Parameterization polymorphic design system and method for explicit wall thickness and non-closed cavity of thin-wall porous structure

Abstract

The invention discloses an explicit wall thickness and non-closed cavity parameterized polymorphic design system and method for a thin-wall porous structure, and belongs to the field of computer aided design. The parameterized design system comprises a thin-wall porous structure for explicitly controlling the wall thickness, an implicit design module continuously spliced by the thin-wall porous structure, a sealing property attribute analysis module of a spliced structure, and an unclosed cavity automatic optimization module of spliced structure design parameters. The implicit design module is responsible for function representation of a thin-wall porous structure with controllable wall thickness and a splicing structure of the thin-wall porous structure; the attribute analysis module realizes function expression of closure so as to evaluate whether the spliced thin-wall porous structure has a closed cavity or not; and the automatic optimization module optimizes the design parameters of the spliced thin-wall porous structure represented by the function according to the closed attribute numerical calculation result, so as to avoid the generation of a closed cavity in the porous structure. According to the system, diversified, controllable and efficient optimization design of continuous splicing, explicit control of the wall thickness and a thin-wall porous structure without a closed cavity is achieved.

Description

Technical Field

[0001] The present invention belongs to the field of computer-aided design, and relates to a parametric design system and method for explicitly controlling various characteristics in the design of thin-walled porous structures, and particularly relates to a parametric multi-modal design system and method for the explicit wall thickness and non-closed cavities of thin-walled porous structures. Background Art

[0002] There are many specific porous configurations in nature to serve the needs of organisms, thus evolving the physical and mechanical properties of thin-walled porous structure strong response materials with different morphologies. Such thin-walled porous structures can obtain excellent performance by adjusting structural parameters. With the increasing requirements for the design of ultra-high-performance and functional porous structures, the multi-morphology thin-walled porous structures formed by the fusion of diverse geometric shapes and topological configurations have greatly broadened the design space and shown great potential in significantly improving the mechanical properties of materials. In recent years, many academic papers have focused on the design of porous structures composed of multiple triply periodic minimal surfaces, and this direction has become a research hotspot. Related academic research includes: 《Design optimization of multimorphology surface-based lattice structures withdensity gradients》(2021), 《Energy Absorption Capability of Graded HybridTriply Periodic Minimal Surface Structures Based on Fracture ZoneControlling》(2024), 《Stiffness optimization design for TPMS architectedcellular materials》(2022), 《Topology Optimization Via Spatially-Varying TPMS》(2024), 《Triply periodic minimal surfaces based topology optimization for thehydrodynamic and convective heat transfer》(2024), etc. These studies demonstrate the extensive attention and in-depth exploration in this field. However, in the above multi-morphology structure splicing schemes, there are still no effective solutions to the difficult problems of explicitly controlling the thickness while ensuring continuity, especially ensuring no closed cavities, which is also the main advantage of this system. In addition, the porous structure of this system is constructed based on periodic surfaces and has the properties of periodicity and space division, so it is easy to be applied in various physical systems such as biological systems, multi-fluid heat transfer, and multi-continuous mixtures.For example, in the article "Thermal and hydraulic performance of volumetrically heated triply periodic minimal surface heaters" (2024), the application of periodic porous structures in convective heat transfer in the core of nuclear reactors is demonstrated. Summary of the Invention

[0003] The technical problem to be solved by the present invention is how to implicitly represent a thin-walled porous structure using functional methods, perform numerical analysis on its properties, and complete optimization to achieve a multi-modal design of an efficient thin-walled porous structure. Based on technologies such as computer-aided design, the present invention fully represents the thin-walled porous structure and its closed properties in a functional manner. By optimizing the explicit control of wall thickness and hole distribution, a parametric design solution for a thin-walled porous structure that is efficient, easy to expand, has a high degree of design freedom, and is convenient for manufacturing is finally realized.

[0004] The technical solution of the present invention:

[0005] A parametric multi-modal design system for a thin-walled porous structure with explicit wall thickness and no closed cavity, comprising a thin-walled porous structure with explicit wall thickness control and its continuously spliced implicit design module, a closed property analysis module for the spliced structure, and a cavity-free automatic optimization module for the design parameters of the spliced structure;

[0006] (1) Implicit design module

[0007] The implicit design module is used to complete the functional representation of a thin-walled porous structure based on periodic surfaces and its continuous splicing. The user specifies the parameters of the thin-walled porous structure within a fixed area, and uses the structure parameters of the splicing area as design parameters for subsequent property analysis modules and cavity-free automatic optimization modules;

[0008] Parameters of the thin-walled porous structure in the fixed area input by the user, including pore parameters that control the pore shape and distribution and wall parameters that control the thickness of the thin-walled porous structure; for the periodic surface controlled by the pore parameters, which is the mid-surface of the thin-walled porous structure, it is implicitly represented by a signed distance field function defined on the three-dimensional space coordinates, that is: the region where the function value is equal to zero is the surface, the region where the function value is less than zero is the outside of the surface, and the region where the function value is greater than zero is the inside of the surface; based on the periodic surface function, the wall parameters are added to construct a thin-walled porous structure with explicitly controlled wall thickness, which is implicitly represented by a signed distance field function, that is, the region where the function value is greater than or equal to zero belongs to the thin-walled porous structure, and the region where the function value is less than zero belongs to the outside of the structure; the parametric multi-morphology design system combines the radial basis interpolation technique and the structural implicit function, interpolates and splices the pore parameters and wall parameters in the region, outputs a continuous spliced implicit function of the thin-walled porous structure with explicitly controlled wall thickness, and obtains the explicit structural representation for downstream CAD and CAE applications by extracting the isosurface of the function;

[0009] (2) Closed property analysis module

[0010] The closed property analysis module is used to complete the discrimination of the closed property of the thin-walled porous structure with controllable wall thickness obtained by the implicit design module, obtain the value range of the wall thickness parameters of the porous thin-walled structure without closed cavities, further obtain the key point set of the thin-walled porous structure and the corresponding closed property value for each point, and then take the minimization of the closed property as the goal of the automatic optimization module, and obtain the structural design that meets the user's requirements through optimization;

[0011] After the user specifies the wall thickness value, the closed property analysis module numerically represents the closed property of the thin-walled porous structure by using the implicit function obtained by the implicit design module; the parametric multi-morphology design system numerically calculates the periodic surface distance field function to distinguish the key point set representing the local structure closure; then, by comparing the function value at the key point with the wall thickness value given by the user, the closed property value corresponding to each key point is calculated to judge whether a closed cavity is generated in the area near the key point, so as to obtain the closed performance evaluation of the entire thin-walled structure; in addition, if a closed cavity appears, the numerical result of the closed property analysis module is fed back to the cavity-free automatic optimization module to guide the parameter design optimization of the thin-walled porous structure for the goal of no closed cavity;

[0012] (3) Cavity-free automatic optimization module

[0013] The cavity-free automatic optimization module automatically optimizes the designable parameters of the spliced thin-walled porous structure with controllable wall thickness under the drive of the numerically represented closed property result obtained by the closed property analysis module according to the user's target requirements, so as to achieve the cavity-free design of the thin-walled porous structure, especially the splicing area;

[0014] The parametric multi - morphology design system establishes corresponding optimization problems according to the structural wall thickness required by users in actual applications and the need for non - enclosed cavities, including minimizing the objective function of the enclosed property; at the same time, taking hole parameters and wall parameters as design parameters, adjusting the hole shape, hole distribution, and wall thickness of the thin - walled porous structure, thereby affecting the enclosed property of the structure; then, according to the feedback obtained from the property analysis module, calculating the objective value and its gradient with respect to the design parameters; finally, using a gradient - based optimization solver to iteratively optimize and solve the parameters of the continuously spliced thin - walled structure, obtaining a thickness - controllable and cavity - free splicing design result of the thin - walled porous structure that meets the user's requirements, and the generated structure retains the characteristic of being divided into two independent spaces.

[0015] A parametric multi - morphology design method for explicit wall thickness and non - enclosed cavities of thin - walled porous structures is as follows:

[0016] Step 1: The user inputs the shape of the design area and its partition, where the partition includes a splicing area and a fixed area. The structural parameters input for the fixed area include hole parameters and wall parameters, and the structural parameters of the splicing area are initialized;

[0017] For the design area Ω, splicing area Ω g and fixed area Ω f , which satisfy Ω = Ω g ∪Ω f ; the structural parameters of the fixed area input by the user are where the subscript f represents the fixed area, n f is the number of fixed - area parameter points, γ f,i is the hole parameter, t f,i is the wall parameter, and the structural parameters remain unchanged; then, the structural parameters in the splicing area are initialized where the subscript c represents the splicing area, n c is the number of splicing - area parameter points, γ c,i and t c,i are the hole parameter and wall parameter respectively; finally, using the radial basis interpolation method, the structural parameters of any point r in the design area are obtained where is the position vector, x, y, z are the corresponding coordinates, g(·) is the radial basis interpolation function, and these two structural parameters affect the holes and thickness of the thin - walled porous structure, further affecting the enclosed property of the structure. Therefore, the optimized design parameters are determined as used for the construction of the porous structure and also for subsequent property analysis and cavity - free automatic optimization design;

[0018] Step 2: Convert the periodic surface into an implicit representation;

[0019] The periodic surface is the mid-surface of the thin-walled porous structure. For the periodic surface an implicit function representation of the structural parameter γ(r) that depends on any point r within the design region is given as follows:

[0020]

[0021] where is a periodic function that can effectively simulate the porous property, p(r) is the phase of the trigonometric function, λ represents the period of the trigonometric function, is the periodic moment; are three-dimensional basis vectors; f i,j the three-dimensional transformation matrix S in f j (j = 1, 2, 3, 4) and M i (i = 1, 2, 3) are given parameters, are the pore parameters to be interpolated in Step 1. The implicit function representation of this periodic surface satisfies: if r is outside the surface , ψ(Υ(r), r) < 0; if r is on , ψ(Υ(r), r) = 0; if r is inside S, ψ(Υ(r), r) > 0. Meanwhile, this implicit function can well approximate the common triply periodic minimal surface and can also generate complex hole shapes, which is beneficial for users to conduct more diverse structural designs. Additionally, by calculating the gradient of the implicit function, the following formula is obtained:

[0022]

[0023] where T(γ(r), r) represents the geometric distance from r to the periodic surface , and a(γ(r)) and b(γ(r)) are coefficients determined by the pore parameter γ(r). Using the relationship between the geometric distance function T(γ(r), r) and the surface function ψ(Υ(r), r), the wall thickness of the thin-walled porous structure generated by the periodic surface can be explicitly controlled, and users can conduct structural designs through the wall parameter t(r).

[0024] Step 3: Use the implicit function of the periodic surface to convert the implicit representation of the thin-walled porous structure with explicit wall thickness control;

[0025] For the thin-walled porous structure with explicit wall thickness control, based on the implicit representation of the periodic surface, two offset surfaces at distances of t(r) / 2 > 0 and -t(r) / 2 are obtained and ψ out (Υ(r), t(r), r) = -ψ in (γ(r), t(r), r), which are used as the inner wall and outer wall of the thin-walled structure respectively. Then, through Boolean calculation, the implicit function representation of the thin-walled structure is obtained as follows:

[0026]

[0027] Among them, Φ(Υ(r), t(r), r) ≥ 0 is a thin-walled porous structure with a thickness of t(r), and the wall thickness of the structure can be explicitly controlled;

[0028] Step Four: Based on the thin-walled porous structure with controllable wall thickness, convert the continuous splicing structure into an implicit function representation;

[0029] For the implicit function representation of the continuous splicing structure, combine the structure parameter function obtained by the radial basis interpolation method in Step One in the implicit function of the thin-walled porous structure with the displayed wall thickness Finally, obtain the implicit function representation of the continuous splicing structure with the design parameters as independent variables:

[0030]

[0031] Continuous splicing solid structure Obtained from the value of Φ represented by the implicit function: Indicates that r is within the solid structure i.e., the area with materials; Indicates that r is at the boundary of i.e., the boundary between the solid and the void; Indicates that r is outside

[0032] Step Five: Obtain the key point set, and perform a closed property analysis on the spliced thin-walled porous structure according to the wall parameter value T0 specified by the user;

[0033] By numerically calculating the distance field of the implicit function of the periodic surface, identify the key points for judging the closeness of the thin-walled porous structure. The set of the obtained key points is represented as where P m represents the coordinates of the m-th key point, n P is the number of key points, A3(P m ) is the Hessian matrix of the implicit function ψ(γ(r), r), represents the derivative of the determinant of A3(P m ) with respect to P m ; the minimum value of the implicit function value at all key points is where |·| represents the absolute value, and min(·) represents the minimum value within for all P mThe minimum function value obtained by taking values at [the specified point] needs to cover the wall thickness values specified by the user, i.e., satisfy T m > T0; then, based on T m When ≤ T0, a closed cavity will be generated, calculate the closed property value corresponding to the key point, and determine whether a closed cavity is generated in the local area near the key point, so as to obtain the closed performance evaluation of the entire thin-walled structure under the specified wall thickness value range.

[0034] Step 6: Establish an optimization problem model;

[0035] The user specifies the required wall thickness value T0, and through optimization, the wall thickness of the thin-walled structure satisfies T m > T0 at the key points of the structure, so as to meet the user's requirement for no closed cavity; set the goal of minimizing the closed property in the splicing area according to the requirement, and use the parameter value of the interpolation base point of the design parameter as the design variable; construct the following form of the optimization problem:

[0036]

[0037] where H(f) is the Heaviside function, which takes 1 when f ≥ 0 and 0 when f < 0;

[0038] Step 7: Calculate the parameter gradient and automatically iterate for optimization and solution;

[0039] Use an optimization solver based on the gradient method to calculate the optimal solution of the optimization problem model; first calculate the gradient information of the objective function J(γ(r), t(r), r) with respect to the design parameter and substitute it into the optimization solver GCMMA for automatic iterative optimization to obtain the design parameters of the thin-walled porous structure that meet the design requirements; after step 4, the final thin-walled porous splicing structure with controllable wall thickness and cavity-free optimization design is obtained.

[0040] Advantages of the present invention: Through the close cooperation of the above three modules, the system realizes an integrated and automated process from design to analysis and then to optimization, and finally generates a thin-walled porous structure design with controllable wall thickness, no closed cavities, and continuous splicing. The system is completely based on implicit function representation, and unique advantages are demonstrated in the design, analysis, and optimization processes. Specifically, the implicit design module implicitly represents the thin-walled porous structure and its splicing structure with a function. The pore parameters and wall parameters are used as structural design parameters at the same time, allowing users to define complex, diverse, and flexible hole shapes and distributions under a determined wall thickness, and the design result of the final spliced thin-walled porous structure can be changed by simply modifying the function parameters. The attribute analysis module based on implicit functions can write the closed attribute in the form of a computable differentiable function, and by taking the gradient of the differentiable function, quickly analyze the attributes of the thin-walled design structure after parameter adjustment, thereby improving the iterative optimization efficiency in the automatic optimization module and making the entire design process more efficient and flexible. Through the innovative technology proposed by the system, the system can not only enhance the diversity and controllability of the thin-walled porous structure design, ensure various structural characteristics, but also help save the design cycle and manufacturing cost, and promote the development of generative design. Brief Description of the Drawings

[0041] Figure 1 It is a schematic flow diagram of the system.

[0042] Figure 2 It shows a schematic structural diagram of the P porous structure under thickness change, where the light gray surface and the dark gray surface are the surfaces on both sides of the thin wall, and a spherical closed cavity appears when the thickness is 0.96L.

[0043] Figure 3 It shows a schematic diagram of the thin-walled spliced P-G porous structure without using the continuous splicing method within a design domain with a length, width, and height of 4L, L, and L respectively; where the light gray surface and the dark gray surface are the surfaces on both sides of the thin wall, (a) is the top view of the P-G porous structure; (b) is the three-dimensional view of the P-G porous structure.

[0044] Figure 4 It shows schematic diagrams of thin-walled spliced structures with thicknesses of 0.012L, 0.024L, and 0.048L respectively within a design domain with a length, width, and height of 4L, L, and L respectively, where the light gray surface and the dark gray surface are the surfaces on both sides of the thin wall; (a) continuously spliced P-G porous structure; (b) continuously spliced P-D porous structure; (c) continuously spliced P-IWP porous structure; (d) continuously spliced G-D porous structure; (e) continuously spliced G-IWP porous structure; (f) continuously spliced D-IWP porous structure. Detailed Embodiment

[0045] The following combines the technical solution and the drawings to elaborate in detail the specific implementation manner of the present invention.

[0046] A parametric multi - morphology design method for explicit wall thickness and non - enclosed cavity of thin - walled porous structures comprises the following steps:

[0047] Step 1: Implicit design module

[0048] By interpolating hole parameters to effectively and implicitly represent the splicing of different types of periodic surfaces, adding wall parameters on the basis of the spliced surface to generate a thin - walled structure represented by a continuous function, and then transmitting the function representation of the thin - walled structure to the mathematical model for closed - property analysis and optimization;

[0049] First step, radially - basis - interpolate hole parameters and wall parameters. Given the design region Ω, the splicing region Ω g and the fixed region Ω f , satisfying Ω = Ω g ∪Ω f ; within the fixed region, the structural parameters are where the subscript f represents the fixed region, n f is the number of parameter points in the fixed region, γ f,i is the hole parameter, t f,i is the wall parameter, and these structural parameters always remain unchanged; then, initialize the structural parameters in the splicing region where the subscript c represents the splicing region, n c is the number of parameter points in the splicing region, γ c,i and t c,i are the hole parameter and the wall parameter respectively; using the radially - basis - interpolation method, randomly select n = n f +n c interpolation base points in the transition region Ω to obtain the function representations of the structural parameters γ(r) and t(r) at any point r within the design region:

[0050]

[0051]

[0052] where is the position vector, x, y, and z are the corresponding coordinates, g(·) is the radially - basis - interpolation function, N i (r) is the corresponding computable coefficient function determined by the selected interpolation method, is the value of the design parameter at the interpolation base point.

[0053] Second step, implicitly represent the periodic surface. By generalizing common periodic surface functions, obtain the hole parameters in the periodic surface function that control the surface type, and realize continuous splicing by controlling the continuous change of the hole parameters of different periodic surfaces;

[0054] By generalizing common periodic surface functions, obtain the representation of the periodic surface function:

[0055]

[0056] where is the position vector, and x, y, and z are the corresponding coordinates, is the periodic moment, labeled is the three-dimensional base vector, and there are two base vectors h1 and h2, is the phase of the trigonometric function, λ represents the period of the trigonometric function, and the three-dimensional transformation matrix and are: This equation can approximate the periodic surface well and can generate complex surfaces. The parameters in the equation used to control the surface type are the periodic moment the two base vectors h1 and h2, and the phase p. After integration, the variable is represented as The parameter variables of the five common periodic surfaces are:

[0057] P: D: G: I-WP: R-RD: By rewriting the periodic surface function (1.1), obtain a new periodic surface function:

[0058]

[0059] When ψ(r) = C, the gradient of the new periodic surface function is approximately:

[0060]

[0061] Since its gradient is only related to the value ψ of the isosurface when ‖h1‖ + ‖h2‖ and λ are constant, that is, when the surface parameters are determined, the distance from each point on the isosurface ψ(r) = C to the zero isosurface ψ(r) = 0 is the same, and it can be explicitly controlled by specifying the wall thickness value t.

[0062] Step 3: Construct an implicit function representation of the wall thickness controllable structure using the periodic surface function (the mid-surface of the thin-walled porous structure), and represent the thickness of the thin-walled structure with the wall parameter, so as to obtain a functional representation of the thin-walled structure with explicitly controlled wall thickness;

[0063] Based on the pore variable Υ, add the wall parameter t to control the thickness of the thin-walled structure generated by the surface. Combining the two variables, the structural parameters of the thin-walled structure are {Υ, t}. The geometric distance (Euclidean distance) from the points on the isosurface ψ(r) = C to the zero isosurface ψ(r) = 0 can be deduced from the gradient (1.4) of the new periodic surface function, so as to obtain the relationship function between the algebraic distance C and the geometric distance T:

[0064]

[0065] After sorting, obtain the relationship function between the geometric distance T and C:

[0066]

[0067] Next, construct a periodic surface thin-walled structure with thickness t(r). Offset the new periodic function ψ(r) to the inner and outer sides respectively to obtain two offset surfaces with distances of t(r) / 2 > 0 and -t(r) / 2 and ψ out (Υ(r), t(r), r) = -ψ in (Υ(r), t(r), r) are used as the inner wall and outer wall of the thin-walled structure respectively. Then, through Boolean calculation, the implicit representation of the thin-walled structure is obtained as:

[0068]

[0069] where Φ(γ(r), t(t), r) ≥ 0 is a thin-walled porous structure with thickness t(t), and the wall thickness of the structure can be explicitly controlled;

[0070] Step 4: Through continuous interpolation of the structural parameters of different surfaces, realize the continuously controllable wall thickness splicing between multiple porous thin-walled structures.

[0071] The continuous function form of the spliced surface structure obtained from the interpolation functions (1.1)-(1.2) is as follows:

[0072]

[0073] There are many optional interpolation methods, such as polynomial interpolation, B-spline interpolation, etc. Different interpolation coefficient functions will obtain periodic surfaces with different shapes in the transition region. Figure 3 and Figure 4 respectively show the porous structure without continuous splicing and the porous structure with continuous splicing. FromFigure 3 It can be seen that the P-G porous structure without using the continuous splicing method cannot be aligned at the middle splicing point, and the inner and outer surfaces (light gray and dark gray curved surfaces) are confused, that is, the light gray and dark gray curved surfaces are connected. At the same time, Figure 4 the P-G structure in (a) in is smoothly transitioned in the middle region, and the inner and outer surfaces are always consistent, which verifies the effectiveness of the proposed continuous splicing scheme.

[0074] Our splicing method based on the periodic surface structure can ensure the continuity of the splicing structure. However, when the thickness value given by the user is inappropriate, closed cavities may be generated, as Figure 2 shown in, a spherical cavity appears when the thickness of the P structure is 0.096L. Therefore, we derived a closed property function to constrain the continuous splicing of the porous thin-walled structure.

[0075] Step 2: Attribute analysis module

[0076] A closed property analysis method based on the implicit function representation structure is proposed. This method obtains the key point set and the closed property discrimination function according to the wall parameter value T0 specified by the user.

[0077] The first step is to numerically calculate the distance field of the implicit function of the periodic surface to distinguish the key points for judging the closure of the thin-walled porous structure. The set of key points is expressed as:

[0078]

[0079] where A3(P m ) is the Hessian matrix of the implicit function ψ(γ(r), r), which is defined as follows:

[0080]

[0081] The second step is to construct a closed property discrimination function. The minimum value of the implicit function values at all key points is:

[0082]

[0083] It is necessary to satisfy T m > T0; then, according to T m ≤ T0, closed cavities will be generated, and the closed property values corresponding to the key points are calculated:

[0084]

[0085] If the value is 1, a closed cavity is generated in the local area near the key point. Therefore, the closed property value Θ iIt can be used to determine whether a closed cavity is generated in the local area near the key point, so as to obtain the evaluation of the sealing performance of the entire thin-walled structure under the condition of a specified wall thickness value.

[0086] Step 3: Automatic optimization module

[0087] An optimization design method for a wall-thickness controllable and cavity-free spliced multi-hole thin-walled structure based on a periodic surface is proposed. Based on the implicit representation of the surface structure and the expression of the closed attribute function, by establishing an optimization mathematical model, a continuous spliced structure without closed cavities and with explicit wall-thickness control is obtained.

[0088] The first step is to establish an optimization problem model for establishing a mathematical model that maximizes the connectivity J(Υ(r),r) in the transition region of the periodic surface, specifying the wall thickness value T0, and through optimization, the wall thickness of the thin-walled structure satisfies T m >T0 at the key points of the structure to meet the user's requirement for a closed-cavity-free structure; set the goal of minimizing the sealing property in the splicing area according to the requirement, and use the parameter value of the interpolation base point of the design parameter as the design variable, and the design variable is converted from the function {Υ(r),t(r)} to the function values of a finite number of interpolation points to reduce the number of variables. The following optimization problem form is constructed by this parametric design system:

[0089]

[0090] where H(f) is the Heaviside function, which takes 1 when f≥0 and 0 when f<0;

[0091] The second step is to use an optimization solver based on the gradient method to calculate the optimal solution of the optimization problem model; first calculate the gradient information of the objective function J(Υ(r),t(r),r) with respect to the design parameter and substitute it into the optimization solver GCMMA for automatic iterative optimization to obtain the design parameters of the thin-walled porous structure that meet the design requirements; through the implicit representation of the structure in Step 4, the final thin-walled porous continuous spliced structure with controllable wall thickness and no closed cavities is obtained, and the generated structure retains the characteristic of being divided into two independent spaces and can be used for the design of personalized applications such as double-fluid heat exchangers.

Claims

1. A parametric polymorphic design system for thin-walled porous structures with explicit wall thickness and no closed cavities, characterized in that: It includes an implicit design module for thin-walled porous structures with explicit control of wall thickness and their continuous splicing, a module for analyzing the closed properties of spliced ​​structures, and a module for automatic optimization of spliced ​​structure design parameters without cavities; (1) Implicit Design Module The implicit design module is used to complete the functional representation of thin-walled porous structures and their continuous splicing based on periodic surfaces. The user specifies the parameters of the thin-walled porous structure in a fixed area, and uses the structural parameters of the splicing area as design parameters for the subsequent property analysis module and cavity-free automatic optimization module. The parameters of the thin-walled porous structure of a fixed area input by the user include the hole parameters that control the shape and distribution of the holes and the wall parameters that control the thickness of the thin-walled porous structure; for the periodic surface controlled by the hole parameters as the middle surface of the thin-walled porous structure, a signed distance field function defined on the three-dimensional space coordinates is used to implicitly represent it, that is, the area where the function value is equal to zero is the surface, the function value is less than zero is the outside of the surface, and the function value is greater than zero is the inside of the surface; on the basis of the periodic surface function, the wall parameters are added to construct a thin-walled porous structure with explicit control of the wall thickness, which is implicitly represented by a signed distance field function, that is, the area where the function value is greater than and equal to zero belongs to the thin-walled porous structure, and the area less than zero belongs to the outside of the structure; the parametric polymorphic design system combines the radial basis interpolation technology with the structural implicit function, and outputs an implicit function based on the continuous splicing of the thin-walled porous structure with explicit control of the wall thickness by interpolating the hole parameters and wall parameters in the splicing area, and obtains the explicit structural representation for downstream CAD and CAE applications by extracting the isosurface of the function; (2) Closed attribute analysis module The closure property analysis module is used to determine the closure property of the thin-walled porous structure with controllable wall thickness obtained by the implicit design module, obtain the value range of the wall thickness parameter of the porous thin-walled structure without closed cavities, and further obtain the key point set of the thin-walled porous structure and the closure property value corresponding to each point, and then minimize the closure property as the goal of the automatic optimization module, and obtain the structural design that meets the user's needs through optimization; After the user specifies the wall thickness value, the closure property analysis module uses the implicit function representation obtained by the implicit design module to digitize the closure property of the thin-walled porous structure; the parametric polymorphic design system identifies the key point set that characterizes the closure of the local structure through the numerical calculation of the distance field function of the periodic surface; and then calculates the closure property value corresponding to each key point by comparing the function value at the key point with the value of the wall thickness given by the user, so as to determine whether a closed cavity is generated in the area near the key point, thereby obtaining the closure performance evaluation of the entire thin-walled structure; In addition, if closed cavities appear, the numerical results of the closed property analysis module are fed back to the cavity-free automatic optimization module to guide the parameter design optimization of the thin-walled porous structure on the target of no closed cavities; (3) Cavity-free automatic optimization module The cavity-free automatic optimization module automatically optimizes the designable parameters of the spliced ​​thin-walled porous structure with controllable wall thickness according to the user's target needs, driven by the numerical closed property results obtained by the closed property analysis module, so as to achieve the design of thin-walled porous structure, especially the splicing area, without closed cavities; The parametric polymorphic design system establishes corresponding optimization problems according to the structural wall thickness and the requirement of no closed cavity required by the user in practical applications, including minimizing the closed property objective function; at the same time, the pore parameters and wall parameters are used as design parameters to adjust the pore shape, pore distribution and wall thickness of the thin-walled porous structure, thereby affecting the closed property of the structure; Based on the feedback obtained from the property analysis module, the target value and its gradient with respect to the design parameters are calculated. Finally, the parameters of the continuously spliced ​​thin-walled structure are iteratively optimized and solved using a gradient-based optimization solver, resulting in a thin-walled porous structure with controllable thickness and cavity-free splicing that meets user needs. The generated structure retains the characteristic of being divided into two independent spaces.

2. A parametric polymorphic design method for thin-walled porous structures with explicit wall thickness and no closed cavities is performed using the parametric polymorphic design system for thin-walled porous structures with explicit wall thickness and no closed cavities as described in claim 1, characterized in that: Here are the steps: Step 1: The user inputs the shape of the design area and its partitions, the partitions include the splicing area and the fixed area, the structural parameters of the fixed area including the hole parameters and the wall parameters are input, and the structural parameters of the splicing area are initialized; For the design area Ω and the splicing area Ω input by the user g and fixed area Ω f , satisfying Ω=Ω g ∪Ω f ; The structural parameters of the fixed area entered by the user are The subscript f indicates a fixed area, n f is the number of fixed region parameter points, γ f,i is the hole parameter, t f,i are the wall parameters, and the structural parameters remain unchanged; then, the structural parameters are initialized in the splicing area The subscript c represents the splicing area, n c is the number of parameter points in the splicing area, C,i and t c,i are the hole parameters and wall parameters respectively; finally, the radial basis interpolation method is used to obtain the structural parameters of any point r in the design area in is the position vector, x, y, and z are the corresponding coordinates, and g(·) is the radial basis interpolation function. These two structural parameters affect the pores and thickness of the thin-walled porous structure, and further affect the sealing properties of the structure. Therefore, the optimized design parameters are determined as Used for the construction of porous structures, as well as for subsequent property analysis and automatic optimization design without cavities; Step 2: Convert the periodic surface into an implicit representation; The periodic surface is the mid-surface of the thin-walled porous structure. The implicit function expression of the structural parameter Υ(r) that depends on any point r in the design area is given as: in is a periodic function that can effectively simulate porous properties. p(r) is the phase of the trigonometric function, and λ represents the period of the trigonometric function. is the periodic moment; are the three-dimensional basis vectors; f i,j The three-dimensional transformation matrix S in (Υ(r),r) j and M i For given parameters, j = 1, 2, 3, 4, i = 1, 2, 3, n f =7 is the hole parameter to be interpolated in step 1. The implicit function of the periodic surface satisfies: if r is on the surface On the outside, ψ(Υ(r), r) < 0, if r is On the upper side, ψ(Υ(r), r)=0, if r is inside S, ψ(Υ(r), r)>0; by calculating the gradient of the implicit function, we get the following formula: Where T(Υ(r), r) represents the geometric distance from r to the periodic surface S, a(Υ(r)) and b(Υ(r)) are coefficients determined by the pore parameter Υ(r). The relationship between the geometric distance function T(Υ(r), r) and the surface function ψ(Υ(r), r) can be used to explicitly control the wall thickness of the thin-walled porous structure generated by the periodic surface. Users can design the structure through the wall parameter t(r); Step 3: Using the implicit function of periodic surface, the thin-walled porous structure with explicitly controlled wall thickness is transformed into an implicit representation; For thin-walled porous structures with explicitly controlled wall thickness, two offset surfaces with distances of t(r) / 2>0 and -t(r) / 2 are obtained based on the implicit representation of periodic surfaces. and ψ out (Υ(r),t(r),r)=-ψ in (Υ(r), t(r), r), respectively as the inner wall and outer wall of the thin-walled structure; then, the implicit function of the thin-walled structure is obtained by Boolean calculation as follows: Where Φ(Υ(r),t(r),r)≥0 is a thin-walled porous structure with a thickness of t(r), and the wall thickness of the structure can be explicitly controlled; Step 4: Based on the thin-walled porous structure with controllable wall thickness, the continuous splicing structure is transformed into an implicit function representation; For the implicit function representation of the continuous splicing structure, the structural parameter function obtained by the radial basis interpolation method in step 1 is combined with the implicit function of the thin-walled porous structure showing the wall thickness. Finally, the implicit function representation of the continuous splicing structure with the design parameters as independent variables is obtained: Continuously spliced ​​solid structure The value of Φ is obtained by expressing the implicit function: Indicates that r is in the entity structure The interior is the area with materials; Indicates that r is The boundary is the boundary between entity and void; Indicates that r is The outside of the structure is the void area without material; therefore, for the personalized design of the spliced ​​thin-walled porous structure, the design parameters controlled and optimized by the user include: Step 5: Obtain a set of key points, and perform a sealing property analysis on the spliced ​​thin-walled porous structure according to the wall parameter value T0 specified by the user; By numerically calculating the distance field of the implicit function of the periodic surface, the key points for judging the closure of the thin-walled porous structure are identified. The set of key points obtained is expressed as Where P m Represents the coordinates of the mth key point, n P is the number of key points, A3(P m ) is the Hessian matrix of the implicit function ψ(Υ(r),r), A3(P m ) with respect to P m The minimum value of the implicit function at all key points is where |·| represents the absolute value and min(·) represents Inner all p k The minimum function value obtained by taking the value at must cover the wall thickness value specified by the user, that is, satisfy T m >T0; then, according to T m When ≤T0, a closed cavity will be generated. The closed attribute value corresponding to the key point is calculated to determine whether a closed cavity is generated in the local area near the key point, thereby obtaining the closed performance evaluation of the entire thin-walled structure under the condition of a specified wall thickness range; Step 6: Establish optimization problem model; The user specifies the required wall thickness value T0, and through optimization, the wall thickness of the thin-walled structure at the key points of the structure meets T m >T0, so as to meet the user's demand for no closed cavity; Set the goal of minimizing the closed properties in the splicing area according to the requirements, and interpolate the parameter values ​​of the design parameters to the base point As design variables; construct the following optimization problem form: Where H(f) is the Heaviside function, which takes the value 1 when f≥0 and takes the value 0 when f<0; Step 7: Calculate parameter gradients and automatically iterate to optimize the solution; The optimal solution of the optimization problem model is calculated using an optimization solver based on the gradient method; first, the objective function J(Υ(r), t(r), r) is calculated with respect to the design parameters The gradient information is substituted into the optimization solver GCMMA for automatic iterative optimization to obtain the design parameters of the thin-walled porous structure that meets the design requirements; after step four, the final thin-walled porous splicing structure with controllable wall thickness and cavity-free optimized design is obtained.

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