A parametric design method for irregularly shaped multi-curved single-layer reticulated shells

Abstract

This invention provides a parametric design method for a non-circular, multi-curved single-layer reticulated shell, comprising the following steps: S1: Based on the structural characteristics of a bidirectional sine curve, a straight component is used as the main body of the non-circular, single-layer reticulated shell; S2: Static design calculations are performed on the non-circular, single-layer reticulated shell using static model calculation software; S3: The static design calculation results conforming to the design specifications are selected; S4: The locations of the nodes in the non-circular, single-layer reticulated shell are selected, and three-dimensional solid models of the nodes are established using finite element analysis software. The three-dimensional solid models of the nodes are meshed, the materials constituting the three-dimensional solid models of the nodes are given, convergence criteria are set, and iterative convergence calculations are performed; S5: The limit state deformation modes and load-displacement curves of each component at the node locations are obtained to verify whether the cross-sectional shape of the components meets the requirements; S6: If all components meet the design specifications, their geometric parameters are output.

Description

Technical Field

[0001] This invention relates to the field of architectural engineering design technology, and in particular to a parametric design method for irregularly shaped multi-curved single-layer reticulated shells. Background Technology

[0002] Grid shell structures combine the characteristics of component structures and thin-shell structures, offering rational stress distribution and enabling large spans. Grid shell structures can achieve almost anything that conventional thin-shell or grid structures cannot. Based on these characteristics, grid shell structures are commonly used in large-span stadiums, airports, railway stations, or ports. With the increasing popularity of large-span, large-space buildings, examples of hybrid spherical grid shells, hybrid cylindrical grid shells, or hyperbolic paraboloid grid shells have emerged. The overall surface of the grid shell has a streamlined or radial structure. Grid shells used as roofs are supported by multiple pillars, creating internal spaces for personnel activities or structural assembly.

[0003] Figure 1 This paper presents a reticulated shell structure with a roof featuring bidirectional sinusoidal undulations, composed of alternating convex upper shells and concave lower shells. This is an irregular structure, unlike conventional saddle-shaped, elliptical, or spherical structures. Due to its unique shape, the structural stability of this single-layer reticulated shell requires careful consideration. Many factors influence the stability of a reticulated shell, including the connection materials, node types, and load types. Therefore, it is necessary to provide a reliable parametric design method for this irregular, bidirectional sinusoidal undulation single-layer reticulated shell structure. Summary of the Invention

[0004] In view of this, the present invention proposes a parametric design method for the overall structural stability of a single-layer reticulated shell with a unique structure and irregular multi-curved surfaces.

[0005] The technical solution of this invention is implemented as follows: This invention provides a parametric design method for irregularly shaped multi-curved single-layer reticulated shells, comprising the following steps:

[0006] S1: Based on the structural characteristics of the bidirectional sine curve, a straight component (100) is used as the main body of the irregular single-layer reticulated shell, and the cross-sectional shape of the component (100) is set; multiple nodes (200) are formed at the intersection of adjacent components (100); the sag, span, slenderness ratio, edge components (100) and deflection limit of the irregular single-layer reticulated shell are obtained according to the design requirements;

[0007] S2: Obtain the dead load of the irregular single-layer reticulated shell, as well as the variable load, temperature effect, and seismic effect at the location of the irregular single-layer reticulated shell; perform static design calculations using static model calculation software;

[0008] S3: Select the static design calculation results that conform to the design specifications, and obtain the stress ratio of each node (200) respectively;

[0009] S4: Select the location of the node (200) on the contour of the upper convex shell, the contour of the lower concave shell, or the edge of the irregular single-layer reticulated shell. Establish a three-dimensional solid model of the location of the node (200) using finite element analysis software. Mesh the three-dimensional solid model of the location of the node (200). Given the material of the three-dimensional solid model of the location of the node (200), set the convergence criterion and perform iterative calculation.

[0010] S5: Obtain the limit state deformation modes and load-displacement curves of each component (100) at the location of node (200) to verify whether the cross-sectional shape of component (100) meets the requirements.

[0011] S6: If any component (100) where any node (200) is located does not meet the design specifications, repeat steps S1-S5; if all components where all nodes (200) are located meet the design specifications, output the geometric parameters of each component (100) where each node (200) of the irregular single-layer reticulated shell is located.

[0012] Based on the above technical solutions, preferably, in step S1, according to the structural characteristics of the bidirectional sine curve, a straight component (100) is used as the main body of the single-layer reticulated shell. This involves horizontally unfolding the bidirectional sine curve and combining it with any one of the following: a square flat reticulated shell, a Schweidler-type flat reticulated shell, a three-dimensional grid flat reticulated shell, or a geodesic-type flat reticulated shell, to form an irregular single-layer reticulated shell. Each side of the irregular single-layer reticulated shell is a straight component (100), and the common ends of at least two different components (100) together form a node (200).

[0013] Preferably, step S2, which involves using static model calculation software for static design calculations, involves establishing geometric models of the irregular single-layer reticulated shell model and the overall structural model containing the irregular single-layer reticulated shell separately. 3D3S steel structure design software is used as the main static model calculation software, and SAP2000 software is used as the verification static model calculation software. For variable loads, the basic natural period of the wind-induced vibration response is set to be greater than 0.25 seconds. The snow load is determined based on the location of the irregular single-layer reticulated shell. For seismic effects, the modal response spectrum method is used, which includes more than 30 modal vectors, and the seismic source is generated using random vibration. The initial imperfection setting for stability is given as 1 / 300, and the structural stability safety factor is greater than 4.2. For temperature effects, compressive and tensile temperature stresses are artificially assigned.

[0014] Preferably, in step S4, three-dimensional solid models of the locations of nodes (200) are established using finite element analysis software, and the three-dimensional solid models of the locations of nodes (200) are meshed. Given the material constituting the three-dimensional solid models of the locations of nodes (200), a convergence criterion is set, and iterative calculations are performed. This involves establishing three-dimensional solid models of nodes (200) at different locations of the irregular single-layer reticulated shell using the finite element analysis software ANSYS, using solid element SOLID185, and generating several tetrahedral elements for each node (200) using free meshing. The given material is steel with an elastic modulus E = 2.06e. 5 N / mm; Poisson's ratio v = 0.3; yield strength is 345 MPa; the given convergence criterion is that the strength stress, deflection value and comfort vibration frequency converge simultaneously.

[0015] Preferably, the node (200) includes a common node (201) and a column top node (202); the common node (201) includes several components (100) and a first connecting part (203), the end of each component (100) is fixedly connected to two adjacent surfaces of the first connecting part (203); the column top node (202) includes several components (100) and a column (204), the column (204) is used to support the single-layer reticulated shell, one end of the component (100) of each column top node (202) is fixedly connected to the surface of the column (204) away from the ground, and the other end of the component (100) of each column top node (202) extends outward in a direction away from the column (204).

[0016] More preferably, the component (100) is a square steel tube with a rectangular cross-section; the column (204) is a hollow steel tube.

[0017] Preferably, the first connecting part (203) includes a plurality of support plates (2031), one end of the plurality of support plates (2031) is fixedly connected to each other, and the other end of the plurality of support plates (2031) extends outward in a direction away from the common end, and the adjacent support plates (2031) are arranged at an angle; one end of each component (100) constituting the ordinary node (201) also extends into the space between the adjacent support plates (2031) and is fixedly connected to the adjacent end faces of the two adjacent support plates (2031), and the other end of each component (100) of the ordinary node (201) extends outward in a direction away from the first connecting part (203), and the angle at which each component (100) of the ordinary node (201) extends away from the first connecting part (203) is not exactly the same.

[0018] More preferably, the column top node (202) further includes a plurality of second connecting portions (205) and a plurality of third connecting portions (206) disposed inside the column (204); the plurality of second connecting portions (205) extend horizontally along the radial direction of the column (204) and are fixedly connected to the inner surface of the column (204), and the ends of the second connecting portions (205) are correspondingly disposed with the ends of two non-adjacent components (100) near the column (204); the plurality of third connecting portions (206) are respectively located between the plurality of second connecting portions (205) and between the inner wall of the column (204) and the second connecting portions (205); the ends of the third connecting portions (206) near the inner surface of the column (204) are correspondingly disposed with the ends of two other non-adjacent components (100) near the column (204).

[0019] Preferably, the angle between the central axes of two non-adjacent members (100) located in the extension direction of the second connecting part (205) is greater than the angle between the central axes of any other two non-adjacent members (100) connected to the column (204); the principle of setting the third connecting part (206) is to make the third connecting part (206) have a larger surface area inside the column (204).

[0020] Preferably, the arrangement of the columns (204) supporting the single-layer reticulated shell at the column top node (202) needs to simultaneously meet the following rules: 1) Each column (204) is offset inward by a certain distance along the outline of the flat reticulated shell that constitutes the irregular single-layer reticulated shell, and the closed shape formed by the sequential connection of the endpoints of the central axis of each column (204) is outwardly convex; 2) The central axis of each column (204) is symmetrically arranged with respect to the longitudinal center plane of the bidirectional sine curve, and is close to the adjacent longitudinal center plane of the bidirectional sine curve. The spacing between the central axes of the columns (204) shall not be less than the spacing between the central axes of adjacent columns (204) on the longitudinal central plane away from the bidirectional sine curve; 3) If an elevated floor or equipment placement floor is set up, columns (204) shall be set up at the edge of the projection position of the elevated floor or equipment placement floor, and reinforcing beams connecting adjacent columns (204) shall be set up between the side surfaces of each adjacent column (204); 4) The outer surface of the end of each column (204) away from the ground shall be fixedly connected to the ends of at least four different components (100).

[0021] The parametric design method for irregularly shaped multi-curved single-layer reticulated shells provided by this invention has the following advantages compared with the prior art:

[0022] (1) This scheme first establishes a set model based on the components using static model calculation software, and combines the effects of static load, variable load and action to screen possible structures of irregular single-layer reticulated shells. Then, it further uses finite element analysis software to model each node of the irregular single-layer reticulated shell, performs convergence-based iterative calculations on each node at different locations, selects components with suitable cross-sectional dimensions and corresponding irregular single-layer reticulated shells, and outputs the geometric parameters such as the dimensions and three-dimensional coordinates of each component. This simplifies the design workload while screening out the overall structure and specific components of the irregular single-layer reticulated shell with good structural stability.

[0023] (2) The first connecting part, the second connecting part and the second connecting part are respectively ordinary nodes or column top nodes to strengthen the structure, while reducing steel consumption, maintaining stability and helping to reduce the overall weight of the irregular single-layer reticulated shell. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 A three-dimensional view of an irregularly shaped, multi-curved, single-layer reticulated shell;

[0026] Figure 2 This is a flowchart of a parametric design method for a non-circular, multi-curved single-layer reticulated shell according to the present invention;

[0027] Figure 3 This is a top view of a component of an irregularly shaped single-layer reticulated shell, which is part of the parametric design method for an irregularly shaped multi-curved single-layer reticulated shell according to the present invention.

[0028] Figure 4 The top view, front view, and left view of the components of the irregular single-layer reticulated shell according to the parametric design method of the irregular multi-curved single-layer reticulated shell of the present invention.

[0029] Figure 5 This is a top view of the structure of a common node in the parametric design method of a non-circular multi-curved single-layer reticulated shell according to the present invention.

[0030] Figure 6 This is a perspective view of the first connection part of a common node in the parametric design method of a non-circular multi-curved single-layer reticulated shell according to the present invention.

[0031] Figure 7 This is a top view of some column top nodes of a parametric design method for a non-circular multi-curved single-layer reticulated shell according to the present invention.

[0032] Figure 8 This is a top view of the column top node, which is another part of the parametric design method for a non-circular multi-curved single-layer reticulated shell according to the present invention.

[0033] Figure 9 The geometric model and finite element mesh diagram of a common node in the parametric design method of a non-circular multi-curved single-layer reticulated shell according to the present invention are shown below.

[0034] Figure 10 This invention provides a stress distribution diagram and load-displacement curve for a common node in a parametric design method for a non-circular, multi-curved single-layer reticulated shell.

[0035] Figure 11 The geometric model and finite element mesh diagram of the column top node of the parametric design method for a non-circular multi-curved single-layer reticulated shell according to the present invention are shown below.

[0036] Figure 12 This invention provides a stress distribution diagram and load-displacement curve for a column top node in a parametric design method for a non-circular, multi-curved single-layer reticulated shell.

[0037] Figure 13 The buckling analysis results of a rectangular tube member under a stress ratio are provided for a parametric design method of a non-circular multi-curved single-layer reticulated shell according to the present invention.

[0038] Figure 14 This invention relates to a parametric design method for irregularly shaped multi-curved single-layer reticulated shells, and presents the buckling analysis results of a rectangular tube component under a stress ratio after adjusting the wall thickness according to design specifications.

[0039] Figure 15 This is a stability analysis result of a rectangular tube component under a stress ratio adjusted according to design specifications, based on the parametric design method of a non-circular multi-curved single-layer reticulated shell according to the present invention.

[0040] Figure 16 This is a buckling analysis result of a rectangular tube component under a stress ratio after readjusting the wall thickness, which is a parametric design method for a non-circular multi-curved single-layer reticulated shell according to the present invention.

[0041] Figure 17 This is a stability analysis result of a rectangular tube component under a stress ratio after readjusting the wall thickness, which is a parametric design method for a non-circular multi-curved single-layer reticulated shell according to the present invention.

[0042] Figure 18 The buckling analysis results of a rectangular tube member under a different stress ratio are based on the parametric design method of the irregular multi-curved single-layer reticulated shell of the present invention.

[0043] Figure 19The results of stability analysis of a rectangular tube component under a different stress ratio are based on the parametric design method of the irregular multi-curved single-layer reticulated shell of the present invention. Detailed Implementation

[0044] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0045] The technical solution of this invention is implemented as follows: Figure 1 As shown in Figure 4, this invention provides a parametric design method for irregularly shaped multi-curved single-layer reticulated shells, comprising the following steps:

[0046] S1: Based on the structural characteristics of the bidirectional sine curve, a straight component 100 is used as the main body of the irregular single-layer reticulated shell, and the cross-sectional shape of the component 100 is set; multiple nodes 200 are formed at the intersection of adjacent components 100; the sag, span, slenderness ratio, edge components 100 and deflection limit of the irregular single-layer reticulated shell are obtained according to the design requirements.

[0047] The structure described here, based on the structural characteristics of a bidirectional sine curve, uses a straight component 100 as the main body of a single-layer reticulated shell. This involves horizontally unfolding the bidirectional sine curve and combining it with any of the following: a rectangular flat reticulated shell, a Schweidler-type flat reticulated shell, a three-dimensional grid flat reticulated shell, or a geodesic-type flat reticulated shell, to form an irregular single-layer reticulated shell. Each side of the irregular single-layer reticulated shell is a straight component 100, and the common ends of at least two different components 100 form a node 200. The aforementioned flat reticulated shells are all conventional flat reticulated shell structural forms. The irregular single-layer reticulated shell in this scheme combines a special bidirectional sine curve at the center of the flat reticulated shell to form a raised or recessed area.

[0048] S2: Obtain the dead load of the irregular single-layer reticulated shell, as well as the variable load, temperature effect, and seismic effect at the location of the irregular single-layer reticulated shell; perform static design calculations using static model calculation software; obtain the natural vibration period, individual displacement, overall displacement, and maximum deflection of the irregular single-layer reticulated shell through static design calculations.

[0049] Step S2 involves using static model calculation software for static design calculations. This involves establishing geometric models of the irregular single-layer reticulated shell model and the overall structural model containing the irregular single-layer reticulated shell separately. 3D3S steel structure design software is used as the main static model calculation software, and SAP2000 software is used as the verification static model calculation software. For variable loads, the basic natural period of the wind-induced vibration response is set to be greater than 0.25 seconds. The snow load is determined based on the location of the irregular single-layer reticulated shell. For seismic effects, the modal response spectrum method is used, which includes more than 30 modal vectors, and the seismic source is generated using random vibration. The initial imperfection for stability is set to 1 / 300, and the structural stability safety factor is greater than 4.2. For temperature effects, compressive and tensile temperature stresses are manually assigned.

[0050] S3: Select the static design calculation results that conform to the design specifications, and obtain the stress ratio of each node at 200; there may be more than one type of irregular single-layer reticulated shell structure with composite requirements, and all of these single-layer reticulated shell structures need to undergo subsequent verification processes.

[0051] S4: Select an irregular single-layer reticulated shell structure, and establish three-dimensional solid models of the parts where node 200 is located, such as the outline of the upper convex shell, the outline of the lower concave shell, or the edge of the irregular single-layer reticulated shell, using finite element analysis software. Mesh the three-dimensional solid models of the parts where node 200 is located, give the material of the three-dimensional solid models of the parts where node 200 is located, set the convergence criteria, and perform iterative calculations.

[0052] The iterative calculation here involves creating a 3D solid model of nodes 200 at different locations of the irregular single-layer reticulated shell using the finite element analysis software ANSYS. Solid elements SOLID185 are used, and each node 200 is meshed using free meshing to generate several tetrahedral elements. The given material is steel with an elastic modulus E = 2.06e. 5 N / mm; Poisson's ratio v = 0.3; yield strength is 345 MPa; the given convergence criterion is that the residual force is less than the allowable residual value and the displacement correction value does not exceed 0.5% of the incremental displacement.

[0053] like Figure 5As shown in Figure 8, it should be noted that node 200 includes ordinary node 201 and column top node 202; ordinary node 201 includes several components 100 and a first connecting part 203, the end of each component 100 is fixedly connected to two adjacent surfaces of the first connecting part 203; column top node 202 includes several components 100 and a column 204, the column 204 is used to support the single-layer reticulated shell, one end of each component 100 of column top node 202 is fixedly connected to the surface of the column 204 away from the ground, and the other end of each component 100 of column top node 202 extends outward in a direction away from the column 204. As a preferred embodiment, component 100 is a square steel tube with a rectangular cross-section; column 204 is a hollow steel tube. Although the components 100 shown in the figures have similar appearances, the horizontal width and wall thickness of the components 100 at different locations of node 200 in the irregular single-layer reticulated shell are not exactly the same.

[0054] like Figure 5 Combination Figure 6 As shown, the first connecting portion 203 includes a plurality of support plates 2031, one end of which is fixedly connected to each other, and the other end of which extends outward toward the direction away from the common end. Adjacent support plates 2031 are arranged at an angle. One end of each component 100 constituting the ordinary node 201 extends into the space between adjacent support plates 2031 and is fixedly connected to the adjacent end faces of two adjacent support plates 2031. The other end of each component 100 of the ordinary node 201 extends outward toward the direction away from the first connecting portion 203, and the angles at which each component 100 extends away from the first connecting portion 203 are not entirely the same. The number of support plates 2031 included in the first connecting portion 203 is the same as the number of components 100 it connects to. The adjacent support plates 2031 can provide sufficient contact area for the end faces of the components 100, giving the node sufficient strength. Compared to the solid steel balls conventionally used at node connections, the weight of the first connecting portion 203 is significantly reduced.

[0055] like Figure 7 and 8As shown, the column top node 202 also includes a plurality of second connecting portions 205 and a plurality of third connecting portions 206 disposed inside the column 204; the plurality of second connecting portions 205 extend horizontally along the radial direction of the column 204 and are fixedly connected to the inner surface of the column 204, and the ends of the second connecting portions 205 are correspondingly disposed with the ends of two non-adjacent components 100 near the column 204; the plurality of third connecting portions 206 are respectively located between the plurality of second connecting portions 205 and between the inner wall of the column 204 and the second connecting portions 205; the ends of the third connecting portions 206 near the inner surface of the column 204 are correspondingly disposed with the ends of two other non-adjacent components 100 near the column 204. The diagram illustrates a configuration where a second connecting portion 205 and several third connecting portions 206 are arranged inside the column 204. If two non-adjacent components 100 abut against the outer surface of the column 204, and the central axes of the two components 100 are coplanar, then the ends of the second connecting portions 205 will be correspondingly positioned on the inner surface of the column 204 at adjacent locations of the two components 100. If there is no such case where the central axes of the components 100 are coplanar, then two non-adjacent components 100 located in the extending direction of the second connecting portion 205 are selected, and the included angle between their central axes is greater than the included angle between the central axes of any other two non-adjacent components 100 connected to the column 204. The principle for setting the third connecting portions 206 is to give the third connecting portions 206 a larger surface area inside the column 204. Figure 8 A special case is illustrated where the central axes of two pairs of non-adjacent components 100 are located on two orthogonal planes, in which case the second connecting portion 205 and the third connecting portion 206 are also orthogonally arranged. The illustration shows two second connecting portions 205 and three pairs of third connecting portions 206, located between two second connecting portions 205 and between the inner wall of the column and the second connecting portions 205, respectively. The dashed arc in the illustration represents the end cap covering the top of the column 204.

[0056] The placement of columns 204 is designed to maximize the internal space available to buildings or structures. Therefore, when setting the columns 204 supporting the single-layer reticulated shell at the column top node 202, the following rules must be met simultaneously: 1) Each column 204 is offset inward by a certain distance along the outline of the flat reticulated shell that forms the irregular single-layer reticulated shell, and the closed shape formed by the sequential connection of the endpoints of the central axes of each column 204 protrudes outward; 2) The central axis of each column 204 is symmetrically positioned with respect to the longitudinal central plane of the bidirectional sine curve, and is close to... The distance between the central axes of adjacent columns 204 on the longitudinal center plane of the near-bidirectional sine curve is not less than the distance between the central axes of adjacent columns 204 on the longitudinal center plane away from the bidirectional sine curve; 3) If an elevated floor or equipment placement floor is set, columns 204 need to be set at the edge of the projection position of the elevated floor or equipment placement floor, and reinforcing beams connecting adjacent columns 204 are set between the side surfaces of each adjacent column 204; 4) The outer surface of the end of each column 204 away from the ground is fixedly connected to the ends of at least four different components 100. Figure 1 As shown, the reinforcing beams used here are H-beams, which serve both as reinforcements for column 204 and as the planar foundation for the elevated floor or equipment placement floor. The height of the H-beams can be selected from 300, 400, 450, 500, 600, 650, 700, and 750 mm as needed.

[0057] S5: Obtain the limit state deformation modes and load-displacement curves of each component 100 at the location of node 200, and verify whether the cross-sectional shape of component 100 meets the requirements.

[0058] S6: If any component 100 containing any node 200 does not meet the design specifications, repeat steps S1-S5; if all components containing all nodes 200 meet the design specifications, output the geometric parameters of each component 100 containing each node 200 of the irregular single-layer reticulated shell. The geometric parameters of each component 100 output here include the world coordinate system coordinates of each node, the axial length, axial width and wall thickness of each component 100.

[0059] The present invention will be further described in detail below with reference to specific embodiments.

[0060] S101: A straight component 100 is used as the main body of the irregular single-layer reticulated shell, and the cross-sectional shape of the component 100 is set as a rectangular tube; according to the structural characteristics of the bidirectional sine curve, the bidirectional sine curve is horizontally unfolded and combined with any one of the following: a square flat reticulated shell, a Schweidler-type flat reticulated shell, a three-dimensional grid flat reticulated shell, or a geodesic flat reticulated shell to form an irregular single-layer reticulated shell. Figure 1The projected dimensions of the irregular single-layer reticulated shell shown are 68m × 80m. The design conditions for the irregular single-layer reticulated shell and its overall structure are as follows: seismic fortification intensity: 8 degrees, 0.2g, Group 2; maximum horizontal seismic influence coefficient: 0.16; site category: Class III; basic wind pressure: 0.65 kN / m²; basic snow pressure: 0.3 kN / m²; snow distribution coefficient: 2.0; artificially given structural damping ratio; total building height: 18.35m; the first floor above ground is for sports-related auxiliary rooms with a floor height of 4.8m; the second floor above ground is for offices, meeting rooms, and supporting auxiliary rooms with a floor height of 3.9m.

[0061] S102: Obtain the dead load of the irregular single-layer reticulated shell, as well as the variable load, temperature effect, and seismic effect at the location of the irregular single-layer reticulated shell; perform static design calculations using static model calculation software.

[0062] For both the irregular single-layer reticulated shell model and the overall structural model containing the irregular single-layer reticulated shell, 3D3S steel structure design software was used as the main static model calculation software, and SAP2000 software was used as the verification static model calculation software. Geometric models of the irregular single-layer reticulated shell were established in different modeling software. During the design selection, the steel structure plan dimensions were input as 80m / 60m; the rise-to-span ratio was 4.98m / 30.6m; the grid size was 1.86m–3.74m, and the grid angle was greater than 30°; the edge members were four-sided supports of the steel structure; the deflection limits were 1 / 400 in the short direction and 1 / 200 for cantilever. For variable loads, the fundamental natural period of the wind-induced vibration response was set to be greater than 0.25 seconds; the snow load was determined based on the location of the irregular single-layer reticulated shell. For seismic loads, the modal response spectrum method is used, which includes more than 30 modal vectors. The seismic source is generated using random vibration. The initial imperfection for stability is set to 1 / 300, and the structural stability safety factor is greater than 4.2. For temperature loads, compressive and tensile temperature stresses are manually assigned. If the calculation results from two static model calculation software programs differ by more than 5%, recalculation is required, or the component parameters must be adjusted before recalculation. If the difference between the calculation results from the two static model calculation software programs is less than 5%, the constructed parameters are considered reliable.

[0063] Calculations using static model software show that the roof's strength, stiffness, and stability meet design specifications. The maximum deflection at mid-span is 88mm, with an allowable maximum deflection of 76.5mm, meeting requirements after cambering by 3 / 1000. Natural vibration periods: T1 = 0.9219, T2 = 0.8181, T3 = 0.6622. These three natural vibration periods correspond to three different natural vibration modes: T1 corresponds to the applied X-axis translational mode, T2 to the applied Y-axis translational mode, and T3 to the applied Z-axis torsional mode. The numerical value of the natural vibration period indicates the time required for vibration to cease after the applied natural vibration mode. The individual displacements obtained from the two static model calculation software programs are 1 / 497 and 1 / 492, referring to the displacement of the irregular single-layer reticulated shell. The overall displacements obtained from the two static model calculation software programs are 1 / 482 and 1 / 465, including not only the irregular single-layer reticulated shell but also the supporting structure beneath it. The calculated maximum deflection is 56 mm.

[0064] S103: Select static design calculation results that conform to the design specifications, and obtain the stress ratio of each node at 200 mm.

[0065] S104: Select an irregular single-layer reticulated shell structure, and establish three-dimensional solid models of the parts where node 200 is located, such as the outline of the upper convex shell, the outline of the lower concave shell, or the edge of the irregular single-layer reticulated shell, using finite element analysis software. Mesh the three-dimensional solid models of the parts where node 200 is located, give the material of the three-dimensional solid models of the parts where node 200 is located, set the convergence criteria, and perform iterative calculations.

[0066] The iterative calculation here involves creating a 3D solid model of nodes 200 at different locations of the irregular single-layer reticulated shell using the finite element analysis software ANSYS. Solid elements SOLID185 are used, and each node 200 is meshed using free meshing to generate several tetrahedral elements. The given material is steel with an elastic modulus E = 2.06e. 5 N / mm; Poisson's ratio v = 0.3; yield strength is 345 MPa; the given convergence criterion is that, under a given initial defect value, the strength stress, deflection value and comfort vibration frequency all converge.

[0067] The nodes mainly include ordinary node 201 and column top node 202. Finite element analysis is performed on the ordinary nodes, such as... Figure 9 As shown, after free meshing of ordinary nodes, the equivalent stress distribution of the component under a 1.0 times control load combination is as follows. Figure 10 As shown in Figure a, the load-displacement curve for the entire process is as follows: Figure 10 As shown in b. (As shown in...) Figure 11As shown, after free meshing of the column top nodes, the stress distribution of the member under a 2.6 times control load combination is as follows. Figure 12 As shown in Figure a, the load-displacement curve for the entire process is as follows: Figure 12 As shown in b. The results above indicate that the node fails later than the component.

[0068] S5: Obtain the limit state deformation modes and load-displacement curves of each component 100 at the location of node 200, and verify whether the cross-sectional shape of component 100 meets the requirements.

[0069] The component 100 used in this scheme includes alternative structures such as rectangular tubes of 400×180×5×5, 400×150×5×5, 400×120×5×5, and 400×250×8×8, the wall thickness of which can be adjusted as needed. The morphological analysis of the component is as follows:

[0070] 1. Select a 400×150×5×5 rectangular tube, set the stress ratio to 1.3, and select the maximum internal force under the combination of static and variable loads for this type of cross-section. Perform linear eigenvalue buckling analysis on the member. The buckling analysis results are as follows: Figure 13 As shown, the linear eigenvalue buckling coefficient indicates that buckling first occurs on the side of the member, and the buckling coefficient is relatively low. The eigenvalue buckling represents the upper limit of the system's stability bearing capacity; according to relevant regulations, a stability analysis considering nonlinear effects should also be performed. Based on the eigenvalue buckling coefficient, it can be determined that the member's bearing capacity does not meet the requirements.

[0071] The wall thickness was selected according to the height-to-thickness ratio specified in the code. Based on the limitations on the height-to-thickness ratio in the steel structure code, the wall thickness of the member was adjusted to 12mm, and the height-to-thickness ratio was 33.3. Linear eigenvalue buckling analysis was then performed on the member again, and the results are as follows: Figure 14 As shown; based on the linear eigenvalue buckling coefficient and buckling modes, the lowest-order buckling mode of the structure is overall buckling, and the buckling coefficient is relatively high. According to relevant regulations, a stability analysis considering nonlinear effects should also be performed. The limit state deformation modes and load-displacement curves for the stability analysis of the component with an adjusted wall thickness of 12 are shown below. Figure 15 As shown, the elastic process analysis shows that the safety factor of the ultimate bearing capacity of the current component is about 7, which meets the requirements.

[0072] If the wall thickness is taken according to the specification, it will affect the overall structure's economy. Therefore, the wall thickness is adjusted to 8mm, and linear eigenvalue buckling analysis is performed again. The buckling analysis results are as follows: Figure 16 As shown in the figure. From the linear eigenvalue buckling coefficient and buckling modes, it can be seen that the lowest-order buckling mode of the structure is overall buckling, and the buckling coefficient is relatively high. According to relevant regulations, a stability analysis considering nonlinear effects should also be performed. The limit state deformation modes and load-displacement curves for the stability analysis of the component with an adjusted wall thickness of 8 are shown in the figure. Figure 17As shown, the elastic process analysis shows that the safety factor of the ultimate bearing capacity of the current component is about 4.3, which meets the requirements.

[0073] 2. Still selecting a 400×150×5×5 rectangular tube, setting the stress ratio to 0.5, and selecting the maximum internal force under the combination of static and variable loads for this type of cross-section, a linear eigenvalue buckling analysis is performed on the member. The buckling analysis results are as follows: Figure 18 As shown; based on the linear eigenvalue buckling coefficient and buckling modes, the lowest-order buckling mode of the structure is local buckling. According to relevant regulations, a stability analysis considering nonlinear effects should also be performed. The stability analysis of this component under the current stress ratio is as follows: Figure 19 As shown in the figure, the ultimate bearing capacity safety factor of the component is approximately 8.9, which meets the requirements.

[0074] S6: If the cross-sectional dimensions of any member 100 containing any node 200, after repeated adjustments within the selectable range, still cannot meet the design specifications, then try replacing it with another irregular single-layer reticulated shell structure whose static design calculation results conform to the design specifications, and repeat steps S1-S5; if all members containing nodes 200 meet the design specifications, then output the geometric parameters of each member 100 containing each node 200 of the irregular single-layer reticulated shell. The geometric parameters of each member 100 output here include the world coordinate system coordinates of each node, the axial length, axial width, and wall thickness of each member 100. During output, each node and each member is numbered separately and output sequentially.

[0075] Through the above process, the components of the irregular single-layer reticulated shell and the whole can be modeled twice, namely geometric modeling and three-dimensional solid modeling, before the output rod structure. The appropriate irregular single-layer reticulated shell structure and its components can be selected, and the parameterized three-dimensional dimensions of each component and the world coordinate system coordinates of the geometric center of each node can be output, which greatly simplifies the workload of engineering design.

[0076] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A parametric design method for a single-layer reticulated shell with irregular multi-curved surfaces, characterized in that, Includes the following steps: S1: Based on the structural characteristics of the bidirectional sine curve, a straight component (100) is used as the main body of the irregular single-layer reticulated shell, and the cross-sectional shape of the component (100) is set; multiple nodes (200) are formed at the intersection of adjacent components (100); the sag, span, slenderness ratio, edge components (100) and deflection limit of the irregular single-layer reticulated shell are obtained according to the design requirements; S2: Obtain the dead load of the irregular single-layer reticulated shell, as well as the variable load, temperature effect, and seismic effect at the location of the irregular single-layer reticulated shell; perform static design calculations using static model calculation software; S3: Select the static design calculation results that conform to the design specifications, and obtain the stress ratio of each node (200) respectively; S4: Select the location of the node (200) on the contour of the upper convex shell, the contour of the lower concave shell, or the edge of the irregular single-layer reticulated shell. Establish a three-dimensional solid model of the location of the node (200) using finite element analysis software. Mesh the three-dimensional solid model of the location of the node (200). Given the material of the three-dimensional solid model of the location of the node (200), set the convergence criterion and perform iterative calculation. S5: Obtain the limit state deformation modes and load-displacement curves of each component (100) at the location of node (200) to verify whether the cross-sectional shape of component (100) meets the requirements. S6: If any component (100) where any node (200) is located does not meet the design specifications, repeat steps S1-S5; if all components where all nodes (200) are located meet the design specifications, output the geometric parameters of each component (100) where each node (200) of the irregular single-layer reticulated shell is located.

2. The parametric design method for a non-circular, multi-curved single-layer reticulated shell according to claim 1, characterized in that, Step S1 describes the use of a straight component (100) as the main body of a single-layer reticulated shell, based on the structural characteristics of a bidirectional sine curve. This involves horizontally unfolding the bidirectional sine curve and combining it with any one of the following: a square flat reticulated shell, a Schweidler-type flat reticulated shell, a three-dimensional grid flat reticulated shell, or a geodesic flat reticulated shell, to form an irregular single-layer reticulated shell. Each side of the irregular single-layer reticulated shell is a straight component (100), and the common ends of at least two different components (100) together form a node (200).

3. The parametric design method for a non-circular, multi-curved single-layer reticulated shell as described in claim 2, characterized in that, Step S2 involves using static model calculation software for static design calculations. This involves establishing geometric models of the irregular single-layer reticulated shell model and the overall structural model containing the irregular single-layer reticulated shell separately. 3D3S steel structure design software is used as the main static model calculation software, and SAP2000 software is used as the verification static model calculation software. For variable loads, the basic natural period of the wind-induced vibration response is set to be greater than 0.25 seconds. The snow load is determined based on the location of the irregular single-layer reticulated shell. For seismic effects, the modal response spectrum method is used, which includes more than 30 modal vectors, and the seismic source is generated using random vibration. The initial imperfection for stability is set to 1 / 300, and the structural stability safety factor is greater than 4.

2. For temperature effects, compressive and tensile temperature stresses are manually assigned.

4. The parametric design method for a non-circular, multi-curved single-layer reticulated shell as described in claim 3, characterized in that, Step S4 involves establishing three-dimensional solid models of the locations of nodes (200) using finite element analysis software, meshing the three-dimensional solid models of the locations of nodes (200), specifying the material of the three-dimensional solid models of the locations of nodes (200), setting convergence criteria, and performing iterative calculations. This involves establishing three-dimensional solid models of nodes (200) at different locations of the irregular single-layer reticulated shell using the finite element analysis software ANSYS, using solid element SOLID185, and generating several tetrahedral elements for each node (200) using free meshing. The given material is steel with an elastic modulus E = 2.06e. 5 N / mm; Poisson's ratio v = 0.3; yield strength is 345 MPa; the given convergence criterion is that the strength stress, deflection value and comfort vibration frequency converge simultaneously.

5. The parametric design method for a non-circular, multi-curved single-layer reticulated shell according to claim 2, characterized in that, The node (200) includes a regular node (201) and a column top node (202); the regular node (201) includes several components (100) and a first connecting part (203), the end of each component (100) is fixedly connected to two adjacent surfaces of the first connecting part (203); the column top node (202) includes several components (100) and a column (204), the column (204) is used to support the single-layer reticulated shell, one end of the component (100) of each column top node (202) is fixedly connected to the surface of the column (204) away from the ground, and the other end of the component (100) of each column top node (202) extends outward in a direction away from the column (204).

6. The parametric design method for a non-circular, multi-curved single-layer reticulated shell according to claim 5, characterized in that, The component (100) is a square steel tube with a rectangular cross section; the column (204) is a hollow steel tube.

7. The parametric design method for a non-circular, multi-curved single-layer reticulated shell according to claim 6, characterized in that, The first connecting part (203) includes a plurality of support plates (2031), one end of which is fixedly connected to each other, and the other end of which extends outward toward the direction away from the common end. The adjacent support plates (2031) are arranged at an angle. One end of each component (100) constituting the ordinary node (201) extends into the space between the adjacent support plates (2031) and is fixedly connected to the adjacent end faces of the two adjacent support plates (2031). The other end of each component (100) of the ordinary node (201) extends outward toward the direction away from the first connecting part (203), and the angle at which each component (100) of the ordinary node (201) extends away from the first connecting part (203) is not exactly the same.

8. The parametric design method for a non-circular, multi-curved single-layer reticulated shell according to claim 7, characterized in that, The column top node (202) further includes a plurality of second connecting parts (205) and a plurality of third connecting parts (206) disposed inside the column (204); the plurality of second connecting parts (205) extend horizontally along the radial direction of the column (204) and are fixedly connected to the inner surface of the column (204), and the ends of the second connecting parts (205) are correspondingly disposed with the ends of two non-adjacent components (100) near the column (204); the plurality of third connecting parts (206) are respectively located between the plurality of second connecting parts (205) and between the inner wall of the column (204) and the second connecting parts (205); the ends of the third connecting parts (206) near the inner surface of the column (204) are correspondingly disposed with the ends of two other non-adjacent components (100) near the column (204).

9. The parametric design method for a non-circular, multi-curved single-layer reticulated shell according to claim 8, characterized in that, The angle between the central axes of two non-adjacent members (100) located in the extension direction of the second connecting part (205) is greater than the angle between the central axes of any other two non-adjacent members (100) connected to the column (204); the principle of setting the third connecting part (206) is to make the third connecting part (206) have a larger surface area inside the column (204).

10. The parametric design method for a non-circular, multi-curved single-layer reticulated shell according to claim 6, characterized in that, The arrangement of the columns (204) supporting the single-layer reticulated shell at the column top node (202) must simultaneously meet the following rules: 1) Each column (204) is offset inward by a certain distance along the outline of the flat reticulated shell that constitutes the irregular single-layer reticulated shell, and the closed shape formed by the sequential connection of the endpoints of the central axis of each column (204) is outwardly convex; 2) The central axis of each column (204) is symmetrically arranged with respect to the longitudinal center plane of the bidirectional sine curve, and the adjacent columns close to the longitudinal center plane of the bidirectional sine curve are also arranged in a manner that is consistent with the overall arrangement of the columns. The spacing between the central axes of (204) shall not be less than the spacing between the central axes of adjacent columns (204) on the longitudinal central plane away from the bidirectional sine curve; 3) If an elevated floor or equipment placement floor is set up, columns (204) shall be set up at the edge of the projection position of the elevated floor or equipment placement floor, and reinforcing beams connecting adjacent columns (204) shall be set up between the side surfaces of each adjacent column (204); 4) The outer surface of the end of each column (204) away from the ground shall be fixedly connected to the ends of at least four different components (100).

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