NURBS parameterization and IGA

(3) The basic functions and derivatives of the Bezier unit extraction operator and the Bezier unit are pre-calculated, and the basic functions and derivatives are specifically as follows:

t-spline mixing function based on Bezier extraction method can be expressed as

N^e(ξ,η)＝C^eB(ξ,η)

And (3) with

In the method, in the process of the invention,

(4) According to Bezier extraction, a topology description model can be established, and the main steps comprise two parts: constructing a local DDF at each Bezier unit using a corresponding Bernstein basis function, and assembling the local DDF into a global DDF that represents the structural topology. As shown in fig. 3 (a), constructing a local DDF comprises the following 4 steps:

Where Φ _l is the local DDF, which can also be regarded as the density response surface of the Bezier units. Is a vector of smooth control density,/>Is a vector of Bernstein polynomials of the corresponding Bezier unit. /(I)

As shown in FIG. 3 (B), given a number N _b of Bezier units in the domain, the corresponding global DDF can be expressed as

In the method, in the process of the invention,Representing the structural topology of the entire design domain. Perfect and natural connection between adjacent Bezier units can keep no gap of global DDF, so that global DDF phi _g and global structure topology/>Has sufficient smoothness and continuity. The structural topology is deduced by optimizing the DDF until the expected structural performance is reached, and the optimized topological structure is trimmed into a single watertight T-spline surface along the contour line, and the single watertight T-spline surface can be used as a new analysis input surface.

(5) The unknown response of the structure is solved by adopting a Gaussian product method, and the method is mainly used for solving the IGA unit stiffness matrix. In order to effectively solve the overall stiffness matrix K, first, an IGA cell stiffness matrix K _e needs to be calculated, and a specific two-dimensional mathematical equation is as follows:

Where E _min is the solid material stiffness, E ₀ is the minimum material stiffness, γ is the penalty factor, J is the jacobian of the mapping from parent cell space to physical space, N _g is the total number of Gaussian intersection points, ω _g is the weight of the corresponding Gaussian point, and g is the matrix combination for solving the plate and shell structure, expressed as

Wherein t is the thickness of the plate-shell structure, v is poisson's ratio,Is a film strain matrix,/>Representing a bending strain matrix, H being a transformation matrix from a local coordinate system to a global coordinate system, calculated specifically as

(6) Calculating the structural flexibility minimization objective function and constraint conditions of the structure, and the corresponding mathematical model of the isogeometric topological optimization of the plate-shell structure based on the T spline is as follows:

Where φ _i denotes the initial density of Bezier control points, the range of variation of the design variables during the optimization is [ φ _min,1].φ_min is the minimum value of the design variables, usually equal to 1e-6 in order to avoid singular points during the optimization. J represents an objective function, i.e. the structural mean compliance used to describe the load capacity. G _ε and G _κ correspond to the film stress tensor coefficient and the bending stress tensor coefficient, respectively, specifically calculated as

U represents the displacement field of the design domain Ω calculated by T-spline based IGA. V represents the material volume constraint, where V ₀ is the solid volume fraction and V ₀ is the maximum material consumption. a is the bilinear energy and δu is the virtual displacement field belonging to the kinematically tolerable space H ¹ (Ω). g provides a specified displacement vector on Dirichlet boundary Γ _D, l is a linear load function, expressed as:

(7) The sensitivity being obtained by derivatives of the objective function and of the constraint, respectively, on the design variables, in particular

(8) And updating the control density phi _i, namely the design variable by using an OC method, substituting the updated design variable into a topology description model for updating the design domain representing the complex structure, updating a displacement field by using the updated model, thereby updating and calculating the objective function and the sensitivity calculation to obtain a new control variable, judging whether convergence conditions are met, and continuing the iterative process if the convergence conditions are not met, so that the optimized topology optimization configuration is obtained. The convergence criterion is that the node density difference between two consecutive iterations is less than 1%, or a maximum of 150 iteration steps is reached.

The results of the optimization of the quarter saddle surface structure are shown in fig. 4, including the optimized structure topology in fig. 4 (b) and the reconstruction results in fig. 4 (c). The optimization result can be easily observed, the characteristics of the optimized topological structure are that an obvious interface exists between the entity and the gap, and the smooth and clear boundary of the final design can be ensured based on the topological description model developed by the invention. By combining T-splines and IGA, the geometry and parameter domains of the shell surface are precisely described in the proposed method, which means that the reconstructed optimization results in CAD systems can be directly analyzed, and the z-direction displacement image of the re-analysis of the optimization results is shown in fig. 4 (d). From the displacement results, it can be seen that the displacement variation is mainly distributed in the upper part of the structure (above the curvature maximum), which is caused by external load. The larger displacement is distributed in the top region of the housing structure. The optimized structure creates a more complex configuration in the vicinity of the applied load area and the support for transferring the applied load. The current example has complex geometry, which also demonstrates the modeling ability of T-splines based on Bezier extraction. Therefore, the application example can prove the effectiveness and powerful functions of the proposed isogeometric topological optimization method facing the complex design domain on the shell structure with any shape, and can also reveal the great potential of the isogeometric topological optimization method in future application.

As shown in fig. 5, the isogeometric topology optimization system for a complex design domain provided by the embodiment of the present invention includes:

The geometric model modeling and grid dividing module is used for modeling a geometric model with a complex design domain in CAD software based on T spline, dividing grids and deriving a model file;

The density distribution function construction module is used for constructing a corresponding local density distribution function in each Bezier unit, the tensor product characteristic of the Bezier curved surface in each unit ensures the smoothness and continuity of the local DDF, and all the local DDFs are assembled to obtain a structural topology global DDF for presenting continuity and smoothness; firstly constructing a local density distribution function, and then assembling the local density distribution function into a global density distribution function;

An application embodiment of the present invention provides a computer device, where the computer device includes a memory and a processor, and the memory stores a computer program, where the computer program, when executed by the processor, causes the processor to execute steps of an isogeometric topology optimization method for a complex design domain.

An application embodiment of the present invention provides a computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of an isogeometric topology optimization method for a complex design domain.

The embodiment of the application of the invention provides an information data processing terminal which is used for realizing an isogeometric topology optimization system oriented to a complex design domain.

The invention will be described in detail with reference to a specific application example shown in fig. 6:

(1) Modeling an initial geometric model of the vehicle shell in the Rhino, locally refining the initial geometric model at the position where the curvature structure changes, and finally, the initial model of the vehicle shell is shown in fig. 6 (a);

(2) Importing a model file and converting the model file into data suitable for analysis, wherein the related data of the hull structure in T spline parameterization and IGA are shown in table 1, and the related data comprise polynomial orders of T spline basis functions, the number of control points and the number of isogeometric analysis units, and a geometric design model is constructed by utilizing T splines according to the parameters; the penalty factor is 3, the maximum value of the volume fraction is set to 65%;

table 2 relevant data of hull structure in NURBS parameterization and IGA

t-spline mixing function based on Bezier extraction method can be expressed as

N^e(ξ,η)＝C^eB(ξ,η)

And (3) with

In the method, in the process of the invention,

The optimization results of the hull structure are shown in fig. 6, and include three views of the structure topology after optimization in fig. 6 (b), three views of the reconstruction results in fig. 6 (c), and the displacement image of the re-analysis of the optimization results in fig. 6 (d). From the final optimized configuration, the optimized topology has smooth structural boundaries and obvious solid material-void interfaces. Structural geometric features in the optimized topology structure can show continuity and smoothness of the local DDFs, naturalness of connection among the local DDFs and effectiveness of the generated global DDFs. The corresponding design results indicate that the T-spline based on Bezier extraction is indispensable for the description of the structure topology. In the current invention, the initial discrete layout of the control density on the points can be removed, and the key problem of T spline topology optimization in the past work is effectively solved. Furthermore, it can be seen from fig. 6 (c) that the solid material in the initial structure that has no or less effect on improving the structural performance is rejected during the optimization process. In addition, due to the adoption of local refinement grids in different areas, the optimized vehicle shell can generate a plurality of fine structural features, which shows the advantages of the proposed geometric topology optimization method facing the complex design domain. As shown in fig. 6 (d), an optimally configured displacement field is also provided. In the optimization process, the structural flexibility of the vehicle shell is improved, and materials are reasonably distributed to bear loads and boundary conditions. Therefore, the application example can prove the effectiveness and powerful functions of the proposed isogeometric topology optimization method facing the complex design domain on engineering structures, and can also reveal the great potential of the isogeometric topology optimization method in future application.

(1) Improving the numerical precision: the invention is established based on an isogeometric analysis method, eliminates the inconsistency between a geometric model and an analysis model in the traditional finite element method and the model conversion operation between different models, and improves the numerical precision in the process of optimizing analysis;

(2) Complex geometry is constructed: the invention establishes a geometric model with a complex design domain based on T spline, breaks through the limit of NURBS tensor product, and other methods for constructing complex shapes (a multi-piece method and a pruning method) have the following disadvantages:

① The complex design domain constructed by the multi-piece method has no higher continuity on the connection boundary, and the parameter settings of different pieces are different, so that the multi-piece structure cannot be directly solved and analyzed;

② The surface treated by the pruning method generally has no independent representation capability and cannot be used for numerical analysis;

③ The multi-piece method is often combined with the trimming method, but gaps and overlapping usually occur in the connection of the multi-pieces after trimming, and the C ⁰ continuity requirement of the plate-shell structure cannot be met.

The local refinement property of the T spline ensures the establishment of a single watertight model of any design domain, the problems are radically avoided, the derivation and expression of the T spline are similar to NURBS, and the method has strong applicability, so that the method can optimize a complex engineering structure with any design domain, and the optimization result obtained by the optimization of the method can be directly derived and utilized and subjected to subsequent re-analysis and the like due to the special property of the T spline, thereby improving the practicability and convenience of the optimized engineering.

(3) Optimizing result boundary smoothing: the current topology optimization based on T-splines defines a discrete distribution of T-spline control point densities instead of a continuous density distribution to represent the structure topology, resulting in "zig-zag" features in the optimization result. And the T spline does not have global tensor product characteristics, and a density distribution function with continuity and smoothness cannot be constructed by using the T spline. The invention establishes a local density distribution function based on the Bezier unit, applies a smoothing mechanism in the local density distribution function, and finally assembles all the local distribution functions into a global density distribution function to represent the structure topology. Considering the local density distribution function of the smoothing mechanism ensures the smoothness and continuity of the topology result, while the consistency of the control points and the basis functions of the adjacent Bezier units ensures a perfect connection of the local density distribution function. The method can effectively avoid the difficulty of directly using the T spline to construct the DDF, ensure the smooth use of a direct smoothing mechanism and ensure the smooth and clear boundary of an optimization result;

(4) The effectiveness is strong: at present, the topological optimization based on the T spline introduces numerical limitation due to the numerical realization of the T spline in a structural geometric model and the existence of abnormal points in the T spline, the IGA condition based on the T spline is complex and cannot be directly expanded to other more complex structures, but the invention adopts Bezier extraction to construct the same expression form for any point in the T spline, so that the isogeometric analysis can be simply realized, and the effectiveness of the isogeometric topological optimization method based on the T spline is increased;

(5) The expansibility is strong: at present, the problem of the isogeometric topological optimization design based on T-spline only considers the classical flexibility minimization of the structure of a two-dimensional plane, and the problem of the design of a three-dimensional complex space shell structure is not involved, but the topological optimization of the plate shell structure is also a difficult problem in the field of structural design research and is commonly used in the industrial field. The invention has clear functions, and the corresponding modules are expanded to a simple and convenient plate-shell structure, and the embodiment and the application example also well illustrate that the invention can be suitable for the optimized design of a more complex industrial shell structure.

The above aspects are embodied in the end results of the examples and application examples.

In the description of the present invention, unless otherwise indicated, the meaning of "a plurality" is two or more; the terms "upper," "lower," "left," "right," "inner," "outer," "front," "rear," "head," "tail," and the like are used as an orientation or positional relationship based on that shown in the drawings, merely to facilitate description of the invention and to simplify the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore should not be construed as limiting the invention. Furthermore, the terms "first," "second," "third," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.

It should be noted that the embodiments of the present invention can be realized in hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or special purpose design hardware. Those of ordinary skill in the art will appreciate that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, such as provided on a carrier medium such as a magnetic disk, CD or DVD-ROM, a programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The device of the present invention and its modules may be implemented by hardware circuitry, such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., as well as software executed by various types of processors, or by a combination of the above hardware circuitry and software, such as firmware.

The foregoing is merely illustrative of specific embodiments of the present invention, and the scope of the invention is not limited thereto, but any modifications, equivalents, improvements and alternatives falling within the spirit and principles of the present invention will be apparent to those skilled in the art within the scope of the present invention.

Claims

1. The isogeometric topology optimization method for the complex design domain is characterized by comprising the following steps of:

s1, modeling a geometric model with a complex design domain in CAD software based on T spline, dividing grids, and deriving a model file;

S3, constructing a corresponding local density distribution function in each Bezier unit, ensuring the smoothness and continuity of the local DDF by tensor product characteristics of the Bezier curved surfaces in each unit, and assembling all the local DDFs to obtain a structural topology global DDF with continuity and smoothness;

2. The method for optimizing an isogeometric topology for a complex design domain according to claim 1, wherein the implementation manner of step S1 comprises:

S101, creating, editing and converting a T-spline-based surface model by combining with Rhinoceros 3D and Autodesk T-splines plug-ins, wherein the visual process of the geometric modeling step can be realized, and the realization of the current T-spline geometric model is only limited to untrimmed hyperboloid. In the invention, the construction of the curved surface model with complex geometry mainly comprises two modes: (1) Drawing NURBS curved surfaces, dividing grids to obtain grid models, converting the grid models into T spline models through T-splines plug-ins, and performing smoothing and other operations according to specific conditions of the models; (2) direct modeling by a T-splines plug-in;

(2) nodeN-total number of spline control points;

(3) elemN-defining the total number of Bezier units of the T spline surface;

(4) Data of control points: the designated format of each T spline control point is node x y z w;

(5) Bezier unit data: the Bezier unit data is block data comprising Bernstein polynomials and unit extraction operators; the first row of data is the global data of the cell, including the base function support number and the order of the two directions, denoted by belem n p _ξp_η; the global index of each non-zero T-spline basis function in the second row is a ₁ A₂…A_n. In the next n rows, the extraction operator is specified as:

3. the method for optimizing an isogeometric topology for a complex design domain according to claim 1, wherein the implementation manner of step S2 comprises:

N^e(ξ,η)＝C^eB(ξ,η)；

And (3) with

4. The isogeometric topology optimization method for a complex design domain according to claim 1, wherein the topology description model is built based on Bezier extraction mainly comprises the following parts:

in the method, in the process of the invention, Is the weight function of control point Q _i, which is constructed from radial basis functions with C4 continuity, n is the total number of control densities affecting the current control density,/>Representing a smoothed Bezier control density;

5. The isogeometric topological optimization method for a complex design domain according to claim 1, wherein a two-dimensional numerical equation of the isogeometric unit stiffness matrix K _e calculated based on a gaussian orthogonal method is as follows:

6. The method for optimizing an isogeometric topology for a complex design domain according to claim 1, wherein step S5 comprises:

S501, initializing design variables;

7. A complex design domain oriented isogeometric topology optimization system implementing the complex design domain oriented isogeometric topology optimization method of any one of claims 1-6, comprising:

8. A computer device 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 the complex design domain oriented isogeometric topology optimization method of 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 perform the steps of the complex design domain oriented isogeometric topology optimization method of any one of claims 1 to 6.

10. An information data processing terminal for implementing the complex design domain oriented isogeometric topology optimization system of claim 7.