A self-adaptive geometric modeling method for combined thin-walled element structures for integrated modeling-analysis-optimization

Abstract

The present invention provides a self-adaptive geometric modeling method for a combined thin-walled element structure for the integration of modeling-analysis-optimization, which firstly uses a free-form deformation technique MNFFD based on multi-level NURBS to realize accurate geometric modeling for the combined thin-walled element structure. Secondly, based on the MNFFD method, a modeling-analysis integrated model is established for the iso-geometric analysis of the combined thin-walled element structure. Finally, based on the MNFFD method, a modeling-analysis-design integrated model is established for the cooperative design of the combined thin-walled element structure shape and reinforcement layout. The present invention fundamentally solves the robustness problem of the modeling of the gap and overlap between thin-walled elements caused by the traditional modeling method lacking accurate topology consistency, provides a new tool for the optimization design of engineering thin-walled structures, greatly improves the design accuracy of products, and shortens the development period. The MNFFD is used to realize the geometric dimension reduction transformation from the 3D design domain to the 2D design domain, and breaks through the difficulty of the self-adaptive update of the design model, thereby realizing the non-interference of the design domain of the combined thin-walled element structure with complex assembly relationships.

Description

[Technical field]

[0001] The present invention relates to the related technical fields of structural mechanics and digitalized design, and more particularly to a self-adaptive geometric modeling method for combined thin-walled element structures for integrated modeling-analysis-optimization. [Background technology]

[0002] Combination thin-walled element structures (combination thin-walled element structures are usually composed of two or more simple thin-walled elements, such as braced plate shell structures, multi-wall structures, multi-rib structures, sandwich structures, and thin-walled dot structures) are widely applied in various engineering fields due to their unique advantages in terms of high specific stiffness. Structural optimization is an important tool in product design, and the development level of this technology is directly related to the bearing performance and weight reduction of the structure. In the traditional design system, CAD system modeling and CAE system are used to perform finite element analysis, and data exchange between the two systems needs to be performed through a semi-automated grid model. This design flow is not only inefficient for model systems with complex assembly relationships, but also difficult to realize automation. In recent years, these problems have been solved by isogeometric analysis, which enables the development of a large-scale seamless integrated analysis and design platform. This is because isogeometric analysis directly applies CAD interpolation models to geometric and physical fields, integrating modeling and analysis into an integrated model, and realizing seamless integration between CAD and CAE systems. Although isogeometric analysis has achieved great success in many scientific fields, in many cases it is still not possible to directly create complete analytical models from CAD systems, especially for combinatorial thin-walled element structures commonly found in processing engineering. This is mainly because the use of NURBS modeling is severely limited by its tensor product structure. For complex models, they can only be generated by Boolean operations, which usually requires a large number of NURBS sheets, and the interior of the NURBS sheets uses a large number of trimming curves. For this reason, global discretization with NURBS cannot be directly applied to isogeometric analysis.

[0003] At present, there are mainly two kinds of solutions, and the purpose of both methods is to realize true automated analysis. The first kind solves this problem from the viewpoint of analysis. The finite element method is an extension of the classical finite element method, and its main idea is to extend the boundary of the physical domain to a larger embedded domain with a simple geometric structure, which can be discretized by structuring the grid. This method is mainly aimed at the analysis of three-dimensional structures, and avoids the reparametric of NURBS entities. For thin-walled structures, the well-known modeling method in CAD systems is the B-Rep model based on NURBS. The second kind looks at this problem from the viewpoint of modeling. The reparametric method can convert the trimmed B-Rep model into an untrimmed NURBS surface. Scholars propose to perform the reparametric of CAD embedding by the global parametric of the framework field guide. The obtained geometry can be used for design and analysis without further grid or geometric processing. Reconstructing the untrimmed NURBS model makes the application of IGA in complex construction objects easier and more convenient.

[0004] In fact, NURBS modeling rules not only affect analysis, but also bring difficulties to structural optimization. In the analysis and design workflow, it is necessary to analyze only once from the geometric model to the analysis model, but in the design optimization workflow, it is necessary to change the geometric model based on the design variables, and the analysis program is repeatedly called in the structural optimization framework, and the control of the geometric model and the structural analysis must both be automated. Multi-stage reinforced thin-walled structures can be regarded as the same kind of assembly structure, and there is a strict assembly relationship between the thin-walled elements. In the design flow of reinforced structures, how to guarantee the existing assembly relationship when the shape is modified is a difficulty. In the isogeometric optimization paradigm, the position of the control points of NURBS curves, surfaces, and bodies is always taken as a design variable, and shape control can be realized by a small amount of design variables, but this also brings a series of problems, and after moving the control points, the assembly relationship between the original thin-walled elements is destroyed. In short, for the design analysis optimization workflow, not only a model suitable for analysis but also a model suitable for optimization is required. Therefore, an interactive isogeometric modeling and analysis platform based on parametric design, as well as an indirect modeling paradigm are proposed by scholars. Indirect modeling is a representation method of trimming, in which the display range is defined by a curve in the NURBS surface parameter domain, and can be understood as a mapping relationship from the two-dimensional parameter domain to the three-dimensional physical domain.

[0005] Another method that adopts a similar approach is the free-form deformation technique (FFD), whose basic idea is to embed objects into parametric entities. When the parametric entities are deformed, the deformation is transferred to the embedded objects. This ensures that the original assembly relationship does not change when deformation occurs. Compared with classical FFD algorithms, NFFD has greater flexibility and controllability. The same effect can be achieved by embedding objects into the parameter space of NURBS surfaces and NURBS entities. In previous studies, both FFD and NFFD have only one-layer mapping relationships. For complex engineering thin-wall structures, it is always necessary to nest multi-layer thin-wall elements, so a multi-layer NFFD method, i.e., MNFFD method, is proposed to realize the integrated geometric modeling of the combined thin-wall element structure. Summary of the Invention [Problem to be solved by the invention]

[0006] The present invention mainly solves the technical problems of poor modeling analysis accuracy and low optimization efficiency of the combined thin-walled element structure of the prior art. In the traditional design system, data exchange between the two systems, CAD and CAE, is required through a semi-automated grid model. For a model system with complex assembly relationships, such a design flow is not only inefficient, but also difficult to realize automation. In addition, the traditional B-rep modeling method uses a large number of trimming surfaces, which seriously affects the geometric accuracy and watertightness of the model. In response to the above problems, the present invention provides a geometric modeling method for the integration of modeling-analysis-optimization of combined thin-walled element structures, realizes the integrated geometric modeling of combined thin-walled element structures, improves the accuracy of combined thin-walled element structure modeling, improves the calculation efficiency and calculation accuracy of analysis design, and achieves the purpose of shortening the product design cycle. [Means for solving the problem]

[0007] In order to achieve the above objectives, the technical solutions of the present invention are as follows:

[0008] The self-adaptive geometric modeling method of a combined thin-walled element structure for integrated modeling-analysis-optimization includes the following steps.

[0009] In step 100, a multi-level NURBS-based free-form deformation technique (MNFFD) is utilized to realize accurate geometric modeling for the combined thin-walled element structure, which includes the following sub-steps:

[0010] In step 101, the indirect characterization relationship of the complex thin-walled structural module is established by using NURBS-based free-form deformation technology (NFFD), which specifically includes the following two kinds of mapping relationships: the first is to embed the NURBS curve into the parameter space of the NURBS surface; JPEG2025511421000002.jpg18170. By embedding an object into the parameter space of a NURBS surface or a NURBS entity, an indirect geometric definition of the curves in the surface and the surfaces in the entity is obtained.

[0011] In step 102, according to the two kinds of mapping relationships mentioned in step 101, based on the original single-layer level mapping NFFD method, allow the structure to have multi-layer and composite mapping to provide an MNFFD method, and establish an indirect characterization relationship of the combined thin-walled element structure module based on MNFFD. By utilizing the multi-layer mapping relationship of MNFFD, the nesting model can satisfy the assembly relationship and geometric constraints between different thin-walled elements, and finally realize the accurate geometric modeling of the combined thin-walled element structure.

[0012] In step 200, based on the MNFFD method, a modeling-analysis integrated model is established which is applied to the iso-geometric analysis of the combined thin-walled element structure, and includes the following sub-steps:

[0013] In step 201, the theoretical formulas of the 6-DOF degenerate shell unit and the 6-DOF degenerate beam unit based on the MNFFD mapping model are derived based on the isogeometric paradigm.

[0014] In step 202, in the isogeometric analysis based on MNFFD, a domain decomposition method is used to establish the coupling relationship of non-congruent NURBS surface sheets, and realize the propagation between the solution surfaces or mapping surfaces.

[0015] In step 300, based on the MNFFD method, an integrated model of modeling-analysis-design is established which applies to the collaborative design of combined thin-walled element structural shape and reinforcement layout, and includes the following sub-steps:

[0016] In step 301, in the optimization design of the thin-walled structure, an integrated model of modeling-analysis-design is established based on the MNFFD method, the design space is transformed from the 3D physical space to the 2D or 3D standard parameter space, and the shape and reinforcement layout of the shell body are jointly optimized. In terms of the shape optimization of the combined thin-walled element structure, the mapping surface in the MNFFD model is used to represent the skin, rib plate, brace or other structure, the mapping surface is embedded into the 3D NURBS entity, the control points are moved or the weight values ​​are modified to change the shape of the surrounding NURBS entity, and the deformation is directly transferred to the object geometry represented by the mapping surface.

[0017] In step 302, in the brace layout design of the combined thin-walled element structure, the parametric design of the brace layout can be specifically divided into two parts: brace curve shape optimization and brace layout optimization, in which the brace curve shape is defined using a quadratic NURBS mapping curve, each curve is represented by at least three control points, and a geometric step function is defined for the pitch of the brace curve family to represent the pitch between each brace curve control point.

[0018] Furthermore, in step 202, the domain decomposition method includes the penalty method, the Lagrange multiplier method and the Nitsche method. Effect of the Invention

[0019] The innovative analysis and beneficial effects of the present invention are as follows:

[0020] The present invention provides a MNFFD geometric modeling method for combined thin-walled element structures, which fundamentally solves the robustness problem of modeling gaps and overlaps between thin-walled elements caused by the traditional modeling method lacking accurate topology consistency, and integrates the representation forms of design models, analysis models and optimization models based on isogeometric paradigm, providing a set of integrated novel tools for the optimization design of engineering thin-walled structures, which is expected to greatly improve the design accuracy of products and shorten the development period. The multi-layer nesting composite spline structure in MNFFD allows deformation to be transmitted between thin-walled elements, which not only realizes the geometric dimension reduction transformation from the 3D design domain to the 2D design domain, but also breaks through the difficulty of self-adaptive update of the design model, and realizes the non-interference of the design domain of combined thin-walled element structures with complex assembly relationships.

[0021] The present invention first uses NURBS-based free-form deformation technology (NFFD) to establish indirect characterization relationships of complex thin-walled structural modules, and obtains indirect geometric definitions of curves in surfaces and surfaces in entities by embedding objects into the parameter space of NURBS surfaces or NURBS entities. Then, based on the original single-layer level mapping NFFD method, it allows the structure to have multi-layer and composite mapping, and provides an MNFFD indirect modeling method for reinforced thin-walled structures that applies to multi-layer assembly relationships. The indirect modeling method can effectively avoid watertightness problems and is favorable to improving the modeling and analysis accuracy based on the MNFFD model. By utilizing the multi-layer mapping relationship of MNFFD, the nesting model can automatically satisfy the assembly relationships and geometric constraints between different thin-walled elements, and finally realizes accurate geometric modeling of combined thin-walled element structures. In order to realize the integrated modeling of modeling and analysis, the present invention extends the MNFFD model to an isogeometric paradigm and realizes isogeometric analysis based on MNFFD. The geometric analysis adopts a 6-degree-of-freedom degenerate shell unit and a 6-degree-of-freedom degenerate beam unit, and based on the MNFFD modeling, a series of theoretical formulas of the mapping unit can be derived for the mapping surface and mapping curve, and key problems such as multi-sided sheet bonding can be solved. In terms of the design of the combined thin-walled element structure, based on the MNFFD method, an integrated model of modeling-analysis-design is established, and the design space is transformed from the three-dimensional physical space to the two-dimensional or three-dimensional standard parameter space, simplifying the design model and reducing the difficulty of setting the design variables. In addition, the mapping surface and mapping curve are important thin-walled elements in the MNFFD model, and are fully suitable for models containing multi-stage nesting relationships such as combined thin-walled element structures, among which the mapping curve can be used to characterize the struts and trimming curves, and the mapping surface can be used to characterize the skin, rib plate and strut.Moreover, the indirect modeling method based on MNFFD provides the coupling relationship between thin-walled elements, and deformation can be transmitted between thin-walled elements, and any shape change of the thin-walled elements will not destroy the initial assembly relationship, which is very advantageous for model updating in the optimization design process. All of these factors make the geometric modeling of thin-walled structures based on MNFFD have more significant advantages in design than explicit spline and discrete grid. It is expected that this invention will become one of the main geometric modeling methods for combined thin-walled element structures in the fields of aerospace, marine automobiles, civil engineering and construction in China. [Brief description of the drawings]

[0022] [Figure 1] A schematic diagram of entity definition based on 2D NFFD, in which (a) is the parameter space of an embedded curve, (b) is the embedded curve embedded in the parameter space of a NURBS surface, and (c) is the mapping curve located on the NURBS surface. [Diagram 2] A schematic diagram of an entity definition based on 2D NFFD, in which (a) is the parameter space of an embedded surface, (b) is the embedded surface embedded in the parameter space of a NURBS entity, and (c) is the mapping surface located in the physical space of a NURBS entity. [Diagram 3] Fig. 1 is a schematic diagram of a flow chart of a reinforced structure constructed by MNFFD, in which (a) is the parameter space of the embedded curve, (b) is the embedded curve embedded in the parameter space of the embedded surface, (c) is the mapping curve located in the physical space of the embedded surface and the embedded surface embedded in the parameter space of the NURBS entity, (d) is the dual mapping curve located in the mapping surface, and (e) is the geometric model of the reinforced structure. [Figure 4] FIG. 1 is a schematic diagram of solving the mapping shell unit equation. [Diagram 5]Schematic diagrams of the geometric information of a mapping muscle stripe, in which (a) is the definition of the physical space direction vector of the muscle stripe, and (b) is the definition of the muscle stripe cross section. [Figure 6] FIG. 1 is a schematic diagram of controlling a mapping surface shape by modifying the positions of NURBS entity control points; [Figure 7] FIG. 13 is a schematic diagram of controlling the mapping surface shape by modifying the weights of NURBS entity control points; [Figure 8] FIG. 1 is a schematic diagram of the definition of two families of muscle curves in parameter space. [Figure 9] 1A-1D are schematic diagrams illustrating striated curve pitch using a geometric step function, in which (a) is a uniform definition of control points, (b) is a sparse-dense-sparse definition of control points, (c) is a dense-sparse-dense definition of control points, and (d) is a sparse-dense definition of control points. [Figure 10] The initial model of the roof, including (a) two families of striated curves defined by embedded curves in the embedded surface parameter space, (b) the embedded surface embedded in the parameter space of the NURBS entity, (c) the mapping surface and dual mapping striated curves located in the NURBS entity physical space, and (d) a rendering perspective of the roof. [Figure 11] FIG. 11 is a cloud plot of the initial model displacements for four boundary fixed constraints. [Figure 12] FIG. 12(a) shows the iterative curve of the collaborative optimization of the curved shape and reinforcement layout, FIG. 12(b) shows the optimized layout and analysis results when the algebra of the point marked A in FIG. 12(a) is 4, FIG. 12(c) shows the optimized layout and analysis results when the algebra of the point marked B in FIG. 12(a) is 14, and FIG. 12(d) shows the optimized layout and analysis results when the algebra of the point marked C in FIG. 12(a) is 25. [Figure 13]Optimized reinforced roof geometry and brace layout, of which (a) is the 2D embedded domain, (b) is the 3D embedded domain, (c) is the geometric domain of the structure, (d) is a 3D rendering, and (e) is a rendering of the sub-structure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0023] In order to clarify the technical problem to be solved, the technical solution adopted, and the technical effect achieved by the present invention, the present invention will be described in more detail below with reference to the drawings and examples. It should be understood that the specific examples described herein are used to interpret the present invention, and do not limit the present invention. For ease of description, the drawings show only a part related to the present invention, but not the entire contents.

[0024] The geometric modeling method for integrated modeling-analysis-optimization of combined thin-walled device structures provided in the embodiment of the present invention includes the following steps.

[0025] In step 100, a multi-level NURBS-based free-form deformation technique (MNFFD) is utilized to realize accurate geometric modeling for the combined thin-walled element structure, which includes the following sub-steps:

[0026] In step 101, the NURBS-based free-form deformation technique (NFFD) is used to establish an indirect characterization relationship of the complex thin-walled structural model, in which the NURBS curve is embedded into the parameter space of the NURBS surface; JPEG2025511421000003.jpg17170JPEG2025511421000004.jpg10170JPEG2025511421000005.jpg13170This is achieved by mapping the NURBS surface from parameter space to physical space using the following equation.The expression for the embedded curve shown in Figure 1(b) is as follows: JPEG2025511421000006.jpg20170JPEG2025511421000007.jpg15170The mapping curve on the NURBS surface can be obtained by mapping, which is defined as follows: JPEG2025511421000008.jpg13170JPEG2025511421000009.jpg19170

[0027] This definition ensures that every point of the curve lies on the surface, as shown in Fig. 1(c). The 2D-NFFD based entity is a composite form of NURBS entities, and its mapping function is a composite form of NURBS basis functions. We also define a NURBS surface as a surface that is a part of the parameter space of the NURBS entities, i.e., JPEG2025511421000010.jpg22170JPEG2025511421000011.jpg9170JPEG2025511421000012.jpg18170The surface is embedded into the parameter space of the NURBS entity, and the principle of entity modeling based on three-dimensional NFFD is introduced by taking the surface as an example, as shown in Figure 2. The embedded surface is defined as follows: JPEG2025511421000013.jpg13170JPEG2025511421000014.jpg25170The embedded surface is embedded in the parameter space of a NURBS entity and mapped from the 3D parameter space to the 3D physical space by the NURBS entity basis functions. The mapping surface is defined as follows: JPEG2025511421000015.jpg25170JPEG2025511421000016.jpg43170

[0028] In step 102, based on the two kinds of mapping relationships mentioned in step 101, based on the original single-layer level mapping NFFD method, allow the structure to have multi-layer and composite mapping to provide an MNFFD method, and establish an indirect characterization relationship of the combined thin-walled element structural model based on MNFFD. The entities based on 2D-NFFD and 3D-NFFD are both only single-layer mapping; JPEG2025511421000017.jpg11170JPEG2025511421000018.jpg9170JPEG2025511421000019.jpg27170The dual mapping curve is defined as follows: JPEG2025511421000020.jpg27170JPEG2025511421000021.jpg60170To illustrate with an example, Figure 3 shows a reinforced structure built using the MNFFD method, and the reinforced structure shown in Figure 3(e) is composed of a double mapping curve (struts) and a mapping surface (skin).

[0029] In step 200, based on the MNFFD method, a modeling-analysis integrated model is established which is applied to the iso-geometric analysis of the combined thin-walled element structure, and includes the following sub-steps:

[0030] In step 201, the theoretical formulas of the 6-DOF degenerate shell unit and the 6-DOF degenerate beam unit based on the MNFFD mapping model are derived based on the isogeometric paradigm. For the mapped degenerate shell unit, the geometric model in the physical space is indirectly defined by using the mapping surface. At this time, the classical isogeometric shell unit formula is no longer applicable, so this embodiment establishes a new mapping unit for application to the isogeometric analysis of such a model. The idea of ​​the mapping unit uses the same parameter space, the solution approximation space is discretized by the basis function of the embedding entity, and the geometric model is discretized by the basis function of the mapping entity. In this case, the theory of the kinematics of the shell unit is not changed, but the shell unit formula based on the MNFFD method is different from the conventional NURBS-based shell unit formula in that the mapping-based entity needs to re-derive all physical quantities related to the geometric parameters. Figure 4 shows the process of solving the mapping shell unit formula, in which different form functions are used for geometric parametric and solution approximation, respectively.

[0031] The geometric model of the mapping shell unit is established based on the mapping surface in the 3D-NFFD modeling method. The principle is that the embedded surface is embedded into the parameter space of the NURBS entity, and the mapping transformation relationship of the NURBS entity is used to finally obtain the mapping surface. The embedded surface is defined as follows: JPEG2025511421000022.jpg11170Mapping In the degenerate shell unit formula, an embedding surface is used to discretize the solution approximation. The embedding surface maps to the physical space of the NURBS entity. According to the mapping transformation relationship of 3D-NFFD, the mapping surface is defined as follows: JPEG2025511421000023.jpg11170 The mapping shell unit coordinate vectors are: JPEG2025511421000024.jpg27170JPEG2025511421000025.jpg25170JPEG2025511421000026.jpg31170JPEG2025511421000027.jpg25170JPEG2025511421000028.jpg24170JPEG2025511421000029.jpg22170For the mapped degenerate beam unit, the mapping curve in the MNFFD framework includes a single mapping curve and a double mapping curve, which can be used to represent the trimming curve and the streak in the combined thin-walled element structure. The three-dimensional beam unit adopting the explicit spline curve is improved into a NURBS-based streak unit, the original explicit curve is replaced with the mapping curve, and the mapping streak unit is derived from the classical NURBS-based streak unit.

[0032] The single mapping sinew unit is introduced below, and the definition of the single mapping curve is referred to step 101. The most important thing for the single mapping sinew unit is the direction vector in the local coordinate system of the mapping curve, which directly determines the attribute of the sinew cross section. Figure 5 shows the local direction vectors of the mapping sinew and the skin surface. Generally, the height direction of the sinew coincides with the normal direction of the skin and is defined as follows: JPEG2025511421000030.jpg39170JPEG2025511421000031.jpg21170JPEG2025511421000032.jpg34170JPEG2025511421000033.jpg27170JPEG2025511421000034.jpg15170The partial derivatives with respect to the parameter coordinates are: Based on the previous formula, the direction vector of the width of the muscle unit is: JPEG2025511421000036.jpg18170JPEG2025511421000037.jpg13170JPEG2025511421000038.jpg22170JPEG2025511421000039.jpg28170

[0033] The unique feature of the mapping muscle unit is that the coupling between the muscle curve and the skin surface can be realized naturally, without the need to project the curve into the parameter space of the surface or add a transformation matrix. The principle of natural coupling is that the surface deformation can be automatically transferred to the mapping curve by 2D-NFFD, and the displacement vector of the single mapping 6-DOF degenerate muscle unit is defined based on the control variables of the shell body and the normal direction of the shell body. JPEG2025511421000040.jpg22170JPEG2025511421000041.jpg15170It is used to resolve the displacement of the fiber cross section in the y-direction and to resolve the conflict between the kinematics of the shell body and the kinematics of the beam.

[0034] The following introduces a double-mapping muscle unit, whose structure is similar to that of the single-mapping muscle unit, and the changes include changing from single-mapping composite basis functions and derivatives to double-mapping composite basis functions and derivatives, and changing the representation format of the local coordinate system from the original single-mapping to double-mapping. And the coupling relationship between the double-mapping muscle unit and the mapping shell is still satisfied. The definition of the double-mapping curve is referred to step 102.

[0035] The local coordinate system direction of any point on the dual mapping curve is defined as follows: JPEG2025511421000042.jpg37170JPEG2025511421000043.jpg13170The process of deriving the coordinate vector is the same as that of the single mapping muscle unit, and the coordinate vector at any point of the double mapping muscle unit is expressed as follows: JPEG2025511421000044.jpg22170The displacement vector of the dual mapping 6-DOF degenerate muscle unit is defined by the control variables of the mapping shell and the normal direction of the mapping shell. The displacement vector at any point of the dual mapping muscle unit is expressed as follows: JPEG2025511421000045.jpg21170

[0036] In step 202, in the isogeometric analysis based on MNFFD, the domain decomposition method is used to establish the connection of non-coincident NURBS surface sheets, and the propagation between the solution surfaces or mapping surfaces is realized. In the present invention, the Lagrange multiplier method is used to complete the connection between the thin-walled elements. The Lagrange multiplier method ensures that the interface constraint relationship is satisfied by applying an additional field. When the grids are not coincident, this method is also called the mortar method. The mortar method does not need to introduce stable parameters into the control method, and directly introduces the Lagrange multiplier. In addition, the control variables of the 6-DOF shell unit formula are on the global coordinate system. Therefore, the non-coordinated connection of the rotation variables can be easily realized, especially for structures with torsional deformation.

[0037] In step 300, based on the MNFFD method, an integrated model of modeling-analysis-design is established which applies to the collaborative design of combined thin-walled element structural shape and reinforcement layout, and includes the following sub-steps:

[0038] In step 301, the mapping surface is an important thin-walled element in the MNFFD model, which can represent skin, rib plate and rib, and embeds the mapping surface into a three-dimensional NURBS entity, and changes the shape of the surrounding NURBS entity by moving its control points or modifying its weight value, and the object geometry of the mapping surface inside it will inherit this deformation. The detailed process is shown as follows:

[0039] Regarding the modification of the position of the control points, the shape of the control polygon of the NURBS entity can be modified easily and directly by repositioning the control points along a specified direction. Then, the shape of the NURBS entity is modified, and the deformation is directly transmitted to the mapping surface through the mapping relationship between the NURBS entity and the NURBS surface. A concrete example is shown in Figure 6 (in Figure 6, after modifying the position of one control point on the NURBS entity, the shape of the mapping surface changes synchronously according to the entity deformation). JPEG2025511421000046.jpg8170

[0040] Regarding the modification of the modification weight, in this embodiment, the weight is also used as a design variable for shape optimization. By introducing the weight coefficient, the shape control becomes more flexible. The weight can be directly understood as the attraction degree of the control point to the shape. When the weight is large, the model deforms toward the control point. When the weight is small, the model deforms in the direction away from the control point. A specific example is shown in Figure 7 (in Figure 7, after modifying the weight value of one control point in a NURBS entity, the shape of the mapping surface changes synchronously according to the entity deformation).

[0041] In step 302, the parametric design of the reinforcement layout is specifically divided into two parts: curve shape and reinforcement pitch. Among them, the reinforcement curve shape is defined using a quadratic NURBS mapping curve, and each curve is represented by the position of at least three control points. Similar NURBS curves are called a reinforcement curve family, as shown in FIG. 8 (FIG. 8 shows the parameter definition of two reinforcement curve families in the horizontal and vertical directions in the parameter space, in which each curve is represented by two control points on the boundary and one control point in the middle). In the present invention, the curve grid reinforcement is composed of two types of reinforcement curve families, which are n curves 1 (vertical) and n curves 2 (horizontal), respectively, and the start control point and the end control point are located at the relative boundary of the parameter space, and the shape control of the reinforcement curve family is realized by modifying the pitch between the three sets of control points. In addition, a geometric step function is defined to represent the pitch between the curve control points in the reinforcement curve family, and the geometric step function is defined as follows: JPEG2025511421000047.jpg22170JPEG2025511421000048.jpg11170This formula can obtain different types of non-uniform pitches, as shown in Figure 9 (Figure 9 shows the striated curve family pitches shown by the geometric step function with different parameters).By modifying the geometric step function of a set of control points, the shape, layout and quantity of the striated curve family can be controlled simultaneously.

[0042] In this embodiment, a roof model is selected as an example of shape optimization, and a collaborative design of the shell body shape and reinforcement layout is developed based on the MNFFD geometric modeling method. Figure 10 shows the initial model of the roof, in which the setting of the reinforcement curve family parameters in the roof surface parameter space is shown in Figure 10(a), and each reinforcement curve family shares three sets of control points. For the red reinforcement curve family, the pitch between the control points is: JPEG2025511421000049.jpg6170 changes, and the pitch of each set of control points is defined by one geometric step function. Due to the symmetry of the model, the pitch of the control points of the 1 / 4 model is selected as the design variable. The pitch of the intermediate control points of the red striated curve family is controlled by defining one geometric step function, JPEG2025511421000050.jpg37170The position and weight of the control points of the NURBS entity are changed to control the shape of the shell, and the 9 control points (4 red control points and 5 blue control points) at the top of the NURBS entity are set as design variables. Depending on the symmetry of the model, 1 / 4 of the model (4 red control points) needs to be set as design variables, JPEG2025511421000051.jpg27170This optimization has a total of 17 design variables, including 10 reinforcement layout design variables, 6 shell body shape optimization design variables, and 1 shell body size optimization design variable. The optimization sequence formula is defined as follows: JPEG2025511421000052.jpg76170JPEG2025511421000053.jpg14170This inequality makes it possible to avoid the striations overlapping each other.

[0043] The load type of the structure is uniform vertical (snow) load, and a collaborative optimization design of the shell body shape and the reinforcement layout is developed for the reinforced roof with the boundary condition of four boundary fixed constraints. Modeling and analysis are performed using Matlab code, and a multi-island genetic algorithm based on Isight is optimized, with the population size being 50, the number of islands being 5, and the genetic algebra being 25. Under this boundary condition, the displacement analysis result of the initial model is shown in Figure 11, where the strain energy of the initial model is 0.0124, and the extreme value of the displacement is 2.9351e-4. Figure 12 shows the optimization iteration curve of the reinforcement layout and the shell body shape, and both the strain energy and the volume converge stably. JPEG2025511421000054.jpg19170 Figure 13 shows the optimized bar-reinforced roof model. The bar shape takes the form of a non-uniform curve, and the interaction between the bar-reinforcement layout and the shell body shape can be clearly observed during the optimization iteration process. The strain energy of the optimized model is 6.71e-3, which is 45.9% lower than that of the initial model. The displacement extreme value of the optimized model is 7.1968e-5, which is 75% lower than that of the initial model. With the same quality, the collaborative optimization design effectively improves the overall stiffness of the model.

[0044] The present invention provides a MNFFD geometric modeling method for combined thin-walled element structures, which fundamentally solves the robustness problem of modeling gaps and overlaps between thin-walled elements caused by the traditional modeling method lacking accurate topology consistency, and integrates the representation forms of design models, analysis models and optimization models based on the isogeometric paradigm, providing a set of integrated novel tools for the optimization design of engineering thin-walled structures, which is expected to greatly improve the design accuracy of products and shorten the development period. The multi-layer nesting composite spline structure in MNFFD allows deformation to be transmitted between thin-walled elements, which not only realizes the geometric dimension reduction transformation from the three-dimensional design domain to the two-dimensional design domain, but also breaks through the difficulty of self-adaptive updating of the design model, and realizes the non-interference of the design domain of combined thin-walled element structures with complex assembly relationships. All of these factors make the geometric modeling of thin-walled structures based on MNFFD have more significant advantages than explicit splines and discrete grids in terms of refinement and integrated design. It is expected that this invention will become one of the main geometric modeling methods for combined thin-walled element structures in China's aerospace, marine automobile, civil engineering and construction, athletic protective equipment and other fields.

[0045] Finally, it should be noted that the above embodiments are used to describe the technical solutions of the present invention, and are not intended to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can understand that it is possible to modify the technical solutions described in the above embodiments, or to equivalently replace some or all of the technical features therein, without causing the essence of the corresponding technical solutions to depart from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. Step 100, utilizing a multi-hierarchical NURBS based free-form deformation technique MNFFD to achieve accurate geometric modeling for combined thin-walled element structures; Establishing 200 an integrated model of modeling and analysis based on the MNFFD method, which is applied to the iso-geometric analysis of the combined thin-walled element structure; Step 300 of establishing an integrated model of modeling-analysis-design based on the MNFFD method, which is applied to the collaborative design of combined thin-wall element structural shape and reinforcement layout; A method for self-adaptive geometric modeling of combined thin-walled element structures for integrated modeling-analysis-optimization, comprising:

2. The step 100 includes: The indirect characterization relationship of complex thin-walled structural modules is established using the NURBS-based free-form deformation technique NFFD, which includes the following two kinds of mapping relationships: first, embedding NURBS curves into the parameter space of NURBS surfaces; A sub-step 101 of obtaining an implicit geometric definition of the curves in the surface and the surfaces in the entity by embedding the object in the parameter space of a NURBS surface or a NURBS entity; and sub-step 102, according to the two kinds of mapping relationships mentioned in step 101, based on the original single-layer level mapping NFFD method, allow the structure to have multi-layer and composite mapping to provide a MNFFD method, establish an indirect characterization relationship of the combined thin-wall element structure module based on MNFFD, utilize the multi-layer mapping relationship of MNFFD, so that the nesting model can satisfy the assembly relationship and geometric constraints between different thin-wall elements, and finally realize the accurate geometric modeling of the combined thin-wall element structure. The self-adaptive geometric modeling method of combined thin-walled component structures for integrated modeling-analysis-optimization according to claim 1.

3. The step 200 includes: A sub-step 201 of deriving theoretical equations of a 6-DOF degenerate shell unit and a 6-DOF degenerate beam unit based on the MNFFD mapping model under an isogeometric paradigm; and sub-step 202, in the isogeometric analysis based on MNFFD, using a domain decomposition method to establish a coupling relationship between non-matching NURBS surface sheets and realize the propagation between solution surfaces or mapping surfaces. The self-adaptive geometric modeling method of combined thin-walled component structures for integrated modeling-analysis-optimization according to claim 1.

4. The self-adaptive geometric modeling method of a combined thin-walled element structure for integrated modeling-analysis-optimization according to claim 3, characterized in that in step 202, the domain decomposition method includes a penalty method, a Lagrange multiplier method and a Nitsche method.

5. In the optimization design of thin-walled structure, an integrated model of modeling-analysis-design is established based on the MNFFD method, the design space is transformed from the 3D physical space to the 2D or 3D standard parameter space, and the shape and reinforcement layout of the shell body are jointly optimized. In the shape optimization aspect of the combined thin-walled element structure, the mapping surface in the MNFFD model is used to represent the skin, rib plate, brace or other structures, the mapping surface is embedded into the 3D NURBS entity, and the shape of the surrounding NURBS entity is changed by moving its control points or modifying its weight value, and the deformation is directly transferred to the object geometry represented by the mapping surface. In the brace-reinforced layout design of the combined thin-walled element structure, the parametric design of the brace-reinforced layout specifically includes two parts: brace-curve shape optimization and brace-reinforced layout optimization, in which the brace-curve shape is defined using a quadratic NURBS mapping curve, each curve is represented by at least three control points, and step 302 includes defining a geometric step function for the pitch of the brace-curve family to indicate the pitch between each brace-curve control point. The self-adaptive geometric modeling method of combined thin-walled component structures for integrated modeling-analysis-optimization according to claim 1.

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