Shell structure design method based on fractal geometry and principal stress line distribution

Abstract

The invention discloses a shell structure design method based on fractal geometry and principal stress line distribution, and belongs to the technical field of material structure optimization. The shell structure design method based on fractal geometry and principal stress line distribution comprises the following steps: developing related design parameters according to performance and design constraints of a shell structure model, and initializing the shell structure model by using the related design parameters; and generating a principal stress line according to the corresponding load and boundary conditions of the initialized shell structure model, extracting a main load path of discrete topology of the shell structure model, and then applying the main load path to construction of a stiffening rib layout to determine the layout of stiffening ribs in the shell structure model. According to the shell structure design method based on fractal geometry and principal stress line distribution, the shell structure model with high strength and efficient material utilization rate can be designed, and the shape and layout of the structure can be optimized under different stress conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of material structure optimization, and in particular to a shell structure design method based on fractal geometry and principal stress line distribution. Background Art

[0002] Shell structures are spatial curved structures composed of curved panels or edge components. They withstand spatial forces through tension inside the curved surface, thereby achieving good structural performance. Its greatest feature is that it exhibits a high load-bearing capacity at a relatively thin shell structure thickness. For this reason, shell structures have been widely used in many engineering fields such as large-span building roofs and design. Since the first structural optimization study on shell structures in 1994, the optimization of shell structures in pursuit of better performance has attracted the strong interest of more and more researchers in the engineering and academic communities in the past two decades. In order to achieve better design results, a number of optimization studies have been conducted on shell structures. These studies mainly cover the dimensional optimization of shell structures, which aims to optimize structural performance by adjusting the dimensional parameters of the shell structure; the multi-objective optimization of shell structure parameters, which comprehensively considers multiple objectives to obtain a more balanced design solution; and the important topological optimization, which has received more attention due to its powerful ability to explore the optimal material distribution with expected performance. Early work on the use of topological optimization in the design of shell structures can be traced back to specific studies, including the optimization of internal and external contours and the consideration of design adaptability.

[0003] In the design of shell structures, the design of stiffeners is an important problem. Many studies have explored the arrangement of stiffeners, such as the use of variable base structures, bionic growth methods, B-spline parameterization methods, and other geometric design-analysis-optimization workflows. In recent years, topology optimization has been used to generate curved bars and is considered as the layout design of reinforcement in shell structures. Topology optimization based on principal stress lines (PSLs) has become a powerful tool for optimizing the layout of stiffeners in shell structures.

[0004] Porous infill structures have been widely used in many engineering fields due to their remarkable characteristics such as light weight, strong load-bearing capacity and good impact resistance. In early studies, the inverse homogenization design framework based on topology optimization has been widely explored to optimize honeycomb microstructures with relevant structural properties. Later, in order to maximize the structural performance, many researchers have devoted themselves to optimizing microcells that vary across the design domain, mainly including area infill layout, point infill design, etc. However, the computational cost of point infill optimization is extremely high, and how to effectively and efficiently develop relevant design formulas for various porous infill units has become a key issue in topology optimization. Recently, bio-inspired designs have been considered in topology optimization to achieve point infill design, such as variable periodic Voronoi (Thyssen polygons) and the growth mechanism of aquatic plants. On the other hand, the key property of self-similarity in some microcells has gradually become dominant in porous infill optimization due to high manufacturability and industrial aesthetics. In previous works, some prototypes need to be pre-defined in the optimization, in which the structural dimensions (such as thickness or volume fraction) are iteratively changed to ensure the generation of self-similarity. In the current project, the fractal geometry of several natural plants is introduced into topology optimization to generate self-similar hierarchical micro-units, and the design results can prove its effectiveness in porous filling optimization. In addition, fractal geometry can be easily integrated into CAD systems to realize feature-based parametric design models.

[0005] However, there is no widely accepted design framework in engineering, especially for thin shell structures, that can effectively integrate the optimization of reinforcement layout and porous filling elements. And although there are many studies on the design of stiffening ribs in shell structures, it is difficult to improve the material utilization rate while meeting the strength requirements of the shell structure, resulting in incomplete structural design and layout. Summary of the invention

[0006] The purpose of the present invention is to overcome the problems in the prior art and provide a shell structure design method based on fractal geometry and principal stress line distribution, which can design a shell structure model with high strength and efficient material utilization, and can optimize the shape and layout of the structure under different stress conditions.

[0007] The present invention provides a shell structure design method based on fractal geometry and principal stress line distribution, comprising the following steps:

[0008] Develop relevant design parameters according to the performance and design constraints of the shell structure model, and initialize the shell structure model using the relevant design parameters;

[0009] Generate principal stress lines according to the corresponding loads and boundary conditions of the initialized shell structure model, extract the main load paths of the discrete topology of the shell structure model, and then apply the main load paths to construct the stiffening rib layout to determine the layout of the stiffening ribs in the shell structure model;

[0010] Based on the obtained shell structure model of stiffening rib layout, the optimization is carried out, and the fractal geometry method is further applied to realize the porous filling design of the shell structure model. The distribution method is based on the principle that the stiffening rib layout part is dense and the rest is sparse.

[0011] The final output is the optimized shell structure design.

[0012] Preferably, in the process of initializing the shell structure model, the geometric shape of the shell structure model is first set according to the design requirements, and the key features of the shell structure model are described by design parameters. These design parameters include the thickness, size, curvature and boundary conditions of the shell structure model. All parameters need to comprehensively consider the mechanical properties and engineering constraints of the shell structure model. These engineering constraints include manufacturing process and material selection. These design parameters are input into the non-uniform rational B-spline model, and the initialized shell structure model is generated by numerical calculation, and node vectors are allocated in different directions in the non-uniform rational B-spline model to ensure the smoothness and adjustability of the shell structure model surface.

[0013] Preferably, in the process of generating principal stress lines and determining the layout of stiffening ribs based thereon, it is first necessary to apply corresponding load conditions and boundary conditions to the initialized shell structure model, wherein the load conditions include external forces and temperature changes, and the boundary conditions define the fixed or constrained state of the shell structure model. The numerical calculation method of finite element analysis is used to simulate the influence of load conditions and boundary conditions on the shell structure model, and the stress and deformation distribution of each point on the shell structure model is calculated to obtain a stress distribution diagram. By analyzing the stress distribution diagram, the main load path on the shell structure model is extracted, and the main load path is the principal stress line. The principal stress line is used to optimize the layout of stiffening ribs in the shell structure model.

[0014] Preferably, in the process of realizing self-similar porous filling in the shell structure model, the Thiessen polygon pattern is used as the basis of fractal geometry, and the porous units in the shell structure model are generated by the Thiessen polygon pattern.

[0015] Preferably, when outputting the optimized shell structure model design, a comprehensive analysis is performed on various parts of the shell structure model to ensure that the shell structure model has sufficient strength and stiffness under specific load conditions, and the material processing difficulty and manufacturing accuracy of the shell structure model in the actual manufacturing process need to be combined. The final output shell structure model design includes the geometry of the shell structure model, material distribution, stiffening rib layout and pore distribution.

[0016] Preferably, in the process of constructing the stiffening rib layout, the virtual strain field of the shell structure model is combined with the distribution of the principal stress lines to accurately determine the area on the shell structure model where the stiffening ribs need to be arranged.

[0017] Preferably, in the porous filling design of the shell structure model, an iterative function system is used to iteratively map the seed points to generate pore structures at different scales, and the distribution density and morphology of the pores are controlled by adjusting the number of iterations and the mapping rules. After iteration of the iterative function system, a highly self-similar and structurally stable porous shell structure model is generated.

[0018] Compared with the prior art, the present invention has the following beneficial effects: a shell structure design method based on fractal geometry and principal stress line distribution can design a shell structure model with high strength and high material utilization rate by combining fractal geometry with topological optimization guided by principal stress lines. And by utilizing the self-similarity and recursive characteristics of fractal geometry, the shape and layout of the structure can be optimized under different stress conditions, thereby effectively reducing weight and enhancing bearing capacity.

[0019] The present invention can improve the design flexibility and adjustability of porous filling structures. The present invention uses the adjustable dimension characteristics of fractal geometry to allow designers to adjust the density, stiffness and stability of porous filling materials according to engineering requirements. This flexibility enables the method to be adapted to engineering applications in different fields, such as aerospace, automobile manufacturing, etc., thereby minimizing material waste while ensuring performance.

[0020] The present invention can achieve multi-scale optimization and local and overall consistency. By combining fractal geometry with PSLs-guided topology optimization, the present invention can achieve multi-scale optimization of structural design. The layout of stiffening ribs is optimized on a macro scale, while the unit distribution is optimized on a micro scale to ensure that local stress concentration is effectively alleviated and the stability and consistency of the overall structure are maintained. This design method helps to improve the performance of shell structure models under different loads and address the limitations of traditional geometric design methods.

[0021] The present invention can improve structural strength, increase material utilization, provide multi-scale optimization solutions, enhance design flexibility, overcome the limitations of traditional geometric design, simplify the manufacturing process, etc. These advantages enable the present invention to be widely used in the design and manufacture of high-performance structures, especially in the fields of aerospace, automobiles, construction, etc., which require high strength, low weight and high material utilization. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a discrete topological design flow chart of a self-similar porous filler of a shell structure guided by a principal stress line provided by an embodiment of the present invention;

[0023] Figure 2 is a schematic diagram of a thin shell structure provided by an embodiment of the present invention;

[0024] Figure 3 It is a flow chart for generating principal stress lines for stiffening rib layout;

[0025] Figure 4 is a schematic diagram of PSLs generation provided by an embodiment of the present invention;

[0026] Figure 5 It is a display diagram of several grid patterns in fractal geometry provided by an embodiment of the present invention;

[0027] Figure 6 It is a diagram of the entire design process of the perforated shell structure under the condition of the deadweight of the free-form surface provided by the embodiment of the present invention;

[0028] Figure 7 It is a diagram of the entire design process of a satellite fairing under predefined loads and boundary conditions provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0029] The following is combined with Figure 1-Figure 7 , the specific implementation of the present invention is described in detail, but it should be understood that the protection scope of the present invention is not limited by the specific implementation. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0030] like Figure 1-Figure 7 As shown, the present invention provides a shell structure design method based on fractal geometry and principal stress line distribution, comprising the following steps:

[0031] developing relevant design parameters according to the performance and design constraints of the shell structure model, and initializing the shell structure model using the relevant design parameters;

[0032] According to the corresponding loads and boundary conditions of the shell structure model, principal stress lines (PSLs) are formed, and the main load paths of the discrete topology of the shell structure model are extracted. Then, the main load paths are applied to construct the stiffening rib layout to determine the layout of the stiffening ribs;

[0033] Using fractal geometry to achieve self-similar porous filling in shell structure models;

[0034] The final output is the optimized shell structure model design.

[0035] The working principle of the above embodiment is briefly described:

[0036] Figure 2 In the figure, (a) is the initial design domain, (b) is the multi-faceted non-uniform rational B-spline (NURBS) surface in the three-dimensional physical domain, and (c) is the multi-faceted NURBS with control points;

[0037] Figure 3 In the figure, (a) is the setup of the free-form shell surface, (b) is the generation of PSLs for the entire surface, and (c) is the extraction of the main load paths to generate the stiffener layout in the entire domain;

[0038] Figure 4 In the figure, (a) shows the type of optimal region in the Michell beam, the blue solid line and the red dashed line represent the tension rod and the compression rod, respectively, and (b) shows the generation of PSLs in the whole domain;

[0039] The following are combined Figure 6 A specific application embodiment shown and Figure 7 The present invention is described in detail with reference to the actual engineering structure of the satellite fairing shown.

[0040] First from Figure 6 Start description:

[0041] Step 1: Initialize the shell structure model using design parameters.

[0042] Define the free-form surface shell structure model: First, consider a free-form surface shell structure model and Figure 6 The basic representation of the free-form surface is shown in Figure 4. In order to adapt to the design diversity of different engineering applications, four different loading conditions will be considered in the optimization design.

[0043] Set loads and boundary conditions: Figure 6 As shown in (a), the loads and boundary conditions are given, where the displacements of the nine nodes are fixed in the three displacement directions, and the rotational displacements of the nine nodes along the z-axis are constrained. These displacement constraints ensure that the shell structure model can be fixedly supported when the load is applied.

[0044] Figure 6 The design flow chart in shows the optimization results in different steps.

[0045] Step 2: Generate principal stress lines (PSLs) to determine the layout of stiffeners.

[0046] Figure 6 (b) shows the dense distribution of principal stress lines (PSLs) in the entire domain, reflecting the transmission path in the shell structure model when the load is applied.

[0047] Discrete topology design guided by principal stress lines:

[0048] Figure 6 (c) shows the layout of the reinforcements extracted according to the principal stress lines in the shell structure model, i.e., the discrete topology design guided by the principal stress lines. The main purpose of this step is to generate structural reinforcements through the discrete topology design guided by the principal stress lines, so as to effectively bear the applied loads.

[0049] Step 3: Use fractal geometry to achieve self-similar porous filling in the shell structure model.

[0050] Figure 6 (d) shows the final filling design scheme considering fractal geometry, which realizes the generation of self-similar porous units through Voronoi tessellation. In this step, the self-similar design principle of fractal geometry is reflected in the entire structure filling.

[0051] The role of discrete topological design guided by principal stress lines: Figure 6 In (b), the dense distribution of the principal stress lines clearly reflects the path of load propagation in the shell structure model, and the main paths are extracted to obtain the discrete topology design of the shell structure model. The discrete topology design can be regarded as the layout of the stiffeners, in which the shell structure model can carry the applied load to the greatest extent. Therefore, the discrete topology design guided by the principal stress lines is a direct and efficient reinforcement generation method that helps to improve the overall performance of the structure.

[0052] Fractal geometry and porous cell design: Figure 6 In (d), the final porous filling design demonstrates the effectiveness of fractal geometry, considering the Voronoi tessellation design, in which the self-similar design principle is fully reflected in the filling distribution. The distribution resolution of the cells changes with the reinforcement layout, ensuring the reasonable distribution of cells in different sub-areas.

[0053] Advantages of comprehensive design solutions: The discrete topology design guided by principal stress lines plays an indispensable role in porous unit design. It effectively ensures that the cells can be reasonably distributed according to different compactness in the entire design field, thereby ensuring that the porous unit design can fully consider the load and boundary conditions and provide better structural performance. Compared with previous research methods that use multi-scale topology optimization and have high computational costs, this design process is simpler, more effective and more efficient to implement.

[0054] The resulting self-similar porous filling design has a unique geometry, which improves manufacturability and enables better practical engineering applications.

[0055] Step 4: Finally output the optimized design of the shell structure model.

[0056] Consider an open shell structure model with free-form surfaces. Figure 6 The basic representation of free-form surfaces is given. At the same time, in order to reflect the diversity of design and adapt to different engineering applications, four different load conditions will be considered in the optimization design of the open shell structure model.

[0057] First, if Figure 6 As shown in (a), the shell structure model is defined, where the displacements of the 9 nodes in the 3 normal directions are fixed, and the rotational displacements of the 9 nodes along the z-axis are also constrained. These displacement constraints are defined to ensure that the shell structure model is fixedly supported when the load is applied in the domain. Figure 6 The design flow chart and step-by-step optimization results are given. Figure 6 (b) represents the generation process of dense PSLs in the whole domain; Figure 6 (c) shows the extraction of stiffeners in the open shell structure model based on PSLs, i.e., the corresponding PSLs-guided discrete topology design process; Figure 6 (d) shows the final filling design process of the shell structure model after the self-similar porous unit cell generation is realized considering fractal geometry. Figure 6 The dense distribution of PSLs in (b) can clearly reflect the transmission path of the applied load in the open shell structure model in the whole domain. Figure 6 By extracting the main path in (b), the discrete topology design of the shell structure model can be obtained. We know that the discrete topology design can also be regarded as the corresponding arrangement of steel bars in the open shell structure model to bear the applied load as much as possible. Therefore, the discrete topology design guided by the principal stress line is a direct and effective method for generating reinforcement bodies of the shell structure model, which can improve the structural performance. At the same time, Figure 6 The porous filling structure in (d) also reflects the effectiveness of fractal geometry when considering the Voronoi tessellation, and the self-similar design principle can be clearly seen in the entire distribution. Figure 6 (c) shows the initial layout of the reinforcement, and the distribution resolution of the unit has also changed. Therefore, the discrete topology design guided by the principal stress line is also indispensable for the later design of the porous unit, which can effectively ensure the reasonable distribution of units with different densities in the unique sub-regions of the entire design domain, so that the design of the porous unit can fully consider the load and boundary conditions, thereby obtaining better performance.

[0058] Figure 7 The satellite fairing, an actual engineering structure shown, further verifies the engineering applicability and superior characteristics of the proposed design framework. In this numerical example, the satellite fairing is simplified to remove some details of the structural domain in order to better optimize the shell structure model while maintaining versatility. By using the method of the present invention, the shell structure model of the fairing can be effectively optimized, its compressive strength can be improved, its weight can be reduced, and its applicability in actual engineering can be improved, especially for the design requirements of high-performance aerospace structures.

[0059] The shell structure design method based on fractal geometry and principal stress line distribution of the present invention can design a shell structure model with high strength and efficient material utilization by combining fractal geometry with topological optimization guided by principal stress lines (PSLs). By utilizing the self-similarity and recursive characteristics of fractal geometry, the shape and layout of the structure can be optimized while meeting different stress conditions, thereby effectively reducing weight while enhancing the load-bearing capacity.

[0060] The present invention provides a new thin shell structure design method, the process is as follows Figure 1 As shown, the following steps are included:

[0061] (1) In the development of CAD field, NURBS (non-uniform rational B-spline) has become a classic tool for constructing structural CAD models, which can describe and capture structural boundaries with high precision and efficiency. At the same time, in structural numerical analysis, NURBS is widely used as a basis function to replace the traditional Lagrangian shape function to construct a finite space of unknown field, thereby realizing the organic combination of CAD model and CAE model and effectively eliminating numerical artifacts in the analysis process. In this method, NURBS is used to develop the geometric model of shell structure model, which is not only a promotion of B-spline method, but also broadens its application scope in geometric modeling. When constructing B-spline, this method requires a set of node vectors Ξ=[ξ1 ξ2…ξ] to be pre-defined in a certain parameter direction. n+p+1 ], the related B-spline can be expressed by the following equation:

[0062]

[0063] This method takes thin shell structures as optimization objects and has wide applicability. The notable feature of thin shell structures is that their surface curvature radius is much larger than twenty times the shell thickness, a feature that is reflected in most shell structures in the engineering field. For thin shell structures, the classic Kirchhoff-Love theory is mainly used to establish its CAE model, and its basic assumptions are as follows: ignore the transverse normal stress; assume that the cross section remains straight during deformation; there is a linear relationship between the strain field and the shell thickness; the cross section of the shell structure is always perpendicular to the mid-plane. Based on these assumptions, the displacement field in the thin shell structure can be expressed by the following equation:

[0064]

[0065] in and x represent the position vector of any point on the surface in the reference configuration and the actual configuration, respectively, θ 1 and θ 2 is the curvilinear coordinate. Since the transverse shear strain of the thin shell structure is neglected, the Green-Lagrange strain tensor of the thin shell can be expressed as:

[0066] E αβ =ε αβ +θ 3 κ αβ ;

[0067] where α and β are taken from 1 and 2 respectively, θ 3 Indicates the physical coordinate in the thickness direction. Constant ε αβ The part represents the membrane strain, κ αβ The linear part represents the bending strain. The specific contents of these two constants can be expressed by the following formula:

[0068]

[0069] The covariant basis vectors are and It can be defined as:

[0070]

[0071] The total potential energy of a thin shell structure can be obtained in a number of ways and is expressed as:

[0072] δΠ=δW int +δW ext =0;

[0073] in,

[0074]

[0075] In the formula, δΠ is virtual work, which represents the principle of virtual work of the system in equilibrium state, δW int represents the internal virtual work, δWext represents the external virtual work W int and W ext are internal work and external work respectively, n and m are membrane internal force tensor and bending internal force tensor respectively, C is the material constitutive tensor, t is the shell thickness, f q is the uniform load per unit area, f N is the axial force per unit length, u is the mid-surface point displacement of the shell defined by equation (3), and ε corresponds to the membrane strain tensor ε of the shell αβ , κ corresponds to the shell bending strain tensor κ αβ , Ω and Γ are the volume and boundary area of ​​the shell, respectively.

[0076] (2) This method also uses the same NURBS basis function as the shell structure to construct the numerical space of the displacement field. The corresponding mathematical formula of the displacement field in the thin shell structure can be expressed as:

[0077]

[0078] where u i，j represents (i, j) th The displacement of the control point, R i，j (ξ, η) represents the NURBS basis function, which is defined in formula (3). The corresponding ε and κ of the NURBS-based isogeometric shell element can be expressed by the following equations:

[0079] ε=M e u e ,κ=B e u e

[0080] where u e Represents the displacement field in a thin shell element of constant geometry. represents the membrane strain matrix. represents the bending strain matrix. The related calculation of these two terms can be expressed as:

[0081]

[0082] Where (e1, e2, e3) is a unit vector. Substituting the above derivation into the principle of virtual work, the corresponding equilibrium equation can be expressed as:

[0083] Ku=F;

[0084] The stiffness matrix K and load vector F of the thin shell structure can be calculated as:

[0085]

[0086] Where D is the elastic matrix of the material, and R is the shape function matrix constructed by NURBS basis functions.

[0087] Furthermore, the shell structure model generated by the above steps is used as a carrier, and the implementation of S2 includes:

[0088] (3) The structural topology optimization of discrete variables is applied to the shell structure model, aiming to propose a new topological design scheme for thin shell structures by introducing the concept of principal stress lines (PSLs). This method defines the topology and shape of the structure, combines the basic principle of principal stress lines, and uses a discretized form to optimize the material layout. Specifically, in this method, the structure is discretized into a network consisting of finite nodes and line elements (usually rods or beams) connecting the nodes. During the design process, by introducing principal stress lines in this network, the designer can more accurately optimize the shape and topology of the structure to meet specific performance requirements and load conditions.

[0089] This method points out that the principal stress lines in irregular shell structures have more complex geometric forms than those in beam elements. Specifically, the principal stress lines in adjacent beam elements usually present similar geometric features. For example, when the starting points of two principal stress lines are close, their end points are usually close, and these curves generally show obvious concave and convex features. Based on this feature, when classifying the principal stress lines in beam elements, when using the K nearest neighbor (KNN) algorithm, only the endpoints or midpoints need to be extracted as geometric features to effectively achieve classification.

[0090] However, in the irregular shell structure model, adjacent principal stress lines cannot maintain similar geometric features and present a more complex shape. Due to the geometric irregularity of the shell structure model, adjacent principal stress lines may have large differences, so the traditional classification method based on endpoint or midpoint geometric features cannot be effectively applied to the classification of principal stress lines in irregular shell structures. Therefore, this method further improves the classification and analysis of principal stress lines, and proposes a more accurate classification algorithm for the complex geometric features of principal stress lines in irregular shell structures to ensure accuracy and efficiency in the optimization design process.

[0091] The KNN algorithm (K nearest neighbor algorithm) determines the point closest to the test point and classifies it by majority voting. In the previous calculation step, characteristic points (endpoints or midpoints) are directly extracted from the principal stress lines and compared with the test points based on distance.

[0092] The new statistical calculation step extracts multiple characteristic points and equidistant points from the principal stress lines. It calculates their distances from the corresponding test points and classifies them according to the sum of these comparison distances. The specific calculation process is as follows Figure 3As shown in Figure 1, the figure depicts the classification of a set of principal stress lines into two classes (Class 1 and Class 2) along the new lead curve. Before classification, the designer can freely define the initial principal stress lines according to the geometric characteristics and then construct the corresponding classes. After selecting the initial principal stress lines for each class, their equidistant points should be set as test points C. i ={C i-1 , C i-2 , …, C i-n}, let i represent the index number of the class and n represent the number of equidistant points. Calculate the Euclidean distance between the initial test point of each Dist and the equidistant point T of the remaining principal stress line. Where m represents the index number T of the remaining principal stress line m ={T m-1 , T m-2 ,...T}, as shown in the following formula.

[0093]

[0094] Subsequently, these distance values ​​are added to calculate Sum_Dist and then iteratively compared with each other to obtain the minimum distance sum between each principal stress line and each Clas-i, i.e., Min_Value, as shown in the following formula.

[0095]

[0096] The value of Min_Value indicates the geometric similarity between the principal stress line and the nearest class. Once the value of Min_Value is determined, the classification is completed. The specific formula can be referred to as:

[0097] Min_Value = Min{Sum_Dist (m,1) ,Sum_Dist (m,2) ,…,Sum_Dist (m,i)};

[0098] is the index number of the class to which each principal stress line belongs, as shown in the following formula:

[0099]

[0100] Finally, the centroids of the equidistant points in each class, Centroid-n(x, y, z), are calculated as shown in the following formula, where j represents the number of principal stress lines in each class. New paths can be obtained by connecting these centroids, thus obtaining the guiding curve.

[0101]

[0102] (4) The method in (3) above proposes an implementation method of structural topology optimization technology based on principal stress lines, aiming to improve the stiffness-to-weight ratio and energy-to-weight ratio of the structure by accurately guiding the material distribution and stiffener layout. In practical engineering, especially in the fields of civil engineering and architecture, principal stress lines are widely used to determine the direction of steel bars. Especially in shell structure models, the layout of steel bars is often consistent with the direction of the maximum principal stress line. Therefore, in this method, the principal stress line is not only the basis for structural optimization, but also serves as the basis for the layout of stiffener bars (or main load rods).

[0103] In this method, the core goal of structural design is to determine a structure with the least weight that can safely carry a specific load while being firmly connected to the specified support points. To achieve this goal, this method first needs to calculate the stress distribution in a given design area to ensure that the shell structure model can maintain its integrity and stability during loading. The curve depicted along the direction of the principal stress is called the principal support line. When the truss members are subdivided, new members are usually added in the direction orthogonal to the principal support line. For any two given nodes N1 and N2 in the structure, the straight line connecting them will provide lower structural compliance than any other curve. Specifically, if the two nodes are connected by a curve instead of a straight line segment, the axial forces F1 and F2 at the two nodes will act along the tangent direction of the curve. This will cause internal strains and generate shear force F3, causing the structure to generate additional internal forces. If the connecting curve is a straight line segment, the shear force will be zero.

[0104] Therefore, when refining the structure, it is necessary not only to insert new nodes to split the existing components, but also to add new components orthogonal to the direction of the principal stress at the subdivided nodes. The role of this new component is to ensure that the shell structure model can bear the external load to the maximum extent and maintain stability during the optimization process. To this end, according to the optimality condition of the Michell structure, it is stipulated that subdivision should only occur at points with orthogonal tensile and compressive principal stresses. This is because the new components in the subdivision process must be able to effectively share the load and maintain the optimal stress state of the structure. To further characterize the virtual strain field, this method defines a virtual strain field Its mathematical expression is as follows:

[0105]

[0106] Where f represents the force in the virtual stress field, sgn is the sign function, and k is a constant coefficient. This virtual strain field defines the strain distribution in different situations, ensuring that the subdivision process meets the optimal structural design conditions, that is, the structure is subdivided only at points where the compression and tension principal stresses are orthogonal. This condition ensures the stability and optimal performance of the structure under load.

[0107] In this way, the method can effectively guide the material layout and optimize the topology and shape of the structure so that it has the minimum weight and can carry the specified load while meeting safety requirements.

[0108]

[0109] In this method, and They represent the principal related strains, and f1 and f2 represent the corresponding component forces. Figure 4 The distribution of each optimal region and its common symbol are shown. In these regions, the following characteristics can be observed:

[0110] (1) In the R region, the member extends in only one direction and all forces in this region have the same sign.

[0111] (2) In the S region, components with a force of a given sign can extend in any direction and have greater degrees of freedom.

[0112] (3) In the T region, the compression members and the tension members are orthogonal to each other. According to the optimality condition of the Michell structure, the subdivision should only occur in the T region because this is the only region that meets the orthogonality requirement of the compression and tension principal stresses.

[0113] Therefore, in this method, R + , R - , S + , S - The points in the region R and T are called + Point, R - Point, S + Point, S - Points and T-points. The division of these areas provides a theoretical basis for further optimizing the structural topology. After performing stress-strain analysis of the design domain, this method determines the type of point by calculating the component forces (f1, f2) along the main directions, and completes the classification of each point type by matching these forces with the optimal criteria listed in Formula A. This process helps to accurately identify which areas are suitable for subdivision, thereby ensuring the stability and optimal performance of the structure during the optimization process.

[0114] With this method, the structure will strictly follow the Michell optimality condition during the subdivision process and will only be subdivided in the T region that meets the orthogonality requirement. This ensures that the final designed structure can achieve the minimum weight and meet the mechanical performance requirements while carrying a specific load. Finally, through stress and related optimal region analysis, the structural topology of the local area containing the applied load and support can be understood. After the optimal region analysis, it is known that the load point is point T and the two fixed supports are points S + and point S- . Therefore, a pair of orthogonal tension members should intersect at the load point. A pair of tension members should end at the support point. For cantilevers, they should be either parallel to the free boundary or at right angles to the free boundary. In the middle, due to bending, the normal stress should vanish and the first and second principal stress lines intersect the median axis at 45°.

[0115] Furthermore, it can be seen from S2 that the above method can make the principal stress lines densely distributed in the entire thin shell domain, extract the main transfer path of the applied load, as the discrete topological design of the shell structure, and be used to determine the overall layout of the stiffening ribs (mainly load-bearing rods) in the domain to improve the structural performance. In order to maintain the manufacturability and higher aesthetics of the structure, this method introduces fractal geometry and various principles, and develops a numerical flow chart for the self-similar porous filling design in the shell structure model, in which the above-mentioned stiffening ribs determine the compactness of the layout of the porous unit in the unique local area. The main stress line structural topology optimization technology under the guidance of fractal geometry describes the model mainly including the following parts:

[0116] (5) In order to achieve effective design and optimization of porous structures, this method introduces variable period Voronoi tessellation (VPVT), which is an effective design framework that can accurately map variables to porous units. The VPVT method divides the design domain into basic units and uses frequency grid interpolation technology to assign specific frequency values ​​to the corner nodes of each grid to determine the location of the seed points. Based on these seed points, the porous structure is constructed using Voronoi tessellation. In addition, the number and overall layout of seed points can be flexibly adjusted to optimize the porous units. Figure 5 As shown, a Voronoi tessellation for generating porous cells is provided. The design domain is divided into M×N elements, called Region of Interest (ROI), also named by the frequency grid. In the grid, each corner of these elements is assigned a predefined frequency factor. The frequency factor f(x, y) at any specific point (x, y) in the design domain can be calculated by a linear interpolation process. Subsequently, the design domain that satisfies {(x, y)|x∈[0, L x ],y∈[0,L y The points in the ]} are identified as Voronoi seeds. These seed points are then used to generate VPVT cells to form the desired porous structure.

[0117] |sin(C0·2πf(x,y)x)|+|sin(C0·2πf(x,y)y)|=0;

[0118] Alternatively, the above equation can be rewritten as the following two trigonometric functions. These functions also provide equivalent mathematical representations, providing a different perspective on the relationship described by the above equation. The corresponding equations are as follows:

[0119]

[0120] In this context, represents the magnification, and f(x, y) represents the distribution of frequency factors within each "frequency grid". To analyze and calculate equation (30), it can be simplified to a one-variable cubic equation using a frequency grid based on linear interpolation. Following these steps, the VPVT bracket structure is produced, as shown in Figure 5 Throughout the optimization process, the deliberate adaptability of the lattice geometry enables the precise replication of biological structures while laying a solid foundation for improved material properties and outstanding mechanical functions.

[0121] Based on this design method, the level set function can be used to describe the topology of the complete VPVT structure. th The coordinates of the root truss rods are determined numerically and are represented as the set {(x 1，i ,y 1，i ), (x 2，i ,y 2，i )}. Based on this representation, in the specified design domain D m The material at any position (x, y) in is defined as follows:

[0122]

[0123] in,

[0124]

[0125] The region Ω is defined by φ(x) ≥ 0, representing the final topological geometry of the VPVT structure, where x = [x, y] is a coordinate vector. i corresponds to the unique ID of the truss component in the VPVT structure. th The default shape of a truss component consists of a rectangular body and two circular ends. These components are defined by the geometric function φ i，r (x, y, t), φ i，c1 (x, y, t) and φ i，c2 (x, y, t). i represents the thickness of the rectangular body and the diameter of the circular endpoints. th The center of the rectangular body of each truss component is represented by (x i，0 ,y i，0 ), and (x i，1 ,y i，1 ) and (x i，2 ,y i，2 ) represent the endpoints of the truss and the centers of the two circular areas.

[0126] Specifically, φ i，c1 (x, y, t), φi，c2 (x, y, t) and φ i，r (x, y, t) quantifies the distance from a given point to the center of each of these geometric regions. If φ i，c1 (x, y, t), φ i，c2 (x, y, t) or φ i，r If (x, y, t) is greater than zero, then the point is within a rectangular or circular region. The complete VPVT structure can be constructed by applying a Boolean merge operation to combine the rectangular and circular regions of all truss components. This merge is performed by applying a Boolean merge operation to the term φ. i This is achieved by performing a Max operation as defined in equation (32).

[0127] S302. Iterated Function Systems (IFS) are a widely used deterministic method for generating fractal objects. They consist of a set of specific contraction mappings that transform the entire object into its components. By combining these components and iteratively applying the mappings, the system converges to an invariant set representing the fractal structure

[76] . Assume S is a nonempty compact set in the metric space (X, d). The combinatorial transformation F: X → X to X can be defined as:

[0128]

[0129] Therefore, F k The kth iteration of can be expressed as:

[0130]

[0131] Where n represents the function f in equation (34) i , k is a positive integer representing the number of iterations. If k is large enough, the fractal will be represented as a highly detailed and complex model, and the fractal set will become invariant. This means that there exists a unique non-empty compact set It is invariant under F. Specifically, A satisfies the condition:

[0132] F(A)=A;

[0133] in,

[0134] This invariant set A is called the attractor of the IFS. Taking the Koch snowflake as an example, its fractal primitive is a line segment, and the construction starts from a triangular initiator. This initiator involves three transformations: I1, I2 and I3. The IFS consists of four functions: F = {f1, f2, f3, f4}. These transformations together describe the iterative process of generating the Koch snowflake. The IFS of the Koch curve is expressed as:

[0135]

[0136] where Fk (S) represents k in the initial set S th When k→∞, the system converges to the unchanged Koch curve, thus forming a characteristic fractal structure.

[0137] Through the above steps, an optimized filling configuration can be finally obtained.

[0138] The application embodiment of the present invention provides a discrete topological design and fractal geometry optimization method based on principal stress lines (PSLs), which is mainly used for the design of classic open shell structures. First, taking the open shell structure with free-form surfaces as an example, the effectiveness of the discrete topological design and fractal geometry method guided by principal stress lines in generating self-similar porous fillers is verified. By defining different loads and boundary conditions, the present invention can successfully generate several different shell structure model designs, demonstrating the superiority of the proposed framework in improving structural performance and optimizing material distribution.

[0139] The advantages and positive effects of the technical solution to be protected by the present invention are:

[0140] First, improve structural strength and material utilization. Based on the self-similarity of fractal geometry, the present invention designs a structural unit with hierarchical structure and repetitive characteristics. This self-similarity not only enhances the effect of discrete topological design guided by PSLs, but also significantly improves the performance of the structure while meeting the manufacturability.

[0141] (1) Efficient material utilization: The present invention can maximize the strength of the structure while minimizing the use of materials by combining the self-similarity of fractal geometry and topological optimization design guided by PSLs. By utilizing the characteristics of fractal geometry, the designed structure has self-similar characteristics at multiple scales, thereby reducing material waste while ensuring structural strength. By optimizing material distribution, the material utilization rate is greatly improved while maintaining the stability of the structure.

[0142] (2) Lightweight design: The present invention can achieve lightweight structure while meeting specific load requirements. In traditional design, excessive material is often used due to uneven material distribution or excessive structural strength. However, the present invention can reduce unnecessary materials, reduce the mass of the overall structure, and improve the overall stiffness and strength ratio through precise topological optimization.

[0143] Second, multi-scale optimization design. In this method, fractal geometry is combined with discrete topology design guided by PSLs to perform multi-scale optimization. Through this optimization, the stiffening rib layout of the shell structure model can be optimized at the macro scale, while the unit distribution can be optimized at the micro scale.

[0144] (1) Macro-scale layout optimization: Through PSLs-guided topology optimization, the present invention can optimize the overall layout of the shell structure model on a macro scale, reasonably configure stiffening ribs, and ensure that the shell structure model can maintain maximum stability when subjected to external loads. The macro-layout optimization of the structure not only improves the overall performance, but also effectively disperses stress concentration and improves impact resistance and deformation resistance.

[0145] (2) Optimization of micro-scale details: At the same time, the present invention combines the multi-level characteristics of fractal geometry to optimize the distribution of units at the micro-scale, so that each structural unit can be reasonably laid out according to the local stress distribution. In high-stress areas, the stability and bearing capacity of the shell structure model are ensured by increasing the grid density and refining the design.

[0146] (3) Collaborative optimization at the macro and micro levels: This design method can simultaneously optimize the structural characteristics at the macro and micro scales, and enhance the overall performance of the structure through collaborative optimization. This multi-scale design scheme can effectively balance strength and weight and improve the overall performance of the engineering structure.

[0147] Third, improving design flexibility and adjustability. In the process of generating porous filling materials, the present invention designs a plurality of adjustable fractal parameters to give full play to the unique advantages of fractal geometry.

[0148] (1) Adjustable fractal dimension: One of the core features of the present invention is the use of an adjustable fractal dimension design method, which allows designers to adjust the geometry, density, stiffness, and stability of porous filling materials according to different engineering requirements. By adjusting the fractal dimension, the porosity and distribution of the structure can be controlled, and the response characteristics of the structure under different loads can be fine-tuned.

[0149] (2) Customized design: This adjustability enables the invention to adapt to a variety of engineering needs, including aerospace, automotive manufacturing and other fields. In these fields, designers can flexibly adjust design parameters according to specific load conditions, manufacturing process requirements and performance requirements to achieve customized optimization of the structure.

[0150] (3) Adaptability to different application fields: Due to the flexibility of the design, the present invention can be widely used in various fields requiring high-strength, low-weight, and porous structures, especially those high-end engineering projects that require precise control of material distribution and mechanical properties.

[0151] Fourth, optimize local layout and reduce stress concentration. By optimizing the distribution of porous units in different areas, the local stress concentration of the structure can be alleviated, thereby improving the bearing capacity.

[0152] (1) Local stress optimization: Through PSLs-guided topology optimization, the present invention can accurately identify and optimize the areas of local stress concentration in the shell structure model. In these stress-concentrated areas, by optimizing the mesh density or adding porous units, the stress is evenly distributed, reducing the risk of local overload.

[0153] (2) Enhance local strength: Increase material thickness or use different structural unit configurations in stress concentration areas to enhance local compression and tension resistance. These local optimization designs effectively avoid plastic deformation or damage to local structures due to excessive stress.

[0154] (3) Avoiding material waste: By precisely adjusting the material distribution in local areas, the present invention can avoid excessive use of materials, making the structure more economical, while ensuring that each local area can withstand the maximum load it requires.

[0155] Fifth, overcome the limitations of traditional geometric design. The combination of topological principles and fractal geometry provides an innovative design concept for this method. Topology studies the invariant properties of shapes during continuous deformation, while fractal geometry focuses on the self-similar characteristics of irregular and fragmented shapes. By combining the two, it is possible to optimize the shell structure model while ensuring that the geometric form of the shell structure model has similarity and continuity at all scales, thereby improving the overall strength and stability of the structure.

[0156] (1) Breaking through the limitations of regular geometric shapes: Traditional design methods usually rely on regular geometric shapes (such as circles, rectangles, triangles, etc.), which may not fully realize the potential of the structure when facing complex stress fields. The present invention breaks the constraints of regular geometric shapes by introducing fractal geometry, so that the structure can have a more complex shape that is more in line with the actual stress distribution.

[0157] (2) Complex structures that better meet actual needs: The self-similar nature of fractal geometry makes the design more consistent with the complex patterns in nature. While efficiently carrying loads, different structural units can be designed according to actual load conditions. Compared with traditional designs, the structural design of the present invention has stronger adaptability and optimization.

[0158] (3) Adaptation to irregular load conditions: The combination of fractal geometry and PSLs-guided topology optimization can better adapt to irregular load distribution, especially in the case of uneven force or non-uniform material distribution, while still maintaining the efficiency and stability of the structure.

[0159] As a preferred solution, Figure 1As shown, in the process of initializing the shell structure model, the geometric shape of the shell structure model is first set according to the design requirements, and the key features of the shell structure model are described by design parameters. These design parameters include the thickness, size, curvature and boundary conditions of the shell structure model. All parameters need to comprehensively consider the mechanical properties and engineering constraints of the shell structure model. These engineering constraints include manufacturing process and material selection. These design parameters are input into the non-uniform rational B-spline model, and the initialized shell structure model is generated by numerical calculation, and the node vectors are allocated in different directions in the non-uniform rational B-spline model to ensure the smoothness and adjustability of the shell structure model surface.

[0160] In order to ensure the accuracy and efficiency of the structure, the non-uniform rational B-spline (NURBS) technology is first used to initialize the shell structure model. NURBS is a mathematical tool widely used in computer-aided design (CAD). It can accurately represent complex surfaces and curves, and is particularly suitable for modeling tasks that deal with curved free-form surfaces. Compared with traditional polynomial curves or surfaces, NURBS can control the shape of the surface more flexibly and is more accurate in representing complex geometries.

[0161] During the initialization process, the geometry of the shell structure model is first set according to the design requirements, and its key features are described by design parameters. These design parameters include the thickness, size, curvature, boundary conditions, etc. of the shell structure model. All parameters need to comprehensively consider the mechanical properties of the shell structure model and some engineering constraints (such as manufacturing process, material selection, etc.). These parameters will be input into the NURBS model, and the preliminary geometry of the shell structure model will be generated through numerical calculation.

[0162] Specifically, the position of each point in the NURBS model is controlled by a set of node vectors, and the selection of node vectors directly affects the shape of the surface. During the design process, it is also necessary to consider how to distribute these nodes in different directions of the shell structure model to ensure the smoothness and adjustability of the shell structure model surface. By initializing these design parameters, a preliminary model of the shell structure model can be obtained as the basis for subsequent optimization and improvement.

[0163] As a preferred solution, Figure 1As shown, in the process of generating principal stress lines and determining the layout of stiffening ribs based thereon, it is first necessary to apply corresponding load conditions and boundary conditions to the initialized shell structure model, the load conditions include external forces and temperature changes, the boundary conditions define the fixed or constrained state of the shell structure model, and the numerical calculation method of finite element analysis is used to simulate the influence of load conditions and boundary conditions on the shell structure model, and the stress and deformation distribution of each point on the shell structure model is calculated to obtain a stress distribution diagram, and by analyzing the stress distribution diagram, the main load path on the shell structure model is extracted, and the main load path is the principal stress line, and the principal stress line is used to optimize the stiffening rib layout in the shell structure model.

[0164] Generating principal stress lines (PSLs) and determining the layout of stiffeners based on them is a key step to improve the performance of shell structural models. PSLs are a path that can accurately reflect the stress conditions of the structure, usually distributed along the main stress transfer direction in the shell structural model. By generating PSLs, we can identify the areas with high stress in the shell structural model and the parts that need to be strengthened.

[0165] In this step, first, the corresponding load conditions and boundary conditions need to be applied according to the shell structure model. Load conditions usually include external forces, temperature changes, etc., while boundary conditions define the fixed or constrained state of the structure. Using numerical calculation methods such as finite element analysis (FEA), the influence of these load conditions and boundary conditions on the shell structure model can be simulated, and the stress and deformation distribution of each point can be calculated. Subsequently, by analyzing the stress distribution diagram, the main load paths are extracted, which are the principal stress lines (PSLs).

[0166] After PSLs are determined, they can be used to optimize the stiffening rib layout in the shell structure model. The role of stiffening ribs is to improve the stiffness and bearing capacity of the shell structure model, and a reasonable stiffening rib layout can effectively disperse stress and reduce local stress concentration. Through PSLs, the positions in the shell structure model where stiffening ribs are most needed can be intuitively determined, thereby avoiding over-design and material waste. Compared with traditional stiffening rib design methods, using PSLs to determine the stiffening rib layout is simpler and more efficient, and can more directly reflect the actual stress conditions of the shell structure model.

[0167] The design of the stiffening rib layout not only depends on PSLs, but also needs to be optimized in combination with the material distribution and manufacturing process. Through careful design, we can ensure that the shell structure model can evenly distribute stress when subjected to external loads, and improve the stability and safety of the final designed shell structure.

[0168] As a preferred solution, Figure 1As shown, in the process of realizing self-similar porous filling in the shell structure model, the Thiessen polygon pattern is used as the basis of fractal geometry, and the porous units in the shell structure model are generated through the Thiessen polygon pattern.

[0169] In order to improve the manufacturability, mechanical properties and aesthetic effects of the shell, the present invention introduces fractal geometry and Voronoi patterns to achieve porous filling. Fractal geometry is a geometric structure with self-similar and recursive properties. It can repeat the same form at different scales, thus having better structural performance and visual effects.

[0170] Specifically, the present invention uses the classic Voronoi pattern as the basis of fractal geometry, and generates porous units in the shell structure model through the Voronoi diagram. The Voronoi diagram is a geometric structure that divides a plane into multiple regions, each of which is determined by a seed point, and any point in the region is closest to its corresponding seed point. In this way, a uniform porous structure can be generated for the shell structure model, which can ensure the strength of the structure, reduce the weight, and improve the material utilization rate.

[0171] In addition, fractal geometry has the property of self-similarity, which means that even if we look at these pores at different scales, their shapes and structures will show similar patterns. In this way, the pore distribution in the shell structure model is more reasonable, which can effectively reduce the amount of material used while ensuring the structural strength.

[0172] Through the combination of fractal geometry and Voronoi patterns, not only can the mechanical properties of the shell structure model be optimized, but also the aesthetic effect of the structure can be improved, making it visually present a more refined and orderly texture.

[0173] As a preferred solution, Figure 1-Figure 5 As shown, when designing the shell structure model after outputting the optimization, a comprehensive analysis is performed on each part of the shell structure model to ensure that the shell structure model has sufficient strength and stiffness under specific load conditions, and it is necessary to combine the material processing difficulty and manufacturing accuracy of the shell structure model in the actual manufacturing process. The final output shell structure model design includes the geometry of the shell structure model, material distribution, stiffening rib layout and pore distribution.

[0174] After initializing the shell structure model, generating PSLs, and designing porous fillings, the final step is to output the optimized shell design. This process further refines the design based on the data and results from the previous steps to ensure that the structure can meet all performance requirements in actual use.

[0175] In this step, all design elements need to be combined to form a complete shell structure model. Through comprehensive analysis of each part of the shell structure model, it is ensured that it has sufficient strength and rigidity under specific load conditions. In addition, the feasibility of the actual manufacturing process needs to be considered, such as the difficulty of material processing and manufacturing accuracy.

[0176] The final output design will include the geometry of the shell structure model, material distribution, stiffening rib layout, pore distribution, etc. This design information will provide guidance for subsequent manufacturing, processing and application, and ensure that the designed shell structure model can achieve the expected performance and effect under actual conditions.

[0177] As a preferred solution, Figure 2-Figure 5 As shown, in the process of constructing the stiffening rib layout, the virtual strain field of the shell structure model is combined with the distribution of the principal stress lines to accurately determine the area on the shell structure model where the stiffening ribs need to be arranged.

[0178] Virtual strain field is a method of describing the deformation state of materials by computer simulation. Through this tool, we can accurately predict the deformation behavior of structures under different loading conditions. In the present invention, the introduction of virtual strain field makes the design process more refined, enables detailed design in stress concentration areas, and further optimizes the mechanical properties of the shell structure model.

[0179] During the design process, the virtual strain field, combined with the distribution of the principal stress lines, can accurately determine which areas require special treatment. For example, when the shell structure model is under tension, the virtual strain field can provide detailed data on local strains. Designers can use this data to reinforce areas with concentrated stress to avoid material damage due to local overload.

[0180] In this way, each part of the shell structure model can be refined and designed under optimal stress conditions, so that the overall structure not only has high bearing capacity but also ensures sufficient durability.

[0181] As a preferred solution, Figure 1 and Figure 5 As shown, in the porous filling design of the shell structure model, an iterative function system is used to iteratively map the seed points to generate pore structures at different scales, and the distribution density and morphology of the pores are controlled by adjusting the number of iterations and the mapping rules. After iteration of the iterative function system, a highly self-similar and structurally stable porous shell structure model is generated.

[0182] Iterated Function System (IFS) is a mathematical method for generating fractal structures by repeatedly applying certain mathematical mappings. IFS can generate self-similar graphs, and the complexity of the graphs can be controlled according to the number of iterations of the mapping. By introducing IFS, the present invention can realize highly complex and regular fractal structures in the design of porous filling structures.

[0183] Specifically, in the design process of the shell structure model, IFS is used to generate the details of the fractal geometry. In the porous filling design of the shell structure model, IFS can generate pore structures at different scales by iterative mapping of seed points, and control the distribution density and morphology of the pores by adjusting the number of iterations and mapping rules. Finally, the result after IFS iteration can generate a highly self-similar and structurally stable porous shell structure model.

[0184] The core advantage of this process is that designers can significantly reduce the weight of the final designed shell structure by increasing the porosity without sacrificing structural strength. At the same time, the pore structure generated by IFS can ensure the uniformity and adaptability of the pore distribution.

[0185] While the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that many changes, modifications, substitutions and variations can be made to the embodiments without departing from the principles and spirit of the invention.

Claims

1. A shell structure design method based on fractal geometry and principal stress line distribution, characterized in that: The following steps are involved: Develop relevant design parameters according to the performance and design constraints of the shell structure model, and initialize the shell structure model using the relevant design parameters; Generate principal stress lines according to the corresponding loads and boundary conditions of the initialized shell structure model, extract the main load paths of the discrete topology of the shell structure model, and then apply the main load paths to construct the stiffening rib layout to determine the layout of the stiffening ribs in the shell structure model; Based on the obtained shell structure model of stiffening rib layout, the optimization is carried out, and the fractal geometry method is further applied to realize the porous filling design of the shell structure model. The distribution method is based on the principle that the stiffening rib layout part is dense and the rest is sparse. The final output is the optimized shell structure design.

2. The shell structure design method based on fractal geometry and principal stress line distribution according to claim 1, characterized in that: In the process of initializing the shell structure model, the geometric shape of the shell structure model is first set according to the design requirements, and the key features of the shell structure model are described by design parameters. These design parameters include the thickness, size, curvature and boundary conditions of the shell structure model. All parameters need to comprehensively consider the mechanical properties and engineering constraints of the shell structure model. These engineering constraints include manufacturing process and material selection. These design parameters are input into the non-uniform rational B-spline model, and the initialized shell structure model is generated through numerical calculation. Node vectors are allocated in different directions in the non-uniform rational B-spline model to ensure the smoothness and adjustability of the shell structure model surface.

3. The shell structure design method based on fractal geometry and principal stress line distribution according to claim 2, characterized in that: In the process of generating principal stress lines and determining the layout of stiffening ribs based on them, it is first necessary to apply corresponding load conditions and boundary conditions to the initialized shell structure model. The load conditions include external forces and temperature changes. The boundary conditions define the fixed or constrained state of the shell structure model. The numerical calculation method of finite element analysis is used to simulate the influence of load conditions and boundary conditions on the shell structure model, and the stress and deformation distribution of each point on the shell structure model is calculated to obtain a stress distribution diagram. By analyzing the stress distribution diagram, the main load path on the shell structure model is extracted. The main load path is the principal stress line. The principal stress line is used to optimize the stiffening rib layout in the shell structure model.

4. The shell structure design method based on fractal geometry and principal stress line distribution according to claim 1, characterized in that: In the process of realizing self-similar porous filling in the shell structure model, the Thiessen polygon pattern is used as the basis of fractal geometry, and the porous units in the shell structure model are generated through the Thiessen polygon pattern.

5. The shell structure design method based on fractal geometry and principal stress line distribution according to claim 1, characterized in that: When outputting the optimized shell structure model design, a comprehensive analysis is performed on each part of the shell structure model to ensure that the shell structure model has sufficient strength and stiffness under specific load conditions. It is also necessary to combine the material processing difficulty and manufacturing accuracy of the shell structure model in the actual manufacturing process. The final output shell structure model design includes the geometry of the shell structure model, material distribution, stiffening rib layout, and pore distribution.

6. The shell structure design method based on fractal geometry and principal stress line distribution according to claim 1, characterized in that: In the process of constructing the stiffening rib layout, the virtual strain field of the shell structure model is combined with the distribution of the principal stress lines to accurately determine the area on the shell structure model where the stiffening ribs need to be arranged.

7. The shell structure design method based on fractal geometry and principal stress line distribution according to claim 1, characterized in that: In the porous filling design of the shell structure model, an iterative function system is used to iteratively map the seed points to generate pore structures at different scales, and the distribution density and morphology of the pores are controlled by adjusting the number of iterations and the mapping rules. After iteration of the iterative function system, a highly self-similar and structurally stable porous shell structure model is generated.

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