A design method for constructing a non-regular shape truss base structure based on discrete approximate boundary

Abstract

The application discloses a design method for constructing a non-regular shape truss base structure based on discrete approximate boundary, which comprises the following steps: determining a design area of the truss base structure; performing finite element mesh division on the design domain; extracting node coordinate information of all element meshes of the design domain; taking the mesh nodes as the end points of the rods, and constructing a full-connection truss base structure; performing a bias operation on the concave region of the design domain to obtain a bias curve; performing one-dimensional mesh division on the bias curve to connect adjacent nodes to form a continuous line segment set; regarding the rods in the full-connection base structure as line segments, judging the intersection conditions of the rods and the bias continuous line segment set to delete the rods; and obtaining the truss base structure with all rods located in the design domain. The application solves the problem that in the prior art, when a base structure of a complex non-regular shape design area is constructed, a curve or a surface in an implicit function form is approximated by using a known expression graph, so that part of the generated base structure rods do not meet the requirements.

Description

Technical Field

[0001] This invention relates to the field of discrete structure topology optimization design, and in particular to a design method for constructing irregularly shaped truss base structures based on discrete approximate boundaries. Background Technology

[0002] The most important method for truss topology optimization is the base structure method. The idea is to arrange the nodes of the members in the design area according to certain rules, connect the nodes to form a set of member connections, i.e., the base structure, and then select the best member connections and node combinations from the truss according to certain optimization criteria to obtain the optimal topology.

[0003] Existing base structure methods are generally designed for regularly shaped areas, such as rectangles. They typically arrange nodes of members at equal intervals along the horizontal and vertical directions, connecting them to form a truss base structure without repeating members. However, this method is not applicable to complex-shaped design areas, especially irregular design domains containing concave sections.

[0004] For design domains with irregular geometries, a common approach is to construct the base structure based on finite element meshes. This involves using CAE software to mesh the design domain using finite element methods, and then using the mesh nodes as the endpoints of the members to construct a fully connected truss base structure. Members located outside or intersecting the design domain are deleted using graphical collision detection technology. This involves representing the concave boundaries of the design region with mathematical functions, representing the members with line segment functions, and deleting members based on their intersection relationships, thus obtaining all truss base structures within the design domain. This method effectively solves the problem of constructing base structure members for design domains with irregular geometries. However, this method requires that the concave regions of the design domain have specific functional forms. For some implicitly functional curves or surfaces, since their boundary geometry cannot be directly visualized mathematically, they can only be approximated graphically using known expressions. This often results in some members of the generated base structure not meeting the requirements, such as intersecting with the design region boundary or being partially located outside the design region. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a design method for constructing irregular truss base structures based on discrete approximation boundaries, which approximates complex irregular curves with a set of line segments composed of one-dimensional finite elements, ensuring that all members within the truss are located within the design domain.

[0006] Technical Solution: To achieve the above objectives, the design method for constructing irregularly shaped truss base structures based on discrete approximate boundaries, as described in this invention, includes the following steps:

[0007] Step S1: Determine the design domain of the truss base structure;

[0008] Step S2: Perform finite element mesh generation on the design domain;

[0009] Step S3: Extract the node coordinate information of all element meshes in the design domain;

[0010] Step S4: Use the grid nodes as the endpoints of the members to construct a fully connected truss base structure;

[0011] Step S5: Perform an offset operation on the concave region of the design domain to obtain the offset curve;

[0012] Step S6: Divide the offset curve into a one-dimensional mesh and connect adjacent nodes to form a continuous set of line segments;

[0013] Step S7: Treat the members in the fully connected base structure as line segments, determine their intersection with the offset continuous line segment set, and then remove members.

[0014] Step S8: Obtain the truss base structure in which all members are located within the design domain;

[0015] Specifically, step S1, determining the design domain of the truss base structure, involves: determining the geometric range of the truss base structure design domain Ω, and defining the boundaries of the design domain. Based on shape characteristics, it is divided into convex region boundaries. and concave region boundary

[0016] Specifically, step S2 involves dividing the design domain into finite element meshes as follows: for convex regions with smaller curvatures in the design domain, a sparser mesh is used; for concave regions with larger curvatures, a denser mesh is used; and for curvature transition regions, the meshes are divided based on finite element mesh adaptive technology.

[0017] Specifically, step S3, extracting the node coordinate information of all element meshes in the design domain, involves representing the mesh coordinate information as: Node i (x,y),i=1,...N, where N is the number of grid nodes.

[0018] Step S4, which involves using grid nodes as member endpoints to construct a fully connected truss base structure, includes the following sub-steps:

[0019] S401: Based on the principle that every two nodes constitute a member, a truss base structure can have a maximum of [number missing] members when members are collinear. One pole;

[0020] S402: Sequentially determine the collinearity of each member with the same starting point, and then remove members;

[0021] Assume that connecting nodes A and B yields a rod Bar. ABConnecting nodes A and C yields the rod Bar. AC Connecting nodes B and C yields the rod Bar. BC And their length relationship is Let the cosine of the angle between the two rods be denoted as . in Bar AB The direction vector, considering the influence of numerical error, is replaced by a number close to 1, ColTol, when the two rods are collinear, i.e.:

[0022]

[0023] S403: Traverse all mesh nodes in step S3 and reduce the number of members based on the cosine value of the member angle in step S402, thus ensuring that there are no overlapping members in the resulting fully connected truss base structure. The number of members in the base structure at this time is denoted as Num. * .

[0024] Specifically, step S5 involves performing an offset operation on the concave region of the design domain to obtain an offset curve. This is achieved by using CAD software to perform an offset operation on the concave region of the design domain. The offset distance is h, which is one-hundredth of the shortest side length Lmin of the design domain.

[0025] Specifically, step S6, which involves dividing the offset curve into a one-dimensional mesh and connecting adjacent nodes to form a continuous set of line segments, involves dividing the offset curve in step S5 into a linear element mesh, treating each linear element as a line segment. The mathematical expression for this is:

[0026]

[0027] Where M is the boundary of the concave region. The total number of nodes on and The two endpoints of the k-th line segment are given, and the line segment coefficient t determines the range of variation in the line segment length. Connecting all line segments end to end forms a continuous set of segmented line segments that can approximately describe the shape of the boundary curve of the concave interval.

[0028] Specifically, step S7, which involves treating the members in the fully connected base structure as line segments and determining their intersection with the offset continuous line segment set to reduce the number of members, involves treating the members in the fully connected base structure obtained in step S4 as line segments, expressed mathematically as follows:

[0029]

[0030] Determine its intersection with the biased continuous line segment set in step S6, and solve the function equations of both to obtain the line segment coefficient t:

[0031]

[0032] in, For perpendicular to and Let t be the normal vector of the line segment at the endpoint. If t∈[0,1] is calculated, it indicates that the rod intersects part of the boundary of the concave section of the design domain, that is, the rod part is located outside the design domain, and the rod needs to be deleted from the base structure; otherwise, it indicates that the rod does not intersect the boundary of the concave section, and the rod is entirely located within the design domain, and the rod needs to be retained in the base structure. The intersection of all rods with the boundary is judged in turn, and rod deletion is performed on the fully connected base structure.

[0033] Specifically, obtaining the truss base structure in step S8, where all members are located within the design domain, involves grouping all members in the base structure obtained in step S7 according to their common endpoints and sorting them according to their lengths. The resulting set is the required truss base structure.

[0034] Beneficial effects: The present invention has the following advantages: 1. The present invention solves the problem that complex geometric concave regions of the design domain cannot be expressed by explicit mathematical functions by approximating irregular curves with a continuous line segment set composed of one-dimensional linear rod elements. By combining the adaptive mesh technology of finite element method, the boundary depiction accuracy can be further improved and the efficiency of basic structural rod construction can be improved.

[0035] 2. By judging the intersection of the members in the full-connection base structure with the offset line segment set, members located outside the design domain or intersecting with the boundary can be effectively deleted, thereby obtaining the truss base structure that is entirely within the design domain.

[0036] 3. The method described in this invention can be extended to the construction of three-dimensional spatial truss base structures. That is, by using finite element analysis, irregular curved surfaces are regarded as a set of planes composed of a series of triangular or quadrilateral elements. The intersection of the members in the base structure with the planes in the set is judged and the members are reduced to obtain a spatial truss base structure that meets the requirements. It has wider applicability and universality. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the process of the present invention;

[0038] Figure 2 This is a schematic diagram of the irregular design area and boundary of the present invention;

[0039] Figure 3 This is a schematic diagram of the mesh division on the boundary of the concave region of the present invention;

[0040] Figure 4 This is a schematic diagram of the full-connection base structure truss of the present invention;

[0041] Figure 5This is a schematic diagram of the concave boundary offset curve of the design area of ​​the present invention;

[0042] Figure 6 This is a schematic diagram of a truss base structure in which all members of the present invention are located within the design domain. Detailed Implementation

[0043] The technical solution of the present invention will be described in detail below with reference to the embodiments and accompanying drawings.

[0044] like Figure 1 As shown, the design method for constructing irregularly shaped truss base structures based on discrete approximate boundaries according to the present invention includes the following steps:

[0045] Step S1: Determine the design domain of the truss base structure;

[0046] Specifically, this involves: determining the geometric extent of the truss base structure design domain Ω, and defining the boundaries of the design domain. Based on shape characteristics, it is divided into convex region boundaries. and concave region boundary like Figure 2 As shown, in this embodiment, the length of the design domain is L=2 and the width is H=2.

[0047] Step S2: Perform finite element mesh generation on the design domain;

[0048] Specifically, using Hypermesh software, sparser meshes are used to divide convex regions with smaller curvatures in the design domain; denser meshes are used to divide concave regions with larger curvatures; and for regions with transitional curvatures, meshing is performed based on finite element mesh adaptive techniques, such as... Figure 3 As shown. If it is necessary to improve the fitting accuracy of the mesh edges to the curve shape, the mesh division of the concave region can be further refined, and more finite elements can be used for approximation.

[0049] Step S3: Extract the node coordinate information of all element meshes in the design domain;

[0050] Specifically, the coordinate information of the grid is represented as: Node i (x,y),i=1,...N, where N is the number of grid nodes.

[0051] Step S4: Using the mesh nodes as member endpoints, construct a fully connected truss base structure, including the following sub-steps:

[0052] S401: Based on the principle that every two nodes constitute a member, a truss base structure can have a maximum of [number missing] members when members are collinear. One pole;

[0053] S402: Sequentially determine the collinearity of each member with the same starting point, and then remove members;

[0054] Assume that connecting nodes A and B yields a rod Bar. AB Connecting nodes A and C yields the rod Bar. AC Connecting nodes B and C yields the rod Bar. BC And their length relationship is Let the cosine of the angle between the two rods be denoted as . in Bar AB The direction vector, considering the influence of numerical error, is replaced by a number close to 1, ColTol, when the two rods are collinear, such as ColTol = 0.99999. That is:

[0055]

[0056] S403: Traverse all mesh nodes in step S3 and reduce the number of members based on the cosine value of the member angles in step S402, thus ensuring that there are no overlapping members in the resulting fully connected truss base structure. The number of members in the base structure at this point is denoted as Num. * ,like Figure 4 As shown.

[0057] Step S5: Offset the concave region of the design domain and obtain the offset curve;

[0058] Specifically, using UG software, an offset operation is performed on the concave area of ​​the design domain to obtain an offset curve. The offset distance is h, which is one-hundredth of the shortest side length of the design domain. The offset distance h has a significant impact on the determination of member deletion. If h is too large, some members outside the design domain may not be effectively deleted; if h is too small, members with nodes located on the boundary may be mistakenly deleted. The offset curve refers to the area where the concave region is extracted. In this embodiment, h is set to 0.01.

[0059] Step S6: Divide the offset curve into a one-dimensional grid and connect adjacent nodes to form a continuous set of line segments;

[0060] Specifically, the offset curve in step S5 is meshed using Hypermesh software, with each linear element treated as a line segment. The mathematical expression for this can be written as:

[0061]

[0062] Where M is the boundary of the concave region. The total number of nodes on and The two endpoints of the k-th line segment are given, and the segment coefficient t determines the range of variation in the line segment length. Connecting all line segments end-to-end forms a continuous set of segmented lines that can approximate the shape of the boundary curve of the concave interval, such as... Figure 5 As shown.

[0063] Step S7: Treat the members in the fully connected base structure as line segments, determine their intersection with the offset continuous line segment set, and then remove members.

[0064] Specifically, the members in the fully connected base structure obtained in step S4 are considered as line segments, and can be expressed using mathematical functions as follows:

[0065]

[0066] Determine its intersection with the biased continuous line segment set in step S6, and solve the function equations of both to obtain the line segment coefficient t:

[0067]

[0068] in, For perpendicular to and Let t be the normal vector of the line segment at the endpoint. If t∈[0,1] is calculated, it indicates that the rod intersects part of the boundary of the concave section of the design domain, that is, the rod part is located outside the design domain, and the rod needs to be deleted from the base structure; otherwise, it indicates that the rod does not intersect the boundary of the concave section, and the rod is entirely located within the design domain, and the rod needs to be retained in the base structure. The intersection of all rods with the boundary is determined sequentially, and rod deletion is performed on the fully connected base structure, such as... Figure 6 As shown.

[0069] Step S8: Obtain the truss base structure in which all members are located within the design domain;

[0070] Specifically, in order to clarify the relationship between the lengths of the members in the truss and facilitate subsequent truss topology optimization, all members in the base structure obtained in step S7 are grouped according to their common endpoints and sorted according to their lengths. The set of these members is the required truss base structure.

[0071] This invention solves the problem that complex geometrically concave regions in the design domain cannot be expressed using explicit mathematical functions by approximating irregular curves with a continuous set of line segments composed of one-dimensional linear elements. By combining adaptive meshing technology of finite element method, the accuracy of boundary depiction can be further improved, and the efficiency of constructing base structure members can be increased. Furthermore, the method described in this invention can be extended to the construction of three-dimensional spatial truss base structures. That is, by using finite element meshing to treat irregular curved surfaces as a set of planes composed of a series of triangular or quadrilateral elements, the intersection of members in the base structure with the planes in the set is determined, and members are eliminated to obtain a spatial truss base structure that meets the requirements. This method has wider applicability and universality.

Claims

1. A design method for constructing irregularly shaped truss base structures based on discrete approximate boundaries, characterized in that, Includes the following steps: Step S1: Determine the design domain of the truss base structure; Step S2: Perform finite element mesh generation on the design domain; Step S3: Extract the node coordinate information of all element meshes in the design domain; Step S4: Use the grid nodes as the endpoints of the members to construct a fully connected truss base structure; Step S5: Perform an offset operation on the concave region of the design domain to obtain the offset curve; Step S5 describes the bias operation on the concave region of the design domain to obtain the bias curve. Specifically, the bias operation is performed on the concave region of the design domain, and the bias distance is h, which is one-hundredth of the shortest side length Lmin of the design domain. Step S6: Divide the offset curve into a one-dimensional mesh and connect adjacent nodes to form a continuous set of line segments; Step S6, which involves dividing the offset curve into a one-dimensional mesh and connecting adjacent nodes to form a continuous set of line segments, specifically involves using CAE software to perform linear element meshing on the offset curve from step S5, treating each linear element as a line segment, with the expression being: ； Where M is the boundary of the concave region. The total number of nodes on and The two endpoints of the k-th line segment are given. The line segment coefficient t determines the range of variation in the line segment length. Connecting all the line segments end to end forms a continuous set of segmented line segments that can approximately describe the shape of the boundary curve of the concave interval. Step S7: Treat the members in the fully connected base structure as line segments, determine their intersection with the offset continuous line segment set, and then remove members. Step S8: Obtain the truss base structure in which all members are located within the design domain.

2. The design method for constructing irregularly shaped truss base structures based on discrete approximate boundaries according to claim 1, characterized in that, Step S1, which involves determining the design domain of the truss base structure, specifically includes: determining the design domain of the truss base structure. The geometric extent of the boundary of the design domain. Based on shape characteristics, it is divided into convex region boundaries. and concave region boundary .

3. The design method for constructing irregularly shaped truss base structures based on discrete approximate boundaries according to claim 1, characterized in that, Step S2, which involves dividing the design domain into finite element meshes, specifically involves: dividing the convex regions with smaller curvatures in the design domain into sparser meshes; dividing the concave regions with larger curvatures into denser meshes; and dividing the curvature transition regions into meshes based on finite element mesh adaptive techniques.

4. The design method for constructing irregularly shaped truss base structures based on discrete approximate boundaries according to claim 1, characterized in that, Step S3, which involves extracting the node coordinate information of all element meshes in the design domain, specifically involves representing the mesh coordinate information as follows: , where N is the number of grid nodes.

5. The design method for constructing irregularly shaped truss base structures based on discrete approximate boundaries according to claim 1, characterized in that, Step S4, which involves using grid nodes as member endpoints to construct a fully connected truss base structure, includes the following sub-steps: S401: Based on the principle that every two nodes constitute a member, a truss base structure can have a maximum of [number missing] members when members are collinear. One pole; S402: Sequentially determine the collinearity of each member with the same starting point, and then remove members; Assume that connecting nodes A and B yields a rod Bar. AB Connecting nodes A and C yields the rod Bar. AC Connecting nodes B and C yields the rod Bar. BC And their length relationship is Let the cosine of the angle between the two rods be denoted as ,in Bar AB The direction vector, considering the influence of numerical error, is replaced by a number close to 1, ColTol, when the two rods are collinear, i.e.: ； S403: Traverse all mesh nodes in step S3 and reduce the number of members based on the cosine value of the member angle in step S402, thus ensuring that there are no overlapping members in the resulting fully connected truss base structure. The number of members in the base structure at this time is denoted as Num. * .

6. The design method for constructing irregularly shaped truss base structures based on discrete approximate boundaries according to claim 1, characterized in that, Step S7, which involves treating the members in the fully connected base structure as line segments and determining their intersection with the offset continuous line segment set to reduce the number of members, specifically involves treating the members in the fully connected base structure obtained in step S4 as line segments, represented by the following function: ， Determine its intersection with the biased continuous line segment set in step S6, and solve the function equations of both to obtain the line segment coefficient t: ； in, For perpendicular to and The normal vector of the line segment at the endpoint; if calculated as follows If the bar intersects part of the concave boundary of the design domain, it means that part of the bar is outside the design domain and needs to be removed from the base structure; otherwise, it means that the bar does not intersect the concave boundary and all the bars are inside the design domain and need to be retained in the base structure. The intersection of all bars with the boundary is judged in turn, and the bars are removed from the fully connected base structure.

7. The design method for constructing irregularly shaped truss base structures based on discrete approximate boundaries according to claim 1, characterized in that, The step S8 of obtaining a truss base structure in which all members are located within the design domain specifically involves grouping all members in the base structure obtained in step S7 according to their common endpoints and sorting them according to their lengths. The resulting set is the required truss base structure.

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