3D printing method of self-supporting angle rotation curved concrete structure based on overhang effect

Abstract

The present invention discloses a 3D printing method for a rotational curved concrete structure based on the self-supporting angle of the overhang effect, which belongs to the field of 3D printing construction technology and includes the determination of the self-supporting angle based on the overhang effect and the 3D printing process of the rotational curved concrete structure. The method of the present invention can reduce additional supporting structures while ensuring the molding of components by rationally dividing the curved components, thereby improving printing efficiency and saving construction costs. The method of the present invention combines the principle of the overhang effect and finds the self-supporting angle of the structure through experiments to ensure the stability and accuracy of the printing process. The method is suitable for printing various types of rotational curved concrete components, and at the same time solves the problem that some curved surface structures are difficult or impossible to print directly, providing an innovative solution for the development of concrete 3D printing technology.

Description

Technical Field

[0001] The present invention belongs to the field of 3D printing construction technology, and specifically relates to a 3D printing method for a self-supporting angular rotation curved surface concrete structure based on the overhang effect. Background Art

[0002] In recent years, the application of rotationally curved concrete structures has been increasing. However, the traditional construction process of rotationally curved concrete structures is complex, requiring not only a large number of pre-set formwork but also extensive verification of the support system. This results in long construction periods, high costs, low formwork reuse, and significant labor and material resources. 3D printing construction technology, characterized by its formwork-free, intelligent, and efficient nature, has been gradually adopted in the 3D printing construction of rotationally curved concrete structures in recent years, addressing the challenges of customizing and pre-setting a large number of formwork, the high cost, and the significant environmental impact of these structures.

[0003] During the 3D printing process of rotating curved concrete structures, an overhang effect occurs, significantly impacting the structure's 3D printing process. The overhang effect refers to the phenomenon where a structure bends and deforms under its own weight, forming an overhanging curve. If the curvature of the curved structure changes, the structure should be cut off at the transition point, and each section should be studied separately to ensure the construction of the curved structure.

[0004] However, current 3D printing concrete construction technology still has problems when forming rotational curved concrete structures: first, if the tangent slopes at various points on the busbar of the rotating structure vary significantly, adverse phenomena such as lateral buckling, uneven settlement, and longitudinal cracks will occur during the printing of the structure; in addition, if the structural form is complex or there are large overhangs, the lower layer of concrete lacks sufficient strength to support the overhanging concrete part of the upper layer, which in turn causes deformation and collapse of the structure. Therefore, the current 3D printing construction process has the problem of excessive additional supports during printing and is difficult to manufacture, and it is still difficult to meet the construction requirements of high-quality, high-precision rotational curved concrete structures. In order to break through the bottleneck of curved concrete structure construction technology, a 3D printing method for rotational curved concrete structures based on the self-supporting angle of the overhang effect is proposed to achieve high-quality construction. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for 3D printing of self-supporting angle-rotating curved concrete structures based on the overhang effect, which can solve the problem of excessive additional supports and difficulty in manufacturing during 3D printing of rotating curved concrete structures, meet the construction requirements of high-quality and high-precision rotating curved concrete structures, and realize high-quality construction.

[0006] The technical solution adopted by the present invention to solve the technical problem is: a 3D printing method for rotating curved surface concrete structure based on the self-supporting angle of the overhang effect, including two processes: determining the self-supporting angle based on the overhang effect and 3D printing the rotating curved surface concrete structure;

[0007] The determination of the self-supporting angle based on the overhang effect is carried out according to the following steps:

[0008] 1) Model, slice, and print the target rotating curved surface concrete structure. Observe the process of defects appearing during continuous printing of the structure. When defects appear in the printed structure, causing the structure to be in a critical failure state, record the critical failure state of the structure and measure the vertical projection distance from the starting point where the serious defect appears. and horizontal projection distance ;

[0009] 2) Based on the critical failure state of the structure obtained in 1) and the measured data, draw a simplified diagram for calculating the self-supporting angle of the 3D printed structure in this state;

[0010] 3) Based on the calculation diagram obtained in 2), the starting point of the rotating structure busbar is point A, the ending point of the rotating structure busbar is point B, and the AB curve is fitted with point A as the origin to obtain the curve equation ;

[0011] The vertical projection distance obtained from 1) and horizontal projection distance , determine the coordinates of point A and point B in the calculation diagram obtained according to 2), which are A (0, 0) and B ( , ),

[0012] right Derivative, get the slope at point A and point B and the angle of the corresponding tangent 、 ,

[0013] ,

[0014] ,

[0015] From the geometric relationship, we can see that ,

[0016] ,

[0017] ,

[0018] At this time, the geometric analysis method This is the limit self-support angle under this working condition;

[0019] 4) According to the limit self-supporting angle obtained in 3) In order to ensure the high efficiency and accuracy of structure printing and the safety of the construction process, and to prevent the variability of the actual self-supporting capacity of 3D printed concrete from having a significant impact on the construction process, the self-supporting angle selected in the structure segmentation is not less than , and no more than ,Right now ;

[0020] The 3D printing of the rotating curved surface concrete structure is carried out according to the following steps:

[0021] 1) Structural analysis of the target rotational curved surface concrete structure is performed. Based on the slope changes of each point on the rotation generatrix of the target rotational curved surface concrete structure, the structure is divided into a conventional printing part and a part considering the overhang effect;

[0022] 2) For conventional printing parts, modeling and slicing can be performed directly; for parts considering the overhang effect, further division should be performed based on the location of the transition between the concavity and convexity, ensuring that the generatrix slope of each part is monotonically increasing or decreasing, so as to ensure the subsequent segmentation based on the self-supporting angle;

[0023] 3) Divide the part obtained in 2) into N modules of the same size with the rotation axis as the dividing line, N ≥ 2, and then select a module from each division scheme and perform the first self-support angle division respectively. The self-support angle should meet The dividing plane should be perpendicular to the tangent line of the point corresponding to the selected self-support angle on the busbar at the center of the module. In order to ensure that the bottom surfaces of the parts divided according to the self-support angle have no non-coplanar planes, and at the same time, the number of modules divided by the rotation axis as the dividing line is as small as possible, the smallest N value in which the first dividing plane does not intersect with the bottom surface of the module is selected as the dividing scheme;

[0024] 4) According to the division scheme determined in 3), the equally divided surface structure is divided, and the self-supporting angle of each specimen should meet ;

[0025] 5) Print and build the specimens obtained from the cutting process in step 4, embed connectors or reserve holes in the cross-sections, and then coat and cure after printing. After curing, place rebar or screws in the holes of the printed specimens, fill and connect them with epoxy resin or high-strength mortar, and complete the assembly of the curved structure.

[0026] Furthermore, in the step 1) of determining the self-supporting angle based on the overhang effect, the critical failure state of the structure should be recorded using high-precision equipment such as a high-speed camera.

[0027] Furthermore, in step 1) of the 3D printing of the rotational curved concrete structure, the curve of the conventional printing part is continuous and there is no deflection angle between two adjacent points, while the part considering the overhang effect has a deflection angle and a displacement difference between two adjacent points.

[0028] Furthermore, in step 2) of 3D printing the rotational curved concrete structure, the self-supporting angle is the angle between the perpendicular line of the tangent line of the starting endpoint of the curve and the tangent line of the ending endpoint of the curve. The self-supporting angle is used to measure whether the overhang effect will cause damage to the structure.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] The method of the present invention can reduce additional support structures while ensuring component molding by rationally dividing the curved surface components, thereby improving printing efficiency and saving construction costs. The method of the present invention combines the principle of the drape effect and finds the self-supporting angle of the structure through experiments to ensure the stability and accuracy of the printing process. The method is suitable for printing various types of rotating curved surface concrete components, and at the same time solves the problem that some curved surface structures are difficult or impossible to print directly, providing an innovative solution for the development of concrete 3D printing technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 A schematic diagram of the self-supporting angle analysis of the rotational curved concrete structure provided by the present invention based on the overhang effect;

[0032] Figure 2 A flow chart of 3D printing of a rotating curved concrete structure provided by the present invention;

[0033] Figure 3 Schematic diagram of the initial model of the uniform-thickness circular dome Y11 provided in Example 1 of the present invention;

[0034] Figure 4 Schematic diagram of the Y11 surface division of a circular dome of equal thickness provided in Example 1 of the present invention;

[0035] Figure 5 Schematic diagram of the Y11 curved surface sectioning of a circular dome of equal thickness provided in Example 1 of the present invention;

[0036] Figure 6 Schematic diagram of the printing process of Y31 in Example 1 of the present invention;

[0037] Figure 7 Schematic diagram of the initial model of the hyperbolic cylinder Z11 provided in Example 2 of the present invention;

[0038] Figure 8 Schematic diagram of the conventional printing portion and the portion taking into account the overhang effect of the hyperbolic cylinder Z11 provided in Example 2 of the present invention;

[0039] Figure 9 Schematic diagram of the division of the Z11 surface of the hyperbolic cylinder provided in Example 2 of the present invention;

[0040] Figure 10 Schematic diagram of the cut surface of the hyperbolic cylinder Z11 provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0041] The present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative work are within the scope of protection of the present invention.

[0042] Reference Figure 1 and Figure 2 , a 3D printing method for a rotational curved surface concrete structure based on a self-supporting angle of an overhang effect, including determining a self-supporting angle based on an overhang effect and a 3D printing process for a rotational curved surface concrete structure;

[0043] The determination of the self-supporting angle based on the overhang effect is carried out according to the following steps:

[0044] 1) Model, slice, and print the target rotating curved surface concrete structure. Observe the process of defects appearing during continuous printing of the structure. When defects appear in the printed structure, causing the structure to be in a critical failure state, record the critical failure state of the structure and measure the vertical projection distance from the starting point where the serious defect appears. and horizontal projection distance ;

[0045] 2) Based on the critical failure state of the structure obtained in 1) and the measured data, draw a simplified diagram for calculating the self-supporting angle of the 3D printed structure in this state;

[0046] 3) Based on the calculation diagram obtained in 2), the starting point of the rotating structure busbar is point A, the ending point of the rotating structure busbar is point B, and the AB curve is fitted with point A as the origin to obtain the curve equation ;

[0047] The vertical projection distance obtained from 1) and horizontal projection distance , determine the coordinates of point A and point B in the calculation diagram obtained according to 2), which are A (0, 0) and B ( , ),

[0048] right Derivative, get the slope at point A and point B and the angle of the corresponding tangent 、 ,

[0049] , ,

[0050] From the geometric relationship, we can see that ,

[0051] ,

[0052] ,

[0053] At this time, the geometric analysis method This is the limit self-support angle under this working condition;

[0054] 4) According to the limit self-supporting angle obtained in 3) In order to ensure the high efficiency and accuracy of structure printing and the safety of the construction process, and to prevent the variability of the actual self-supporting capacity of 3D printed concrete from having a significant impact on the construction process, the self-supporting angle selected in the structure segmentation is not less than , and no more than ,Right now ;

[0055] The 3D printing of the rotating curved surface concrete structure is carried out according to the following steps:

[0056] Step 101: Structural analysis is performed on the target rotational curved surface concrete structure. The structure is divided into a conventional printing portion and a portion considering the overhang effect based on the slope variation of each point of the rotation generatrix of the target rotational curved surface concrete structure. The conventional printing portion has a continuous curve with no deflection angle between two adjacent points, while the portion considering the overhang effect has a deflection angle and a displacement difference between two adjacent points.

[0057] Step 102-1: For conventional printing parts, modeling and slicing can be performed directly. Step 102-2: For parts considering the overhang effect, further division is performed based on the locations where the concavity and convexity transitions occur, ensuring that the generatrix slope of each part is monotonically increasing or decreasing, so as to ensure that subsequent slicing based on the self-supporting angle can be performed.

[0058] The self-support angle is the angle between the perpendicular line of the tangent line of the starting endpoint of the curve and the tangent line of the ending endpoint of the curve. The self-support angle is used to measure whether the overhang effect will cause damage to the structure.

[0059] Step 103: Divide the part obtained in step 102-2 into N (N≥2) modules of the same size with the rotation axis as the dividing line. Then select a module from each division scheme and perform the first self-support angle segmentation. The self-support angle should meet , the dividing plane should be perpendicular to the tangent of the point corresponding to the selected self-support angle on the busbar at the center of the module. In order to ensure that the bottom surfaces of the parts divided according to the self-support angle have no non-coplanar planes, and at the same time, the number of modules divided by the rotation axis as the dividing line is as small as possible, the smallest N value in which the first dividing plane does not intersect with the bottom surface of the module is selected as the dividing scheme; for example, in the division process of a certain actual structure, when N=3, the first dividing plane does not intersect with the bottom surface of the module, and the final division scheme is divided into three equal parts;

[0060] Step 104: According to the division scheme determined in step 103, the equally divided surface structure is divided. The self-supporting angle of each specimen should meet ;

[0061] Step 105: The specimens obtained by cutting in step 104 are printed and constructed in sequence, with pre-embedded connectors or reserved holes at the cross-sections. After printing, they are covered with a film and cured. After curing, the holes of the printed specimens are filled with steel bars or screws, and filled and connected with epoxy resin or high-strength mortar to complete the assembly of the curved structure.

[0062] Example 1

[0063] Reference Figures 3 to 6 This embodiment takes a circular dome Y11 of uniform thickness as an example to describe the determination of the self-supporting angle of the structure and the division, cutting, and printing process of the structure.

[0064] The test determination of the Y11 self-supporting angle of a circular dome of uniform thickness is carried out in the following steps:

[0065] 1) The uniform thickness circular dome Y11 was modeled, sliced, and printed. The process of defect occurrence during continuous printing of the structure was observed. When defects occurred in the printed structure, causing the uniform thickness circular dome to be in a critical failure state, the critical failure state of the uniform thickness circular dome was recorded. The vertical projection distance of the severe collapse point relative to the corresponding starting point was measured to be 17.3 cm and the horizontal projection height was 56.3 cm.

[0066] 2) Based on the Y11 critical failure state of the uniform-thickness circular dome obtained in 1), draw a simplified diagram for calculating the self-supporting angle of the 3D-printed structure under this state;

[0067] 3) Based on the calculation diagram obtained in 2), the starting point of the rotating structure busbar is point A and the ending point of the rotating structure busbar is point B. Then, the AB curve is fitted with point A as the origin to obtain the curve equation ;

[0068] According to 1), the vertical projection distance is 17.3 cm and the horizontal projection height is 56.3 cm. In the calculation diagram obtained according to 2), the coordinates of points A and B are determined as A (0, 0) and B (17.3, 56.3), respectively.

[0069] right Derivative, get the slope at point A and point B and the angle of the corresponding tangent 、 , ,

[0070] ,

[0071] ,

[0072] From the geometric relationship, we can see that ,

[0073] ,

[0074] ,

[0075] At this time, the geometric analysis method This is the limit self-support angle of the circular dome Y11 with equal thickness under this working condition;

[0076] 4) The self-supporting angle obtained from 3) In order to ensure the high efficiency and accuracy of Y11 printing of the uniform thickness circular dome and the safety of the construction process, the self-supporting angle selected in the structural segmentation is not less than , and no more than ,Right now In this embodiment, the self-supporting angle of the circular dome Y11 with equal thickness is selected as .

[0077] The 3D printing of the Y11 concrete structure of the uniform thickness circular dome is carried out in the following steps:

[0078] Step 101: Performing a structural analysis on the uniform-thickness circular dome Y11. Based on the deflection of the rotation generatrix of the uniform-thickness circular dome Y11, the uniform-thickness circular dome Y11 is divided into a conventional printing portion and a portion considering the overhang effect. The uniform-thickness circular dome Y11 has no conventional printing portion, and all portions are considered for the overhang effect.

[0079] Step 102: Based on the division results obtained in step 101, the portion of the uniform-thickness circular dome Y11 that takes into account the overhang effect is further divided with reference to the locations of the transition points of the concavity and convexity, ensuring that the generatrix slope of each portion is monotonically increasing (decreasing). Since the uniform-thickness circular dome Y11 does not have a transition point of concavity and convexity, no further division is required.

[0080] Step 103: Divide the part obtained in step 102 into N (N≥2) modules of the same size with the rotation axis as the dividing line, and then select a module from each division scheme to perform the first self-support angle segmentation. The self-support angle is , the dividing plane should be perpendicular to the tangent of the point corresponding to the selected self-support angle on the busbar at the center of the module. In order to ensure that the bottom surfaces of the parts divided according to the self-support angle have no non-coplanar planes, and at the same time, the number of modules divided by the rotation axis as the dividing line is as small as possible, the smallest N value in which the first dividing plane does not intersect with the bottom surface of the module is selected as the dividing scheme; in the division of the uniform thickness circular dome, when the curved surface structure is divided into three equal parts (N=3), the first dividing plane does not intersect with the bottom surface of the module, so the final division scheme is divided into three equal parts (N=3), that is, the uniform thickness circular dome Y11 is divided into three equal parts Y21, Y22, and Y23;

[0081] Step 104: Based on the division scheme determined in step 103, taking Y21 among the three equal parts Y21, Y22, and Y23 as an example, in this embodiment, the self-supporting angle of the equal-thickness circular dome Y11 is selected as ,satisfy , dividing the equally divided surface structure Y21;

[0082] Step 105: Print and construct according to the division scheme obtained in step 103 and the cutting scheme obtained in step 104; taking Y21 as an example, pre-embedded connectors or reserved holes are placed at the cross-sections of the circular dome specimens Y31, Y32, Y33, and Y34 in Y21, and the specimens are covered with a film and cured after printing. After curing, the holes of the printed circular dome specimens are filled with steel bars or screws and connected with epoxy resin or high-strength mortar to complete the assembly and forming of the uniform-thickness circular dome Y11.

[0083] Example 2

[0084] Reference Figures 7 to 10 This embodiment takes the hyperbolic cylinder Z11 as an example to describe the determination of the self-supporting angle of the structure and the division, cutting and printing process of the structure.

[0085] The test determination of the self-supporting angle of the hyperbolic cylinder Z11 is carried out in the following steps:

[0086] 1) Model, slice, and print the hyperbolic cylinder Z11. Observe the appearance of defects during continuous printing. When defects occur in the printed structure, causing the hyperbolic cylinder Z11 to reach a critical failure state, record the critical failure state of the hyperbolic cylinder Z11. The vertical projection distance of the severe collapse point relative to the corresponding starting point is measured to be 9.7 cm, and the horizontal projection height is 56.5 cm.

[0087] 2) Based on the critical failure state Z11 of the hyperbolic cylinder obtained in 1), draw a simplified diagram for calculating the self-support angle of the 3D printed structure under this state;

[0088] 3) Based on the calculation diagram obtained in 2), the starting point of the rotating structure busbar is point A and the ending point of the rotating structure busbar is point B. Then, the AB curve is fitted with point A as the origin to obtain the curve equation ;

[0089] Based on the vertical projection distance of 9.7 cm and the horizontal projection distance of 56.5 cm obtained in 1), the coordinates of points A and B are determined in the calculation diagram obtained in 2), which are A(0, 0) and B(9.7, 56.5), respectively.

[0090] right Derivative, get the slope at point A, point B and the angle of the corresponding tangent 、 ,

[0091] ,

[0092] ,

[0093] ,

[0094] From the geometric relationship, we can see that ,

[0095] ,

[0096] ,

[0097] At this time, the geometric analysis method This is the limit self-support angle of the hyperbolic cylinder Z11 under this working condition;

[0098] 4) The self-supporting angle obtained from 3) In order to ensure the high efficiency and accuracy of the printing of the hyperbolic cylinder Z11 and the safety of the construction process, the self-supporting angle selected in the structure segmentation should not be less than , and no more than ,Right now Therefore, in this embodiment, the self-supporting angle of the hyperbolic cylinder Z11 is selected as .

[0099] The 3D printing of the hyperbolic cylinder Z11 concrete structure is carried out in the following steps:

[0100] Step 101: Perform structural analysis on the hyperbolic cylinder Z11. Based on the deflection of the rotation generatrix of the hyperbolic cylinder Z11, the hyperbolic cylinder Z11 is divided into a conventional printing part and a part considering the overhang effect. Z22 is the conventional printing part, and Z21 and Z23 are the parts considering the overhang effect.

[0101] Step 102: Based on the division results obtained in step 101, the conventional printing part Z22 can be directly modeled and sliced. The parts Z21 and Z23 considering the draping effect are further divided with reference to the locations where the concavity and convexity transition occurs, ensuring that the generatrix slope of each part is monotonically increasing (decreasing). Since there is no concavity and convexity transition point in Z21 and Z23, no further division is required.

[0102] Step 103: Divide the part obtained in step 102 into N (N≥2) modules of the same size with the rotation axis as the dividing line, and then select a module from each division scheme to perform the first self-support angle segmentation. The self-support angle is The dividing plane should be perpendicular to the tangent line of the point corresponding to the selected self-support angle on the busbar at the center of the module. In order to ensure that the bottom surfaces of the parts divided according to the self-support angle have no non-coplanar planes, and at the same time, the number of modules divided by the rotation axis as the dividing line is as small as possible, the smallest N value in which the first dividing plane does not intersect with the bottom surface of the module is selected as the dividing scheme;

[0103] In the division of the hyperbolic cylinder Z11, when the surface structure is divided into two equal parts (N=2), the first dividing plane does not intersect with the bottom surface of the module. Therefore, the final division scheme is adopted, that is, Z21 is divided into two equal parts Z31 and Z32; Z23 is divided into two equal parts Z33 and Z34;

[0104] Step 104: Based on the division scheme determined in step 103, taking Z31 of the two equal parts Z31 and Z32 as an example, in this embodiment, the self-supporting angle of the hyperbolic cylinder Z11 is selected as ,satisfy , dividing the equally divided surface structure Z31;

[0105] Step 105: Print and build according to the division scheme obtained in step 103 and the segmentation scheme obtained in step 104. Taking Z31 as an example, pre-embed connectors or reserved holes are placed at the cross-sections of the hyperbolic cylinder specimens Z41, Z42, and Z43 in Z31. After printing, they are covered with a film and cured. After curing, steel bars or screws are placed in the holes of the printed hyperbolic cylinder specimens, which are then filled and connected with epoxy resin or high-strength mortar to complete the assembly of the hyperbolic cylinder Z11.

[0106] In summary, it can be concluded that the printing method provided by the present invention can realize the printing and construction of rotating concrete curved surface components.

[0107] It should be noted that the relevant printing parameters of the printing device in this embodiment are set according to the requirements of the relevant printing device. Any implementation methods not shown or described in the drawings or the main text of the specification are known to those skilled in the art and are not described in detail. In addition, the above definitions of the various components and methods are not limited to the various specific structures, shapes, or methods mentioned in the embodiments. Those skilled in the art may make simple modifications or substitutions. For example:

[0108] (1) The connections between the above-mentioned dividing and cutting structures can also be made by other connection methods such as clamps and bolts;

[0109] (2) Other high-precision recording methods can also be used to record the critical failure state during the self-support angle measurement experiment;

[0110] (3) Some steps in the above division method can be adjusted in order according to the actual printing situation;

[0111] (4) The above-mentioned cement-based materials may also use other materials such as gypsum, clay, geopolymers, etc.;

[0112] (5) This document may provide examples of parameters containing specific values, but these parameters do not need to be exactly equal to the corresponding values, but may be approximated to the corresponding values ​​within acceptable error tolerances or design constraints.

Claims

1. A 3D printing method for self-supporting angular rotation curved concrete structures based on the overhang effect, characterized by: It includes two processes: determining the self-supporting angle based on the overhang effect and 3D printing of the rotating curved concrete structure; The determination of the self-supporting angle based on the overhang effect is carried out according to the following steps: 1) Model, slice, and print the target rotating curved surface concrete structure. Observe the process of defects appearing during continuous printing of the structure. When defects appear in the printed structure, causing the structure to be in a critical failure state, record the critical failure state of the structure and measure the vertical projection distance from the starting point where the serious defect appears. and horizontal projection distance ; 2) Based on the critical failure state of the structure obtained in 1) and the measured data, draw a simplified diagram for calculating the self-supporting angle of the 3D printed structure in this state; 3) Based on the calculation diagram obtained in 2), the starting point of the rotating structure busbar is point A, the ending point of the rotating structure busbar is point B, and the AB curve is fitted with point A as the origin to obtain the curve equation ; The vertical projection distance obtained from 1) and horizontal projection distance , determine the coordinates of point A and point B in the calculation diagram obtained according to 2), which are A (0, 0) and B ( , ), right Derivative, get the slope at point A and point B and the angle of the corresponding tangent 、 , ， ， From the geometric relationship, we can see that , ， ， At this time, the geometric analysis method That is the limit self-support angle under this working condition, the limit self-support angle is the angle between the perpendicular line of the tangent to the starting endpoint of the curve and the tangent to the ending endpoint of the curve, ∠3 is the angle between the tangent to the starting endpoint of the curve and the horizontal line at the intersection of the perpendicular line and the tangent to the ending endpoint of the curve, and ∠4 is the angle between the perpendicular line of the tangent to the starting endpoint of the curve and the horizontal line at the intersection of the perpendicular line and the tangent to the ending endpoint of the curve; 4) According to the limit self-supporting angle obtained in 3) In order to ensure the high efficiency and accuracy of structure printing and the safety of the construction process, and to prevent the variability of the actual self-supporting capacity of 3D printed concrete from having a significant impact on the construction process, the self-supporting angle selected in the structure segmentation is not less than , and no more than ,Right now ; The 3D printing of the rotating curved surface concrete structure is carried out according to the following steps: 1) Structural analysis of the target rotational curved surface concrete structure is performed. Based on the slope changes of each point on the rotation generatrix of the target rotational curved surface concrete structure, the structure is divided into a conventional printing part and a part considering the overhang effect; 2) For conventional printing parts, modeling and slicing can be performed directly; for parts considering the overhang effect, further division should be performed based on the location of the transition between the concavity and convexity, ensuring that the generatrix slope of each part is monotonically increasing or decreasing, so as to ensure the subsequent segmentation based on the self-supporting angle; 3) Divide the part obtained in 2) into N modules of the same size with the rotation axis as the dividing line, N ≥ 2, and then select a module from each division scheme and perform the first self-support angle division respectively. The self-support angle should meet The dividing plane should be perpendicular to the tangent line of the point corresponding to the selected self-support angle on the busbar at the center of the module. In order to ensure that the bottom surfaces of the parts divided according to the self-support angle have no non-coplanar planes, and at the same time, the number of modules divided by the rotation axis as the dividing line is as small as possible, the smallest N value in which the first dividing plane does not intersect with the bottom surface of the module is selected as the dividing scheme; 4) According to the division scheme determined in 3), the equally divided surface structure is divided, and the self-supporting angle of each specimen should meet ; 5) Print and build the specimens obtained from the cutting process in step 4, embed connectors or reserve holes in the cross-sections, and then coat and cure after printing. After curing, place rebar or screws in the holes of the printed specimens, fill and connect them with epoxy resin or high-strength mortar, and complete the assembly of the curved structure.

2. The 3D printing method for self-supporting angle-rotated curved concrete structures based on the overhang effect according to claim 1 is characterized in that: In the step 1) of determining the self-supporting angle based on the overhang effect, the critical failure state of the structure should be recorded using high-precision equipment.

3. The 3D printing method for a self-supporting angle-rotated curved concrete structure based on the overhang effect according to claim 1 or 2, characterized in that: In step 1) of the 3D printing of the rotational curved concrete structure, the curve of the conventional printing part is continuous and there is no deflection angle between two adjacent points, while the part considering the overhang effect has a deflection angle and a displacement difference between two adjacent points.

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