Continuous wave single-layer suspended rigid net shell structure system and structure form finding method

Abstract

The application discloses a continuous wave single-layer suspended rigid reticulated shell structure system and a structure form-finding method, and relates to the technical field of building structures. The single-layer suspended reticulated shell structure system comprises internal main load-bearing beams, edge-sealing main load-bearing beams, an internal single-layer reticulated shell and support roof columns. The internal main load-bearing beams and the edge-sealing main load-bearing beams are in the shape of catenary lines, and the internal single-layer reticulated shell is in the shape of a suspended surface. The internal single-layer reticulated shell is fixedly connected with the main load-bearing beams to form a single-layer suspended reticulated shell structure system. A plurality of single-layer suspended reticulated shell structure systems are continuously connected to form a continuous wave single-layer suspended rigid reticulated shell structure system. The catenary line and the suspended surface are used to mathematically decompose the structure system. The structure components have excellent buckling stability under the action of vertical loads and wind suction loads. The structure system has low steel consumption and excellent mechanical properties and economic performance.

Description

Technical Field

[0001] This invention relates to the field of building structure technology, and in particular to a continuous wave-shaped single-layer suspended rigid reticulated shell structure system and a structural form-finding method. Background Technology

[0002] Current single-layer reticulated shell structures are spatial structural systems formed by arranging members regularly along a curved surface. Their stress characteristics are similar to thin-shell structures, primarily characterized by a "membrane" effect, meaning most loads are borne by the axial forces of the reticulated shell members. However, in practical engineering applications, due to the varying shapes of building surfaces, single-layer reticulated shell members inevitably experience bending moments, necessitating larger cross-sections. Furthermore, traditional single-layer reticulated shell structures, such as arched shells and spherical shells, exhibit predominantly compressive stress under vertical loads, leading to issues of overall structural stability and localized buckling of members. Based on these findings, a continuous wave-shaped single-layer suspended reticulated structure system is proposed, where members are primarily under tension under vertical loads. Summary of the Invention

[0003] The purpose of this invention is to provide a continuous wave-shaped single-layer suspended rigid reticulated shell structure system and a structural form-finding method. The system uses catenary and suspended surfaces for mathematical deconstruction. The structural components have superior buckling stability under vertical loads and wind suction loads. The structural system uses less steel and has excellent mechanical and economic performance.

[0004] This invention is achieved through the following technical solution:

[0005] A continuous wave-shaped single-layer cantilevered rigid reticulated shell structure system includes an internal main load-bearing beam, an edge-sealing main load-bearing beam, an internal single-layer reticulated shell, and supporting roof columns. The internal main load-bearing beam and the edge-sealing main load-bearing beam are both catenary-shaped, and the internal single-layer reticulated shell is a cantilevered surface. The internal single-layer reticulated shell and the main load-bearing beam are fixedly connected to form a single-layer cantilevered reticulated shell structure system. Several single-layer cantilevered reticulated shell structure systems are continuously connected to form a continuous wave-shaped single-layer cantilevered rigid reticulated shell structure system.

[0006] As a further improvement to the technical solution of this invention, the main load-bearing beam is a continuously curved catenary. The main control parameters of the hyperbolic cosine function describing the catenary include the elevation difference from the start point to the end point of the catenary, the horizontal projection distance from the start point to the end point, and the length of the catenary. The main load-bearing beam is defined as a catenary with a planar projection length L, an elevation difference Δh, and a true curve length l. An xoy rectangular coordinate system is established based on the lowest point of the catenary. Then, the equation of the catenary satisfies y(x)=1 / k[cosh(kx)-1], where k satisfies cosh(kL)-1=k 2 / 2(l 2 -Δh2 ).

[0007] As a further improvement to the technical solution of this invention, a Coons surface is formed by four closed catenary curves, and a single-layer suspended reticulated shell structure system is obtained through suspended shape finding. Specifically, the four closed catenaries constructed based on hyperbolic cosine functions are transformed into third-order high-order non-uniform rational B-spline curves (NURBS curves). Due to the characteristics of NURBS curves, NURBS curves with multiple control points can completely replace the curve characteristics of catenaries.

[0008] Furthermore, the mathematical function expression for constructing a bicubic Königs surface from four NURBS-curved catenaries is:

[0009]

[0010]

[0011] In the formula, C k (u) represents the curve shape of the surface in the direction of the node vector U, C l (v) represents the curve shape of the surface in the direction of the node vector V, N i，p (u) is the p-th order B-spline basis function determined by the node vector U, and the node vector U can be expressed as: N j，q (v) is the q-th order B-spline basis function determined by the node vector V, which can be expressed as:

[0012] Furthermore, the four vertices of the four closed catenary curves are taken as the intersection points of the closed curves, which are also the column points supporting the roof. The mathematical expression for the column points supporting the roof on the bicubic Königs surface is:

[0013] S 0,0 =C k＝0 (u=0)=C l＝0 (v=0)

[0014] S 1,0 =C k＝0 (u=1)=C l＝1 (v=0)

[0015] S 0,1 =C k＝1 (u=0)=C l＝0 (v=1)

[0016] S 1,1 =C k＝1 (u=1)=C l＝1 (v=1)

[0017] Furthermore, in a continuous wavy single-layer cantilevered rigid reticulated shell structure, adjacent cantilevered reticulated shells share a catenary-shaped boundary curve. Based on the wavy characteristics, at the catenary boundary, the two surfaces only cross the boundary C. 0 The transition should be continuous. The new surface formed by the combination of these adjacent curved surfaces will not be a smooth transition at the common boundary, but will have a crease, which matches the continuous wave shape of the roof.

[0018] Furthermore, the bicubic Königs surface can be defined as: S(u,v) = S1(u,b) + S2(u,v) - T(u,v), where: S1(u,v) is C k The cubic surface of (u), S2(u,v) is a C l The cubic surface of (v) is T(u,v), which is a cubic tensor product surface defined by 16 coefficient vectors. S(u,v) is a bicubic Kondratiev surface generated by the catenary boundary line.

[0019] As a further improvement to the technical solution of the present invention, the internal hanging grid of the continuous wave-shaped single-layer hanging grid structure system is a hanging curved surface shape, which is obtained by hanging the shape finding of the double cubic Kondratiev surface composed of 4 closed catenary curves.

[0020] As a further improvement to the technical solution of the present invention, the internal suspended grid structure system consists entirely of straight rods. Compared with the traditional flexible suspended beam structure, the internal suspended grid shell is a rigid structure, and the final grid shape is generated by straight rods that replace curves with straight ones.

[0021] As a further improvement to the technical solution of the present invention, the intersection of the multiple wave-shaped single-layer cantilever curved surfaces is the supporting roof column of the single-layer cantilever reticulated shell structure system, and the connection between the supporting roof column and the single-layer cantilever reticulated shell structure is fixedly connected by universal hinge support.

[0022] As a further improvement to the technical solution of the present invention, the internal suspended mesh shells are all rigid joints or assembled semi-rigid joints, and the internal suspended mesh shells and the main load-bearing beams are connected by fully bolted hinges or welded rigid joints.

[0023] As a further improvement to the technical solution of the present invention, the main load-bearing beams between adjacent suspended reticulated shells share a common catenary, and multiple single-layer suspended reticulated shells are combined to form a continuous wave-shaped single-layer suspended rigid reticulated shell structure system.

[0024] As a further improvement to the technical solution of this invention, a form-finding method for a continuous wave-shaped single-layer suspended rigid reticulated shell structure system includes the following steps:

[0025] Step S1: Extract the main load-bearing beam lines (non-catenary curves) of the building skin, and transform the main load-bearing beams into catenary curve forms based on the hyperbolic cosine function of the catenary.

[0026] Step S2: A bicubic Königs surface is constructed from four enclosed principal catenary lines. An initial mesh is generated based on this surface, and the initial mesh is discretized into a structural finite element model. It should be noted that for a triangular boundary surface formed by one edge-sealing principal beam and two internal principal beams, using only three sides to construct the Königs surface will cause condensation in a certain direction's parameter domain. To avoid this phenomenon, two internal principal beams are used to construct a spatial parallelogram, and the bicubic Königs surface is then constructed based on this spatial parallelogram.

[0027] Step S3: Constrain the main load-bearing beam nodes of one of the inner single-layer reticulated shells of the continuous wave-shaped initial single-layer reticulated shell, apply vertical loads to the inner reticulated shell nodes, and obtain the vertical displacement of the inner single-layer reticulated shell nodes.

[0028] Step S4: Iteratively find the shape of the internal single-layer shell nodes. The moving direction of the internal single-layer shell nodes is determined according to the balanced distance between the internal single-layer shell nodes and the initial building skin. The vertical upward or downward movement state of the internal nodes is determined according to the positive or negative value of the balanced distance. The moving length of each internal node is determined by combining the Monte Carlo method.

[0029] Step S5: To ensure the consistency between the curved surface after form finding and the initial building surface shape, the form finding target can be set to minimize the equilibrium distance between the internal single-layer shell node and the initial building skin. Other form finding targets such as bending strain energy ratio, total strain energy value, and vertical displacement can also be set. The specific form finding target settings can be determined in combination with the actual engineering requirements.

[0030] Step S6: Repeat steps S3 to S5 for each of the internal single-layer reticulated shells that form a continuous wave shape to obtain the suspended reticulated shell configuration of each internal single-layer reticulated shell. Multiple continuous suspended reticulated shells constitute a continuous wave-shaped single-layer suspended rigid reticulated shell structure system.

[0031] It should be specifically pointed out that the continuous wave-shaped single-layer suspended rigid reticulated shell structure system of this invention is a rigid structure. The form-finding method applied to flexible structures such as cable nets is not applicable to this structural system. This is mainly because there is bound to be bending strain energy inside the single-layer suspended reticulated shell structure. The purpose of form-finding the single-layer suspended reticulated shell structure is to find a structural shape that fits the rigid suspended reticulated shell, so as to minimize the proportion of bending strain energy in the structural system, improve the utilization rate of the single-layer reticulated shell and the economy of the overall structure.

[0032] The beneficial effects of this invention are:

[0033] This invention provides a continuous wave-shaped single-layer suspended rigid reticulated shell structure system. The single-layer suspended reticulated shell structure system includes an internal main load-bearing beam, an edge-sealing main load-bearing beam, and an internal single-layer reticulated shell. The internal main load-bearing beam and the edge-sealing main load-bearing beam are catenary-shaped, and the internal single-layer reticulated shell is a suspended surface. The internal single-layer reticulated shell and the main load-bearing beam are fixedly connected to form a single-layer suspended grid structure system. Several single-layer suspended grid structures are continuously connected to form a continuous wave-shaped single-layer suspended rigid grid structure system. This invention uses catenaries and suspended surfaces for mathematical deconstruction of the structural system. The structural components exhibit superior buckling stability under vertical loads and wind suction loads. The structural system uses less steel and has excellent mechanical and economic performance. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of a continuous wave-shaped single-layer suspended reticulated shell structure system according to an embodiment of the present invention;

[0035] Figure 2 This is a schematic diagram of the main control parameters of the hyperbolic cosine function of the catenary of the main load-bearing beam in an embodiment of the present invention;

[0036] Figure 3 This is a schematic diagram of the initial roof main load-bearing beam lines and building skin structure in an embodiment of the present invention;

[0037] Figure 4 This is one of the structural schematic diagrams of a main load-bearing beam formed by converting the initial main load-bearing beam lines into catenary lines in an embodiment of the present invention;

[0038] Figure 5 This is the second schematic diagram of the structure of the main load-bearing beam, which is formed by converting the initial main load-bearing beam lines into catenary lines in an embodiment of the present invention.

[0039] Figure 6 A schematic diagram of the double cubic Kondratiev surface of the main load-bearing suspension beam selected for an embodiment of the present invention;

[0040] Figure 7 This is a schematic diagram of the initial finite element mesh generation for a bicubic Königs surface according to an embodiment of the present invention;

[0041] Figure 8 This is a schematic diagram of a single-layer suspended reticulated shell structure system obtained through suspended form finding in an embodiment of the present invention;

[0042] Figure 9 This is a schematic diagram of a continuous wave-shaped single-layer suspended reticulated shell structure system composed of multiple continuous suspended reticulated shells, as described in an embodiment of the present invention.

[0043] Figure 10 This is a flowchart of a form-finding method for a continuous wave-shaped single-layer suspended rigid reticulated shell structure system according to an embodiment of the present invention.

[0044] Figure 11 This is a schematic diagram of a bicubic Königs surface constructed from four NURBS curves, as an embodiment of the present invention.

[0045] Figure 12 This is a schematic diagram of a bicubic Cowen surface generated by four closed catenary boundaries in an embodiment of the present invention.

[0046] In the attached diagram: 1-Internal main load-bearing beam; 2-Edge sealing main load-bearing beam; 3-Internal single-layer reticulated shell; 4-Structural column; A is a bicubic Königs surface; B is the initial internal mesh. Detailed Implementation

[0047] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions of the present invention are used to explain the present invention, but are not intended to limit the present invention.

[0048] It should be noted that all directional indicators (such as up, down, left, right, front, back, upper end, lower end, top, bottom, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicator will also change accordingly.

[0049] In this invention, unless otherwise explicitly specified and limited, the term "connection" should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral part; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0050] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature. Additionally, the technical solutions of various embodiments can be combined with each other, but only on the basis of being achievable by those skilled in the art. If the combination of technical solutions is contradictory or impossible to implement, such a combination should be considered non-existent and not within the scope of protection claimed by this invention.

[0051] like Figure 1 and Figure 4As shown, a continuous wave-shaped single-layer suspended rigid reticulated shell structure system includes a main load-bearing beam and an inner single-layer reticulated shell 3. Both the inner main load-bearing beam and the edge-sealing main load-bearing beam are catenary-shaped, and the inner single-layer reticulated shell 3 is a suspended surface. The inner single-layer reticulated shell 3 is fixedly connected to the main load-bearing beam to form a single-layer suspended reticulated shell structure system. Several single-layer suspended reticulated shell structures are continuously connected to form a continuous wave-shaped single-layer suspended rigid reticulated shell structure system. This invention uses catenaries and suspended surfaces for mathematical deconstruction of the structural system. The structural components exhibit superior buckling stability under vertical loads and wind suction loads. The structural system uses less steel and has excellent mechanical and economic performance.

[0052] Specifically, in this embodiment, the main load-bearing beam includes an internal main load-bearing beam 1 and an edge-sealing main load-bearing beam 2; both the internal main load-bearing beam 1 and the edge-sealing main load-bearing beam 2 are catenary-shaped.

[0053] Reference Figure 2 and Figure 3 Specifically, in this embodiment, the main load-bearing beam is a continuously curved catenary. The main control parameters of the hyperbolic cosine function describing the catenary include the elevation difference from the start point to the end point of the catenary, the horizontal projection distance from the start point to the end point, and the length of the catenary. The main load-bearing beam is defined as a catenary with a planar projection length L, an elevation difference Δh, and a true curve length l. An xoy rectangular coordinate system is established based on the lowest point of the catenary. The equation of the catenary then satisfies y(x)=1 / k[cosh(kx)-1], where k satisfies cosh(kL)-1=k 2 / 2(l 2 -Δh 2 ).

[0054] It should be noted that the main load-bearing beam is a continuously curved member forming a catenary shape. Since the main load-bearing beam is the primary tension member, high-strength steels such as Q420GJ and Q460GJ are considered for use to reduce the cross-sectional height and steel consumption of the main load-bearing beam.

[0055] Specifically, in this embodiment, a Coons surface is formed by four closed catenary curves, and a single-layer suspended reticulated shell structure system is obtained through suspended shape finding. Specifically, the four closed catenaries constructed based on hyperbolic cosine functions are transformed into third-order high-order non-uniform rational B-spline curves (NURBS curves). Due to the characteristics of NURBS curves, NURBS curves with multiple control points can completely replace the curve characteristics of catenaries.

[0056] Reference Figure 11 and Figure 12 Furthermore, the mathematical function expression for constructing a bicubic Königs surface using four NURBS-curved catenaries is as follows:

[0057]

[0058]

[0059] In the formula, C k (u) represents the curve shape of the surface in the direction of the node vector U, C l (v) represents the curve shape of the surface in the direction of the node vector V, N i，p (u) is the p-th order B-spline basis function determined by the node vector U, and the node vector U can be expressed as: N j，q (v) is the q-th order B-spline basis function determined by the node vector V, which can be expressed as:

[0060] Furthermore, the four vertices of the four closed catenary curves are taken as the intersection points of the closed curves, which are also the column points supporting the roof. The mathematical expression for the column points supporting the roof on the bicubic Königs surface is:

[0061] S 0,0 =C k＝0 (u=0)=C l＝0 (v=0)

[0062] S 1,0 =C k＝0 (u=1)=C l＝1 (v=0)

[0063] S 0,1 =C k＝1 (u=0)=C l＝0 (v=1)

[0064] S 1,1 =C k＝1 (u=1)=C l＝1 (v=1)

[0065] Furthermore, in a continuous wavy single-layer cantilevered rigid reticulated shell structure, adjacent cantilevered reticulated shells share a catenary-shaped boundary curve. Based on the wavy characteristics, at the catenary boundary, the two surfaces only cross the boundary C. 0 The transition should be continuous. The new surface formed by the combination of these adjacent curved surfaces will not be a smooth transition at the common boundary, but will have a crease, which matches the continuous wave shape of the roof.

[0066] Furthermore, the bicubic Königs surface can be defined as: S(u,v) = S1(u,v) + S2(u,v) - T(u,v), where: S1(u,v) is C k The cubic surface of (u), S2(u,v) is a C lThe cubic surface of (v), T(u,v) is a cubic tensor product surface defined by 16 coefficient vectors. The final bicubic Kondratiev surface generated by the catenary boundary line is as follows: Figure 11 As shown.

[0067] Specifically, in this embodiment, the internal suspended grid of the continuous wave-shaped single-layer suspended grid structure system is a suspended curved surface, which is derived from the bicubic Königs surface generated by the catenary linear main load-bearing beam connected to it.

[0068] Specifically, in this embodiment, the suspended curved surface of the internal suspended mesh shell has obvious fabric draping characteristics. The suspended curved surface is obtained by draping and shaping according to the bicubic Kondratiev surface. The internal suspended mesh structure system consists of straight rods. Compared with the traditional flexible suspended beam structure, the internal suspended mesh shell is a rigid structure, and the curved surface is generated by straight rods replacing curves.

[0069] Specifically, in this embodiment, the intersection of multiple wave-shaped single-layer cantilever curved surfaces is the supporting structural column 4 of the single-layer cantilever shell structure system, and the connection between the supporting roof column and the single-layer cantilever shell structure is fixedly connected by a universal hinge support.

[0070] Specifically, in this embodiment, the internal suspended mesh shells are all rigid joints or assembled semi-rigid joints, and the internal suspended mesh shells are connected to the main load-bearing beams by fully bolted hinges or welded rigid connections.

[0071] Specifically, in this embodiment, the internal suspended mesh shell is a suspended curved surface. The main control parameters describing the suspended curved surface are the projected area of ​​the suspended surface, the total area of ​​the suspended surface, the average height difference between the lowest suspended point and the corner point of the curved surface, and the average sag-to-span ratio.

[0072] Specifically, in this embodiment, the main load-bearing beams between adjacent waves share a common catenary, and multiple single-layer suspended mesh shells are combined to form a continuous wave-shaped single-layer suspended rigid mesh structure system.

[0073] Reference Figure 10 Specifically, in this embodiment, a form-finding method for a continuous wave-shaped single-layer cantilevered rigid reticulated shell structure system includes the following steps:

[0074] Step S1: Extract the main load-bearing beam lines (non-catenary curves) from the building facade. Based on the hyperbolic cosine function of the catenary curve, transform the main load-bearing beams into catenary curve forms, referring to... Figure 4 and Figure 5 ;

[0075] Step S2: A bicubic Königs surface is formed by four enclosed principal force catenaries, referring to... Figure 6Based on this surface, an initial mesh is generated, and the initial mesh is discretized into a structural finite element model, referring to... Figure 7 It should be noted that for a triangular boundary surface consisting of one main load-bearing beam and two internal main load-bearing beams, if only three sides are used to construct the Königs surface, it will cause condensation of the parameter domain in a certain direction. To avoid this phenomenon, two internal main load-bearing beams are used to construct a spatial parallelogram, and a bicubic Königs surface is then constructed based on the spatial parallelogram.

[0076] Step S3: Constrain the main load-bearing beam nodes of one of the inner single-layer reticulated shells of the continuous wave-shaped initial single-layer reticulated shell, apply vertical loads to the inner reticulated shell nodes, and obtain the vertical displacement of the inner single-layer reticulated shell nodes.

[0077] Step S4: Iteratively find the shape of the internal single-layer shell nodes. The moving direction of the internal single-layer shell nodes is determined according to the balanced distance between the internal single-layer shell nodes and the initial building skin. The vertical upward or downward movement state of the internal nodes is determined according to the positive or negative value of the balanced distance. The moving length of each internal node is determined by combining the Monte Carlo method.

[0078] Step S5: To ensure the consistency between the curved surface after form finding and the initial building surface shape, the form finding target can be set to minimize the equilibrium distance between the internal single-layer shell node and the initial building skin. Other form finding targets such as bending strain energy ratio, total strain energy value, and vertical displacement can also be set. The specific form finding target settings can be determined in combination with the actual engineering requirements.

[0079] Step S6: Repeat steps S3 to S5 for each internal single-layer reticulated shell constituting the continuous wave shape to obtain the overhanging reticulated shell configuration of each internal single-layer reticulated shell, referring to... Figure 8 Multiple continuous cantilevered reticulated shells form a continuous wave-shaped single-layer cantilevered rigid reticulated shell structure system, referring to... Figure 9 .

[0080] The beneficial effects of this invention are:

[0081] This invention proposes a continuous wave-shaped single-layer suspended grid shell structure system. The single-layer suspended grid structure system includes an internal main load-bearing beam 1, an edge-sealing main load-bearing beam 2, and an internal single-layer grid shell 3. The internal main load-bearing beam 1 and the edge-sealing main load-bearing beam 2 are catenary-shaped, and the internal single-layer grid shell 3 is a suspended surface. The internal single-layer grid shell 3 is fixedly connected to the main load-bearing beams to form a single-layer suspended grid structure system. Several single-layer suspended grid shell structures are continuously connected to form a continuous wave-shaped single-layer suspended rigid grid structure system. This invention uses catenaries and suspended surfaces for mathematical deconstruction of the structural system. The structural components exhibit superior buckling stability under vertical loads and wind suction loads. The structural system uses less steel and has excellent mechanical and economic performance.

[0082] The technical solutions provided by the embodiments of the present invention have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of the embodiments of the present invention. The descriptions of the embodiments above are only for helping to understand the principles of the embodiments of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the embodiments of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A continuous wave-shaped single-layer cantilevered rigid reticulated shell structure system, characterized in that: It includes an internal main load-bearing beam, an edge-sealing main load-bearing beam, an internal single-layer reticulated shell, and supporting roof columns; the internal main load-bearing beam and the edge-sealing main load-bearing beam are both catenary-shaped, the internal single-layer reticulated shell is a cantilevered surface, the internal single-layer reticulated shell is fixedly connected to the internal main load-bearing beam and the edge-sealing main load-bearing beam to form a single-layer cantilevered reticulated shell structure system, and several single-layer cantilevered reticulated shell structure systems are continuously connected to form a continuous wave-shaped single-layer cantilevered rigid reticulated shell structure system. The main load-bearing beam is a continuously curved catenary. The key control parameters describing the hyperbolic cosine function of the catenary include the elevation difference between the start and end points of the catenary, the horizontal projection distance between the start and end points, and the length of the catenary. The length of the main load-bearing beam projected from the plane is set. L elevation difference Δh The actual length of the curve is l The catenary is constructed based on the lowest point of the catenary. xoy In a rectangular coordinate system, the equation of the catenary satisfies y ( x )=1 / k [ cosh ( kx )-1], where k satisfy cosh ( kL ) -1 = k 2 / 2( l 2 - Δ h 2 ).

2. The continuous wave-shaped single-layer cantilevered rigid reticulated shell structure system according to claim 1, characterized in that: A Königs surface is formed by four closed catenary curves. A single-layer suspended reticulated shell structure system is obtained through suspended shape finding. The four closed catenaries, constructed based on hyperbolic cosine functions, are transformed into third-order high-order non-uniform rational B-spline curves. Due to the characteristics of NURBS curves, NURBS curves with multiple control points can completely substitute for the curve characteristics of the catenaries. The mathematical function expression for constructing a bicubic Königs surface from the four NURBS-curved catenaries is: In the formula, Represents the surface at the node vector The shape of the curve in the direction, Represents the surface at the node vector The shape of the curve in the direction, For node vectors Definite B-spline basis functions, nodal vectors It can be expressed as ; For node vectors Definite B-spline basis functions, nodal vectors It can be expressed as .

3. The continuous wave-shaped single-layer cantilevered rigid reticulated shell structure system according to claim 2, characterized in that: The internal suspended reticulated shell of the continuous wave-shaped single-layer suspended rigid reticulated shell structure system is a suspended curved surface shape, which is obtained by suspended shape finding based on the double cubic Kondratiev surface composed of 4 closed catenary curves.

4. The continuous wave-shaped single-layer cantilever rigid reticulated shell structure system according to claim 3, characterized in that: The four vertices of the four closed catenary curves are taken as the intersection points of the closed curves, which are also the column points supporting the roof. The mathematical expression of the column points supporting the roof on the bicubic Königs surface is: In a continuous wavy single-layer cantilevered rigid reticulated shell structure, adjacent cantilevered reticulated shells share a catenary-shaped boundary curve. Due to the wavy shape, the two surfaces only cross the boundary at the catenary line. The transition should be continuous. The new surface formed by the combination of these adjacent curved surfaces should not be a smooth transition at the common boundary, but rather there should be a crease, which matches the continuous wave shape of the roof. The bicubic Coönig surface can be defined as: ,in: yes cubic surfaces, yes cubic surfaces, It is a cubic tensor product surface defined by 16 coefficient vectors; It is a bicubic Kondratiev surface generated by the catenary boundary line.

5. The continuous wave-shaped single-layer cantilevered rigid reticulated shell structure system according to claim 1, characterized in that: The internal suspended grid structure system consists entirely of straight rods. Compared to the traditional flexible suspended beam structure, the internal suspended grid shell is a rigid structure, and the final grid shape is generated by straight rods that replace curves with straight ones.

6. The continuous wave-shaped single-layer cantilevered rigid reticulated shell structure system according to claim 1, characterized in that: The intersection of multiple wave-shaped single-layer cantilever curved surfaces forms the supporting roof column of the single-layer cantilever reticulated shell structure system. The supporting roof column is fixedly connected to the single-layer cantilever reticulated shell structure using universal hinge supports.

7. The continuous wave-shaped single-layer cantilevered rigid reticulated shell structure system according to claim 1, characterized in that: The internal suspended mesh consists of rigid joints or prefabricated semi-rigid joints, and the internal suspended mesh is connected to the main load-bearing beam by fully bolted hinges or welded rigid connections.

8. The continuous wave-shaped single-layer cantilevered rigid reticulated shell structure system according to claim 1, characterized in that: The main load-bearing beams between adjacent suspended grids share a common catenary, and multiple single-layer suspended grid shells are combined to form a continuous wave-shaped single-layer suspended rigid structural system.

9. A form-finding method for a continuous wave-shaped single-layer cantilevered rigid reticulated shell structure system, characterized in that, Includes the following steps: Step S1: Extract the main load-bearing beam lines of the building skin, and transform the main load-bearing beams into catenary forms based on the hyperbolic cosine function of the catenary. Step S2: A bicubic Königs surface is formed by four enclosed main load-bearing catenary lines. An initial mesh is generated on this surface, and the initial mesh is discretized into a structural finite element model. For a triangular boundary surface formed by one edge-sealing main load-bearing beam and two internal main load-bearing beams, if only three sides are used to form the Königs surface, it will cause condensation of the parameter domain in a certain direction. To avoid this phenomenon, two internal main load-bearing beams are used to construct a spatial parallelogram, and a bicubic Königs surface is then constructed based on the spatial parallelogram. Step S3: Constrain the main load-bearing beam nodes of one of the inner single-layer reticulated shells of the continuous wave-shaped initial single-layer reticulated shell, apply vertical loads to the inner reticulated shell nodes, and obtain the vertical displacement of the inner single-layer reticulated shell nodes. Step S4: Iteratively find the shape of the internal single-layer shell nodes. The moving direction of the internal single-layer shell nodes is determined according to the equilibrium distance of the internal single-layer shell nodes from the initial building. The vertical upward or downward movement state of the internal nodes is determined according to the positive or negative value of the equilibrium distance. The movement length of each internal node is determined by combining the Monte Carlo method. Step S5: To ensure the consistency between the curved surface after form finding and the initial building surface shape, the form finding target can be set to minimize the equilibrium distance between the internal single-layer shell node and the initial building skin. Other form finding targets such as bending strain energy ratio, total strain energy value, and vertical displacement can also be set. The specific form finding target settings can be determined in combination with the actual engineering requirements. Step S6: Repeat steps S3 to S5 for each of the internal single-layer reticulated shells that form a continuous wave shape to obtain the suspended reticulated shell configuration of each internal single-layer reticulated shell. Multiple continuous suspended reticulated shells constitute a continuous wave-shaped single-layer suspended rigid reticulated shell structure system.

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