Adaptive geometric modeling method for composite thin-walled component structures for integrated modeling-analysis-optimization

Abstract

An adaptive geometric modeling method for combined thin-walled component structures with integrated modeling-analysis-optimization. First, the free deformation technology MNFFD based on multi-level NURBS is used to realize accurate geometric modeling for combined thin-walled component structures. Secondly, a unified modeling-analysis model suitable for geometric analysis of combined thin-walled component structures is established based on the MNFFD method. Finally, a unified modeling-analysis-design model suitable for the collaborative design of the structural shape and reinforcement layout of combined thin-walled components is established based on the MNFFD method. The present invention fundamentally solves the modeling robustness problem of gaps and overlaps between thin-walled components caused by the lack of precise topological consistency in traditional modeling methods, provides a new tool for the optimal design of engineering thin-walled structures, can greatly improve product design accuracy and shorten the development cycle; the use of MNFFD can realize the geometric dimensionality reduction conversion from three-dimensional design domain to two-dimensional design domain, and breaks through the problem of adaptive updating of design models, and realizes the decoupling of design domains of combined thin-walled component structures with complex assembly relationships.

Description

Technical Field

[0001] The present invention belongs to the technical field related to structural mechanics and digital design, and more specifically, relates to an adaptive geometric modeling method for a combined thin-walled element structure oriented to integrated modeling-analysis-optimization. Background Art

[0002] Composite thin-walled element structures (composite thin-walled element structures are usually composed of two or more simple thin-walled elements, such as stiffened plate-shell structures, multi-wall structures, multi-rib structures, sandwich structures, and thin-walled lattice structures) have been widely used in various engineering fields due to their unique advantages in high specific stiffness. Structural optimization is an important tool in product design, and the development level of this technology is directly related to the load-bearing performance and lightweight of the structure. In the previous design system, modeling was performed through the CAD system and finite element analysis was performed through the CAE system. The two systems needed to exchange data through a semi-automatically constructed mesh model. For model systems with complex assembly relationships, this design process is not only inefficient, but also difficult to automate. In recent years, these problems have been solved through isogeometric analysis, making it possible to develop a large-scale seamless integrated analysis and design platform. This is because isogeometric analysis directly applies CAD interpolation models to geometric fields and physical fields, integrates modeling and analysis into a unified model, and realizes seamless integration of CAD systems and CAE systems. Although isogeometric analysis has achieved great success in many fields of science, in most cases, it is still unavailable to create complete analysis models directly from CAD systems, especially when dealing with combined thin-walled component structures commonly seen in engineering. This is mainly due to the strict limitations of NURBS modeling due to its tensor product structure. For complex models, they can only be generated through Boolean operations, which means that complex models usually require a large number of NURBS slices, and a large number of trimming curves are used inside the NURBS slices. Therefore, global discretization based on NURBS cannot be directly applied to isogeometric analysis.

[0003] At present, there are two main types of solutions, both of which aim to achieve truly automated analysis. The first type is to solve this problem from an analytical perspective. The finite element method is an extension of the classical finite element method. 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 a structured grid. This method is mainly oriented to the analysis of three-dimensional structures and avoids the reparameterization 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 type looks at this problem from a modeling perspective. The reparameterization method can convert the trimmed B-Rep model into an untrimmed NURBS surface. Some scholars have proposed reparameterization of CAD embedding through global parameterization guided by a frame field. The obtained geometry can be used for design and analysis without further mesh and geometry processing. By reconstructing the untrimmed NURBS model, the application of IGA in complex engineering objects is simpler 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, only one analysis is needed from the geometric model to the analysis model, but in the design optimization workflow, the geometric model needs to be changed according to the design variables, and the analysis program needs to be repeatedly called within the structural optimization framework. The control of the geometric model and the structural analysis need to be automated. Multi-level reinforced thin-walled structures can be regarded as a type of assembly structure, and there is a strict assembly relationship between thin-walled components. In the design process of reinforced structures, when the shape is modified, how to ensure the original assembly relationship is a difficult point. Under the isogeometric optimization paradigm, the control point positions of NURBS curves, surfaces, and bodies are often used as design variables. Shape control can be achieved through a small number of design variables, which also brings a series of problems. When the control points are moved, the original assembly relationship between thin-walled components will be destroyed. In short, for the design analysis and optimization workflow, not only a model suitable for analysis is needed, but also a model suitable for optimization. To this end, some scholars have proposed an interactive isogeometric modeling and analysis platform based on parametric design, as well as an implicit modeling paradigm. Implicit modeling is a method of expressing trimming. The display range is defined by curves in the parameter domain of the NURBS surface. It can be understood as a mapping relationship from the two-dimensional parameter domain to the three-dimensional physical domain.

[0005] Another method that adopts the same idea is free-form deformation technology (FFD), whose basic idea is to embed objects into parametric entities. When the parametric entity is deformed, the deformation will be transferred to the embedded object. This ensures that the original assembly relationship remains unchanged when deformation occurs. Compared with the classic FFD algorithm, 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, there is only one mapping relationship between FFD and NFFD. For complex engineering thin-walled structures, it is often necessary to nest multiple layers of thin-walled components. For this reason, we propose a multi-level NFFD method, namely the MNFFD method, to achieve integrated geometric modeling of combined thin-walled component structures. Summary of the invention

[0006] The present invention mainly solves the technical problems of poor accuracy of structural modeling and analysis and low optimization efficiency of combined thin-walled components in the prior art. In the previous design system, the CAD and CAE systems need to exchange data through a semi-automatically constructed mesh model. For model systems with complex assembly relationships, this design process is not only inefficient, but also difficult to automate. In addition, the existing B-rep modeling method uses a large number of trimmed surfaces, which seriously affects the geometric accuracy and watertightness of the model. In response to the above problems, the present invention proposes a geometric modeling method for the integration of modeling, analysis and optimization of combined thin-walled component structures, which realizes the integrated geometric modeling of combined thin-walled component structures, so as to improve the accuracy of structural modeling of combined thin-walled components, enhance the computational efficiency and accuracy of analysis and design, and shorten the product design cycle.

[0007] In order to achieve the above object, the technical solution of the present invention is:

[0008] An adaptive geometric modeling method for a combined thin-walled component structure for integrated modeling, analysis and optimization, comprising the following steps:

[0009] Step 100: Using a multi-level NURBS-based free-form deformation technique (MNFFD), accurate geometric modeling of the combined thin-walled component structure is achieved, including the following sub-steps:

[0010] Step 101: Use NURBS-based free-form deformation technology (NFFD) to establish implicit representation relationships of complex thin-walled structural components. Specifically, it includes the following two mapping relationships: First, embed the NURBS curve into the parameter space of the NURBS surface, that is, from the 2D parameter space R 2 (ξ 1 ,ξ 2 ) to 3D physical space R 3(x, y, z); secondly, embed the NURBS surface into the parameter space of the NURBS entity, that is, from the 3D parameter space R 3 (ξ 1 ,ξ 2 ,ξ 3 ) to 3D physical space R 3 (x,y,z) mapping. The implicit geometric definition of curves on surfaces and surfaces in solids is obtained by embedding objects into the parameter space of NURBS surfaces or NURBS solids.

[0011] Step 102: Based on the two types of mapping relationships mentioned in step 101, on the basis of the original single-level mapping NFFD method, multi-layer and composite mapping is allowed for the structure and the MNFFD method is proposed to establish an implicit representation relationship of the combined thin-walled component structure components based on MNFFD. By using the multi-level mapping relationship of MNFFD, the nested model can meet the assembly relationship and geometric constraints between different thin-walled components, and finally realize the accurate geometric modeling of the combined thin-walled component structure.

[0012] Step 200: Based on the MNFFD method, a unified model for modeling and analysis suitable for geometric analysis of combined thin-walled component structures is established, including the following sub-steps:

[0013] Step 201: Derive theoretical formulas of 6-DOF degenerate shell elements and 6-DOF degenerate beam elements based on the MNFFD mapping model based on the isogeometric paradigm.

[0014] Step 202: In the MNFFD-based isogeometric analysis, the coupling relationship of non-uniform NURBS surface patches is established using the domain decomposition method to achieve the propagation of solutions between surfaces or mapped surfaces.

[0015] Step 300: Based on the MNFFD method, a unified modeling-analysis-design model suitable for the collaborative design of the structural shape and reinforcement layout of the combined thin-walled element is established, including the following sub-steps:

[0016] Step 301: In the optimization design of thin-walled structures, based on the MNFFD method, a modeling-analysis-design integrated model is established to convert the design space from a three-dimensional physical space into a two-dimensional or three-dimensional standard parameter space to perform collaborative optimization of the shell shape and reinforcement layout. In terms of shape optimization of combined thin-walled component structures, the mapping surface in the MNFFD model is used to represent the skin, ribs, ribs or other structures, and the mapping surface is embedded in the three-dimensional NURBS entity. The shape of the surrounding NURBS entity is changed by moving its control points or modifying the weight value, and the deformation is directly transferred to the object geometry represented by the mapping surface.

[0017] Step 302: In the reinforcement layout design of the combined thin-walled element structure, the parametric design of the reinforcement layout can be specifically divided into two parts: rib curve shape optimization and reinforcement layout optimization. The shape of the rib curve is defined by a quadratic NURBS mapping curve, each curve is represented by at least three control points, and the spacing of the rib curve family is represented by defining a geometric series function to represent the spacing between the control points of each rib curve.

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

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

[0020] The present invention proposes a MNFFD geometric modeling method suitable for combined thin-walled component structures, which fundamentally solves the modeling robustness problem of gaps and overlaps between thin-walled components caused by the lack of precise topological consistency in traditional modeling methods, and unifies the expression forms of design models, analysis models and optimization models based on the isogeometric paradigm, providing a set of integrated new tools for the optimization design of engineering thin-walled structures, which is expected to greatly improve product design accuracy and shorten the development cycle. The multi-layer nested composite spline structure in MNFFD allows deformation to be transmitted between thin-walled components, which not only realizes the geometric dimensionality reduction transformation from the three-dimensional design domain to the two-dimensional design domain, but also breaks through the problem of adaptive updating of the design model, and realizes the decoupling of the design domain of combined thin-walled component structures with complex assembly relationships.

[0021] The present invention firstly uses NURBS-based free deformation technology (NFFD) to establish an implicit representation relationship of complex thin-walled structural components, and obtains the implicit geometric definition of curves on the surface and surfaces in the solid by embedding the object into the NURBS surface or NURBS solid parameter space. Next, based on the original single-level mapping NFFD method, multi-layer and composite mapping of the structure is allowed, and an MNFFD implicit modeling method suitable for reinforced thin-walled structures with multi-layer assembly relationships is proposed. The implicit modeling method can effectively avoid the problem of watertightness, which is conducive to improving the modeling and analysis accuracy based on the MNFFD model. And by using the multi-level mapping relationship of MNFFD, the nested model can automatically meet the assembly relationship and geometric constraints between different thin-walled components, and finally realize the accurate geometric modeling of the combined thin-walled component structure. In order to realize the unified modeling of modeling and analysis, the present invention extends the MNFFD model to the isogeometric paradigm and realizes the isogeometric analysis based on MNFFD. The isogeometric analysis uses 6-DOF degenerate shell elements and 6-DOF degenerate beam elements, and a series of theoretical formulas for mapping surfaces and mapping curves are derived based on MNFFD modeling, which can simultaneously solve key problems such as multi-faceted coupling. In the design of combined thin-walled component structures, based on the MNFFD method, an integrated modeling-analysis-design model is established to convert the design space from three-dimensional physical space to two-dimensional or three-dimensional standard parameter space, simplifying the design model and reducing the difficulty of setting design variables. In addition, mapping surfaces and mapping curves, as important thin-walled elements in the MNFFD model, are very suitable for models such as combined thin-walled component structures that contain multi-level nested relationships. Mapping curves can be used to characterize ribs and trimming curves, and mapping surfaces can be used to characterize skins, ribs, and ribs. At the same time, the implicit modeling method based on MNFFD provides a coupling relationship between thin-walled components, so that deformation can be transmitted between thin-walled components, and any shape change of thin-walled components will not destroy the initial assembly relationship, which is very beneficial for model updates during the optimization design process. These factors make the thin-walled structure geometric modeling based on MNFFD have more obvious advantages in design compared with explicit splines and discrete grids. The present invention is expected to become one of the main geometric modeling methods for combined thin-walled component structures in the fields of aerospace, shipbuilding, automobile, civil engineering, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 Schematic diagram of entity definition based on 2D NFFD, where (a) is the parameter space of the embedded curve; (b) is the embedded curve embedded in the parameter space of the NURBS surface; and (c) is the mapping curve on the NURBS surface.

[0023] Figure 2Schematic diagram of entity definition based on 3D NFFD, where (a) is the parameter space of the embedded surface; (b) is the embedded surface embedded in the parameter space of the NURBS entity; and (c) is the mapped surface in the physical space of the NURBS entity.

[0024] Figure 3 The figure is a schematic diagram of the process of constructing a reinforced structure by MNFFD. Among them, (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 on the physical space of the embedded surface and the embedded surface embedded in the parameter space of the NURBS entity; (d) is the double mapping curve located on the mapping surface; (e) is the geometric model of the reinforced structure.

[0025] Figure 4 Schematic diagram for solving the mapped shell element formula.

[0026] Figure 5 Schematic diagram of mapping rib geometry information. (a) is the definition of the rib direction vector in physical space; (b) is the definition of the rib cross section.

[0027] Figure 6 A schematic diagram of controlling the shape of the mapped surface by modifying the positions of the NURBS entity control points.

[0028] Figure 7 A schematic diagram of controlling the shape of the mapped surface by modifying the weights of the NURBS entity control points.

[0029] Figure 8 Schematic diagram of the definition of two rib curve families in parameter space.

[0030] Fig. 9 Schematic diagram of using geometric series function to represent the spacing of rib curves; where (a) is the uniform definition of control points; (b) is the sparse-dense-sparse definition of control points; (c) is the dense-sparse-dense definition of control points; and (d) is the sparse-dense definition of control points.

[0031] Fig.10 The initial model of the roof: (a) is the two rib curve families defined by the embedded curves in the embedded surface parameter space. (b) is the embedded surface embedded in the NURBS entity parameter space. (c) is the mapped surface and double mapped ribs in the NURBS entity physical space. (d) is the rendered perspective view of the roof.

[0032] Fig.11 Displacement contour of the initial model with four fixed boundary constraints.

[0033] Fig.12 (a) Iterative curve for the coordinated optimization of surface shape and reinforcement layout; Fig.12 (b) Fig.12 (a) The optimized configuration and analysis results when the number of steps marked with A is 4; Fig.12 (c) Fig.12 (a) The optimized configuration and analysis results when the number of steps marked with B is 14; Fig.12 (d) Fig.12 (a) The optimized configuration and analysis results when the number of algebras at the C mark is 25.

[0034] Fig.13 The optimized reinforced roof shape and reinforcement layout; (a) is the two-dimensional embedding domain; (b) is the three-dimensional embedding domain; (c) is the structural geometry domain; (d) is the three-dimensional rendering; (e) is the substructure rendering. DETAILED DESCRIPTION

[0035] In order to make the technical problems solved by the present invention, the technical solutions adopted and the technical effects achieved clearer, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It is understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention. It should also be noted that, for the convenience of description, only the parts related to the present invention are shown in the accompanying drawings, rather than all the contents.

[0036] The geometric modeling method for integrated modeling, analysis and optimization of combined thin-walled component structures provided by an embodiment of the present invention comprises the following steps:

[0037] Step 100: Using a multi-level NURBS-based free-form deformation technique (MNFFD), accurate geometric modeling of the combined thin-walled component structure is achieved, including the following sub-steps:

[0038] Step 101: Use NURBS-based free-form deformation technology (NFFD) to establish an implicit representation relationship of the complex thin-walled structure model. In this process, the NURBS curve is embedded into the parameter space of the NURBS surface, that is, from the 2D parameter space R 2 (ξ 1 ,ξ 2 ) to 3D physical space R 3 (x, y, z) mapping, such mapping relationship based on 2D-NFFD modeling method H c The definition is as follows:

[0039]

[0040] in, is the embedded curve The parameter coordinates, ξ 1 and 2are the parametric coordinates of the embedded curve on the NURBS surface, and C is the mapped curve. This is achieved by mapping from the parameter space of the NURBS surface to the physical space in the following equation. Figure 1 The expression of the embedded curve shown in (b) is:

[0041]

[0042] in, NURBS basis functions representing embedded curves; are the control points corresponding to the basis functions; Indicates the number of the control point. The mapping curve on the NURBS surface can be obtained by mapping as follows:

[0043]

[0044] in, Represents the basis function of the NURBS surface; i 1 =1, 2, ..., n 1 Represents ξ 1 Control point number in the direction; i 2 =1, 2, ..., n 2 Represents ξ 2 Control point number in the direction; are the control points corresponding to the NURBS surface basis functions.

[0045] This definition ensures that any point of the curve is on the surface, such as Figure 1 (c) The 2D-NFFD-based entity is a composite form of the NURBS entity, and its mapping function is a composite form of the NURBS basis function. In addition, the NURBS surface is embedded into the parameter space of the NURBS entity, that is, from the 3D parameter space R 3 (ξ 1 ,ξ 2 ,ξ 3 ) to 3D physical space R 3 The basic principle of this type of 3D-NFFD modeling method is the same as that of the 2D-NFFD modeling method. s The definition is as follows:

[0046]

[0047] in, and Is an embedded surface Parameter coordinates of ξ 1 ,ξ 2 and 3are the parametric coordinates of the embedded surface in the NURBS entity; S is the mapped surface. The surface is embedded in the parameter space of the NURBS entity, such as Figure 2 The following is an example of a surface to introduce the solid modeling principle based on 3D NFFD. The definition of embedded surface is:

[0048]

[0049] in, Represents the NURBS basis function of the embedded surface; is the control point corresponding to the basis function; i 1 =1, 2, ..., n 1 express Control point number in the direction; i 2 =1, 2, ..., n 2 express The embedded surface is embedded into the parameter space of the NURBS entity and mapped from the 3D parameter space to the 3D physical space through the NURBS entity basis function. The definition of the mapped surface is:

[0050]

[0051] in, represents the basis functions of the embedded surface; Represents the basis functions of NURBS entities; and Indicates the control point number in the two parameter directions of the embedded surface; i 1 =1, 2, ..., n 1 ,i 2 =1, 2, ..., n 2 and i 3 =1, 2, ..., n 3 Indicates the control point numbers in the three parameter directions of the NURBS entity; are the control points corresponding to the embedded surface basis functions; are the control points corresponding to the basis functions of the NURBS solid.

[0052] Step 102: Based on the two types of mapping relationships mentioned in step 101, on the basis of the original single-layer mapping NFFD method, the structure is allowed to have multi-layer and composite mapping and the MNFFD method is proposed to establish an implicit representation relationship of the combined thin-walled component structure model based on MNFFD. The entities based on 2D-NFFD and 3D-NFFD are only single-time mappings. On this basis, the two types of mappings (H c &H s ), and establish a multi-level NFFD method. Define a double mapping H m :

[0053]

[0054] in, is the embedded curve Parameter coordinates of and is the parameter coordinate of the embedded curve on the embedded surface; ξ 1 ,ξ 2 and 3 are the parametric coordinates of the embedded curve in the NURBS entity; is the embedded curve, is located on the embedded surface The mapping curve in the physical space, C is the double mapping curve located on the mapping surface S. The double mapping curve is defined as:

[0055]

[0056] in, represents the basis function of the embedded curve, represents the basis functions of the embedded surface; Represents the basis functions of NURBS entities; Indicates the control point number of the embedded curve; and Indicates the control point number in the two parameter directions of the embedded surface; i 1 =1, 2, ..., n 1 ,i 2 =1, 2, ..., n 2 and i 3 =1, 2, ..., n 3 Indicates the control point numbers in the three parameter directions of the NURBS entity; are the control points corresponding to the basis functions of the embedded curve; are the control points corresponding to the embedded surface basis functions; are the control points corresponding to the NURBS solid basis functions. For example, Figure 3 A reinforced structure constructed based on the MNFFD method is shown. Figure 3 The reinforced structure shown in (e) is composed of dual mapped curves (ribs) and mapped surfaces (skin).

[0057] Step 200: Based on the MNFFD method, a unified model for modeling and analysis suitable for geometric analysis of combined thin-walled component structures is established, including the following sub-steps:

[0058] Step 201: The theoretical formulas of the 6-DOF degenerate shell element and the 6-DOF degenerate beam element based on the MNFFD mapping model are derived based on the isogeometric paradigm. For the mapped degenerate shell element, the geometric model in the physical space is implicitly defined using the mapping surface. At this point, the classical isogeometric shell element formula is no longer applicable, so this embodiment establishes a new mapping element to be applied to the isogeometric analysis of such models. The idea of ​​the mapping element is to use the same parameter space, the approximate space of the solution is discretized by the basis functions of the embedded entity, and the geometric model is discretized by the basis functions of the mapped entity. In this case, the kinematic theory of the shell element does not change, but unlike the traditional NURBS-based shell element formula, the shell element formula based on the MNFFD method needs to re-derive all physical quantities related to the geometric parameters based on the mapped entity. Figure 4 The solution process of the mapped shell element formulation is shown, where different shape functions are used for geometry parameterization and solution approximation, respectively.

[0059] The geometric model of the mapped shell element is based on the mapped 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 mapped surface. The definition of the embedded surface is:

[0060]

[0061] In the mapping degenerate shell element formula, the embedded surface is used to approximate the discrete solution. The embedded surface will be mapped to the physical space of the NURBS entity. According to the mapping transformation relationship of 3D-NFFD, the mapping surface is defined as:

[0062]

[0063] The coordinate vector of the mapped shell element is:

[0064]

[0065] in, is the normal vector of the mapped surface in the physical space of the NURBS entity; N i represents the basis function of the NURBS surface; ζ represents the parameter coordinate in the thickness direction of the shell; t represents the thickness of the shell; the three direction vectors in the local coordinates of the mapping surface Defined in terms of the derivatives of the mapped surface,

[0066]

[0067] The displacement vector is the translation displacement of the control point {u i ,v i ,w i} T and the rotation angle {αxi ,α yi ,α zi} T Defined by, each control point contains 6 control variables δ i = {u i ,v i ,w i ,α xi ,α yi ,α zi} T , are all in the global coordinate system (xyz),

[0068]

[0069] in,

[0070]

[0071] For the mapped degenerate beam element, the mapping curves under the MNFFD framework include single mapping curves and double mapping curves, which can be used to represent trimming curves and ribs in the composite thin-walled element structure. The three-dimensional beam element using explicit spline curves is improved to a NURBS-based rib element, and the original explicit curve is replaced by the mapping curve. The mapped rib element is derived from the classic NURBS-based rib element.

[0072] The following introduces the single-mapped rib element, and the definition of the single-mapped curve is shown in step 101. The most important thing for the single-mapped rib element is the direction vector of the mapping curve in the local coordinate system, which directly determines the properties of the rib section. Figure 5 The local direction vectors of the mapped ribs and skin surface are shown. In general, the height direction of the ribs is consistent with the normal direction of the skin, which is defined as follows:

[0073]

[0074] in, The direction vector representing the height direction of the rib; They represent the three directional components of the rib height direction. The main direction of the rib is the mapping curve to the parameter coordinate The derivative of

[0075]

[0076] in, The direction vector representing the main direction of the rib; They represent the directional components of the main directions of the reinforcement; P ij Represents the control points of the skin surface; is the multiple NURBS basis function of the mapping curve, writing,

[0077]

[0078] Its parameter coordinates The partial derivative of is

[0079]

[0080] According to the previous formula, the direction vector of the rib element width direction is:

[0081]

[0082] Any point on the mapped rib element The coordinate vector at is as follows:

[0083]

[0084] Among them, {x i ,y i ,z i} is the global coordinate system of the surface; e represents the offset distance from the rib midline to the shell midplane; ζ s Represents the parameter coordinate of the rib height direction; a s Indicates the height of the rib; η s b represents the parameter coordinate in the width direction of the rib; s Indicates the width of the rib; The direction vector representing the width of the rib.

[0085] The uniqueness of the mapped rib element is that it can naturally couple the rib curve with the skin surface without projecting the curve into the surface parameter space or adding a transformation matrix. The principle of natural coupling is that the surface deformation can be automatically transferred to the mapping curve through 2D-NFFD. The displacement vector of the single-mapped 6-DOF degenerate rib element is defined according to the control variables of the shell and the normal direction of the shell.

[0086]

[0087] Among them, {u i ,v i ,w i ,α xi ,α yi ,α zi} is the control variable of the shell, [l 3i ,m 3i ,n 3i ] is the normal direction component of the shell, is the coordinate transformation matrix used to eliminate the displacement of the rib section in the y direction to resolve the conflict between the shell kinematics and the beam kinematics.

[0088] The following introduces the double-mapped rib element. The construction method of this element is similar to that of the single-mapped rib element. The changes include changing the single-mapped composite basis function and derivative to the double-mapped composite basis function and derivative, and the representation of the local coordinate system is also changed from the original single mapping to the double mapping. At the same time, the coupling relationship between the double-mapped rib element and the mapped shell is still satisfied. The definition of the double-mapped curve is shown in step 102.

[0089] The local coordinate system direction of any point on the dual mapping curve is defined as follows:

[0090]

[0091] Among them, C bs represents a double-mapped rib curve; Represents the direction vector in the local coordinate system of the double-mapped rib curve. The derivation process of the coordinate vector is the same as that of the single-mapped rib unit. The coordinate vector at any point of the double-mapped rib unit is expressed as follows:

[0092]

[0093] The displacement vector of the double-mapped 6-DOF degenerate rib element is defined according to the control variables of the mapping shell and the normal direction of the mapping shell. The displacement vector at any point of the double-mapped rib element is expressed as follows:

[0094]

[0095] Step 202: In the isogeometric analysis based on MNFFD, the coupling of non-uniform NURBS surface patches is established using the regional decomposition method to achieve the propagation of solutions between surfaces or mapped surfaces. In the present invention, the Lagrange multiplier method is used to complete the connection between thin-walled elements. The Lagrange multiplier method ensures that the constraint relationship of the interface is satisfied by applying an additional field. For the case of inconsistent meshes, this method is also called the mortar method. The mortar method does not require the introduction of stability parameters in the control equation, but directly introduces the Lagrange multiplier. In addition, the control variables of the 6-DOF shell element formula are located in the global coordinate system. Therefore, the non-coordinated connection of rotational variables can be easily achieved, especially for structures with torsional deformation.

[0096] Step 300: Based on the MNFFD method, a unified modeling-analysis-design model suitable for the collaborative design of the structural shape and reinforcement layout of the combined thin-walled element is established, including the following sub-steps:

[0097] Step 301: The mapping surface is an important thin-walled element in the MNFFD model. It can represent skin, ribs and tendons. The mapping surface is embedded in the 3D NURBS entity. The shape of the surrounding NURBS entity is changed by moving its control points or modifying the weight value. The object geometry of the mapping surface inside will inherit this deformation. The detailed process is as follows:

[0098] Modify control point positioning: By repositioning the control points along the specified direction, the shape of the control polygon of the NURBS entity can be simply and directly modified. Then change the shape of the NURBS entity, and the deformation will be directly transferred to the mapped surface through the mapping relationship between the NURBS entity and the NURBS surface. Figure 6 A specific example is shown ( Figure 6 Middle: After modifying the position of a control point on a NURBS entity, the shape of the mapped surface changes synchronously with the entity deformation).

[0099]

[0100] Modify weight modification: In this embodiment, weight is also used as a design variable for shape optimization. By introducing weight coefficients, shape control becomes more flexible. Weight can be directly understood as the degree of attraction of the control point to the shape. When the weight increases, the model will deform toward the control point. When the weight decreases, the model will deform away from the control point. Figure 7 A specific example is shown ( Figure 7 Middle: After modifying the weight value of a control point on a NURBS entity, the shape of the mapped surface changes synchronously with the entity deformation).

[0101] Step 302: The parametric design of the reinforcement layout is specifically divided into two parts: the curve shape and the rib spacing. The rib curve shape is defined by using a quadratic NURBS mapping curve, each curve is represented by the positions of at least three control points, and a group of similar NURBS curves is called a rib curve family, such as Figure 8 As shown ( Figure 8 Middle: The parameter definition of two rib curve families, the transverse and longitudinal, in the parameter space is shown, where each curve is represented by two control points on the boundary and one control point in the middle). In the present invention, the curved mesh reinforcement is composed of two rib curve families, namely n curves 1 (in the longitudinal direction) and n curves 2 (in the transverse direction). The starting control point and the ending control point are located on the relative boundaries of the parameter space. The shape control of the rib curve family is achieved by modifying the spacing between the three groups of control points. At the same time, a geometric series function is defined to represent the spacing between the curve control points in the rib curve family. The geometric series function is defined as:

[0102]

[0103] Where a and b are design variables, and L is the spacing L i The sum of the lengths of also represents the edge length in the parameter space, and n-1 is the number of curves in the rib curve family. This formula can be used to obtain different forms of non-uniform spacing, such as Fig. 9 As shown ( Fig. 9 Middle: Shows the spacing of the rib curve family represented by the geometric series function under different parameters). By modifying the geometric series function of a set of control points, the shape, layout and number of the rib curve family can be controlled simultaneously.

[0104] This embodiment selects a roof model as an example of shape optimization, and carries out collaborative design of shell shape and reinforcement layout based on the MNFFD geometric modeling method. Fig.10 The initial model of the roof is shown, where the parameter settings of the rib curve family in the roof surface parameter space are shown in Fig.10 (a), each rib curve family has three sets of control points. For the red rib curve family, the spacing between the control points is along Direction changes, for the blue rib curve family, the spacing between control points is along The direction changes, and the spacing of each group of control points is defined by a geometric series function. According to the symmetry of the model, the spacing of the control points of the quarter model is selected as the design variable. The spacing of the middle control points of the red rib curve family is controlled by defining a geometric series function, whose initial variable is a 11 =0, b 11 =0,n 1 = 3. The spacing of the boundary control points is controlled by defining another geometric series function with the initial variable a 12 =0, b 12 =0,n 1 =3. The blue rib curve family uses the same method to define two geometric series functions, which control the intermediate control points and the boundary control points respectively. The initial variable is a 21 =0, b 21 =0,n 2 =6 and a 22 =0, b 22 =0,n 2 =6. During the optimization process, the cross-sectional parameters of the ribs remain unchanged: a s =0.15, b s =0.03 and e=a s / 2. The shape of the shell is controlled by changing the position and weight of the NURBS entity control points, where the nine control points on the top of the NURBS entity (four red control points and five blue control points) are set as design variables. Due to the symmetry of the model, only one quarter of the model (four red control points) need to be set as design variables, including the z-direction coordinate and weight (s1 =8,w 1 =1) and the z-coordinate and weight of control point 2 (s 2 =8,w 2 =1), the z-coordinate of control point 3 (s 3 =8) and the z-coordinate of control point 4 (s 4 =8), the coordinates and weights of the other five blue control points are changed synchronously according to the symmetry. The thickness of the shell (t = 0.05) is also used as a design variable. There are a total of 17 design variables in this optimization, including 10 reinforcement layout design variables, 6 shell shape optimization design variables and 1 shell size optimization design variable. The optimization formula is defined as follows:

[0105] find x s =[a 11 ,b 11 ,a 12 ,b 12 ,n 1 ,a 21 ,b 21 ,a 22 ,b 22 ,n 2 ,s 1 ,s 2 ,s 3 ,s 4 ,w 1 ,w 2 ,t]

[0106]

[0107] stV(x s )-V 0 ≤0,

[0108] min(L i )-2b s ≥0,

[0109] -1≤a 11 ,b 11 ,a 12 ,b 12 ,a 21 ,b 21 ,a 22 ,b 22 ≤1,

[0110] 2≤n 1 ≤5

[0111] 4≤n 2 ≤11

[0112] -8≤s 1 ,s2 ≤16

[0113] 1≤s 3 ,s 4 ≤16

[0114] 1≤w 1 ,w 2 ≤3

[0115] Where f(·) is the structural strain energy, V(·) is the volume of the current model, and V 0 =5.236 is the volume of the initial model, min(L i ) is the minimum value of all spacings. This inequality can prevent the ribs from overlapping each other.

[0116] The load form of the structure is a uniform vertical (snow) load. The shell shape and reinforcement layout of the reinforced roof are optimized under the boundary conditions of four fixed constraints. Matlab code is used for modeling and analysis. The optimization adopts the multi-island genetic algorithm based on Isight, with a population size of 50, 5 islands, and 25 genetic generations. Under this boundary condition, the displacement analysis results of the initial model are shown in Fig.11 , the strain energy of the initial model is 0.0124, and the extreme value of the displacement is 2.9351e-4. Fig.12 The optimization iteration curves of the reinforcement layout and shell shape are shown, and both the strain energy and volume converge stably. The optimal design variables are: a 11 =0.188, b 11 =0.403, a 12 =0.719, b 12 =0.210, n 1 =2, a 21 =0.740, b 21 =0.162, a 22 =-0.424, b 22 =-1,n 2 =10,s 1 =4.419,s 2 =5.679,s 3 =7.830,s 4 =13.309,w 1 =1.203,w 2 =1.770, t=0.05. Fig.13The optimized reinforced roof model is shown. The shape of the reinforcement strips is in the form of a non-uniform curve. The interaction between the reinforcement layout and the shell 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. Under the same mass, the overall stiffness of the model is effectively improved through collaborative optimization design.

[0117] The present invention proposes a MNFFD geometric modeling method suitable for combined thin-walled element structures, which fundamentally solves the modeling robustness problem of gaps and overlaps between thin-walled elements caused by the lack of precise topological consistency in traditional modeling methods, and unifies the expression forms of design models, analysis models and optimization models based on the isogeometric paradigm, providing a set of integrated new tools for the optimization design of engineering thin-walled structures, which is expected to greatly improve product design accuracy and shorten the development cycle. The multi-layer nested composite spline structure in MNFFD allows deformation to be transmitted between thin-walled elements, which not only realizes the geometric dimensionality reduction transformation from the three-dimensional design domain to the two-dimensional design domain, but also breaks through the problem of adaptive updating of the design model, and realizes the decoupling of the design domain of combined thin-walled element structures with complex assembly relationships. These factors make the MNFFD-based thin-walled structure geometric modeling have more obvious advantages in terms of refinement and integrated design compared with explicit splines and discrete grids. The present invention is expected to become one of the main geometric modeling methods for combined thin-walled element structures in the fields of aerospace, shipbuilding, automobiles, civil engineering, and sports protective gear in my country.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that modifying the technical solutions described in the aforementioned embodiments, or replacing part or all of the technical features therein by equivalents, does not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An adaptive geometric modeling method for composite thin-walled component structures for integrated modeling, analysis and optimization. It is characterized in that The following steps are involved: Step 100: Using the multi-level NURBS-based free-form deformation technology MNFFD to achieve accurate geometric modeling of the combined thin-walled component structure; Step 200: Based on the MNFFD method, a unified modeling-analysis model suitable for geometric analysis of combined thin-walled component structures is established; Step 300: Based on the MNFFD method, a unified modeling-analysis-design model suitable for the collaborative design of the structural shape and reinforcement layout of the combined thin-walled element is established; The step 100 includes the following sub-steps: Step 101: Use NURBS-based free deformation technology NFFD to establish implicit representation relationships of complex thin-walled structural components, including the following two mapping relationships: First, embed the NURBS curve into the parameter space of the NURBS surface, that is, from the 2D parameter space R 2 (ξ 1 ,ξ 2 ) to 3D physical space R 3 (x, y, z); secondly, embed the NURBS surface into the parameter space of the NURBS entity, that is, from the 3D parameter space R 3 (ξ 1 ,ξ 2 ,ξ 3 ) to 3D physical space R 3 (x, y, z) mapping; Obtain implicit geometric definitions of curves on surfaces and surfaces in solids by embedding objects into NURBS surface or NURBS solid parameter space; Step 102: Based on the two types of mapping relationships mentioned in step 101, on the basis of the original single-level mapping NFFD method, multi-layer and composite mapping of the structure is allowed and the MNFFD method is proposed to establish an implicit representation relationship of the combined thin-walled component structure components based on MNFFD; using the multi-level mapping relationship of MNFFD, the nested model can meet the assembly relationship and geometric constraints between different thin-walled components, and finally realize the accurate geometric modeling of the combined thin-walled component structure; The step 200 includes the following sub-steps: Step 201: deriving theoretical formulas of a 6-DOF degenerate shell element and a 6-DOF degenerate beam element based on the MNFFD mapping model based on the isogeometric paradigm; Step 202: In the MNFFD-based isogeometric analysis, the coupling relationship of non-uniform NURBS surface patches is established using the domain decomposition method to achieve the propagation of solutions between surfaces or mapped surfaces.

2. According to claim 1, a method for adaptive geometric modeling of a combined thin-walled component structure for integrated modeling, analysis and optimization, It is characterized in that In step 202, the regional decomposition method includes a penalty method, a Lagrange multiplier method, and a Nitsche method.

3. According to the method of claim 1, the method is an adaptive geometric modeling method for composite thin-walled component structure for integrated modeling, analysis and optimization. It is characterized in that The step 300 includes the following sub-steps: Step 301: In the optimization design of thin-walled structures, based on the MNFFD method, a modeling-analysis-design integrated model is established to convert the design space from a three-dimensional physical space into a two-dimensional or three-dimensional standard parameter space, and to perform collaborative optimization of the shell shape and reinforcement layout; in terms of shape optimization of combined thin-walled element structures, the mapping surface in the MNFFD model is used to represent the skin, ribs, ribs or other structures, and the mapping surface is embedded in the three-dimensional NURBS entity. The shape of the surrounding NURBS entity is changed by moving its control points or modifying the weight value, and the deformation is directly transferred to the object geometry represented by the mapping surface; Step 302: In the reinforcement layout design of the combined thin-walled element structure, the parametric design of the reinforcement layout includes two parts: rib curve shape optimization and reinforcement layout optimization; wherein the shape of the rib curve is defined using a quadratic NURBS mapping curve, each curve is represented by at least three control points, and for the spacing of the rib curve family, a geometric series function is defined to represent the spacing between the control points of each rib curve.

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