A 3D modeling method for concrete anchorage teeth blocks

Abstract

The present invention provides a three-dimensional modeling method for concrete anchorage blocks. First, a general initial wedge shape of the concrete anchorage block is defined, and then the initial wedge shape is calculated and constructed by using a digital integration algorithm. Finally, the final model of the anchorage block is obtained by performing a Boolean subtraction operation on the surrounding concrete body scanned according to the AABB bounding box of the initial wedge shape. By inputting key parameters, the spatial shape of the concrete anchorage block can be automatically drawn by the program, and the three-dimensional shape of the anchorage block can be visually presented, which can greatly improve the design efficiency of the three-dimensional design of the bridge and ensure the accuracy of the block structure.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge engineering, and in particular relates to a three-dimensional modeling method for a concrete anchoring tooth block. Technical Background

[0002] Concrete anchor blocks are widely used in the cable anchorage areas of various prestressed concrete bridges and cable-stayed bridges. They bear huge loads and transfer them to the entire structure, and are key load-bearing components. Therefore, in bridge design, the structure of anchor blocks is relatively complex, and their accurate drawing is particularly important.

[0003] Most of the conventional prestressed concrete box girder designs in China use two-dimensional drawings, and the anchor tooth blocks give specific parameters of the general structure. With this design method, designers cannot intuitively imagine the spatial shape of the anchor tooth blocks. With the development of three-dimensional digital design technology for bridges, three-dimensional bridge modeling is increasingly being used in design projects. Three-dimensional modeling software can be used to draw a three-dimensional bridge model. However, due to the complex structure of the anchor tooth blocks, coordinate rotation and positioning are required to be continuously used in the process of drawing the three-dimensional drawing. After drawing the overall shape, it is combined with the box girder for Boolean operations. The accuracy requirements of three-dimensional modeling are high. If the drawing process is not done well, it is easy to cause the Boolean operation to fail. There are many anchor tooth blocks in a bridge, especially for curved bridges. The angles of each anchor tooth block are different, which makes the drawing of the anchor tooth blocks complicated and cumbersome. Therefore, it is necessary to develop a concrete anchor tooth block modeling method based on parametric technology to provide assistance for three-dimensional bridge design, serve engineering design, and effectively improve design quality and efficiency. Summary of the invention

[0004] In order to solve the above problems, the present invention provides a three-dimensional modeling method for concrete anchoring tooth blocks. By inputting key parameters, the spatial shape of the concrete anchoring tooth blocks can be automatically drawn using a program, and the three-dimensional shape of the anchoring tooth blocks can be intuitively presented, which can greatly improve the design efficiency of the three-dimensional design of the bridge and ensure that the tooth block structure is accurate.

[0005] The technical problem to be solved by the present invention is achieved by adopting the following technical solutions:

[0006] A three-dimensional modeling method for concrete anchor tooth blocks is firstly defined, and then a general initial wedge of concrete anchor tooth blocks is calculated and constructed by using a digital integration algorithm. Finally, the final model of the anchor tooth block is obtained by performing a Boolean subtraction operation based on the AABB bounding box of the initial wedge and scanning the surrounding concrete body.

[0007] The concrete anchoring tooth blocks include cable beam anchoring tooth blocks arranged inside the main beam of the cable-stayed bridge, cable tower anchoring tooth blocks inside the main tower of the cable-stayed bridge, and prestressed anchoring tooth blocks inside the prestressed concrete box beam.

[0008] A general initial wedge of a concrete anchorage block, labeled V, is defined as follows Figure 1 as shown, i.e., V = {F, G, H, K1, K2}:

[0009] a) The anchorage plane F;

[0010] b) The anchorage top inclined plane G;

[0011] c) The anchorage bottom plane H;

[0012] d) The anchorage side surface K1;

[0013] e) The anchorage side surface K2.

[0014] The above-mentioned digital integration algorithm calculates and constructs the initial wedge. The characteristics of the algorithm are as follows:

[0015] (1) Define the geometric parameters of the anchorage block, including the angle σ between the anchorage plane F and the anchorage top inclined plane, the anchorage surface size S 1 , the top length L of the block 1 and L 2 , and the spatial curve equation C of the prestressed steel strand;

[0016] (2) Define the direction of the local coordinate system. According to the alignment of the prestressed steel strand, define the tangential direction of the end point O of the prestressed steel strand as the X-axis direction of the local coordinate system, that is, the normal direction of the anchorage plane F. The coordinate axes perpendicular to the X-axis of the local coordinate system are the Y-axis and the Z-axis respectively. Assume the direction vector of the X-axis is (X X , Y X , Z X ), the direction vector of the Y-axis is (X Y , Y Y , Z Y ), and the direction vector of the Z-axis is (X Z , Y Z , Z Z );

[0017] (3) Determine the anchorage plane F according to the normal direction X of the anchorage plane F. The anchorage plane F is perpendicular to the X-axis. The anchorage surface size is the size along the Y-axis direction of the local coordinate system. In the anchorage plane, with the steel strand end point O as the center, move a distance S 1 along the positive Y-axis direction and mark it as point P 1 . With point P 1 as the center, move a distance L 1 along the negative Z-axis direction and mark it as point P 2 . Move a distance L 2 along the positive Z-axis direction and mark it as point P 3 ;

[0018] (4) Define the included angle between the top inclined plane G of the tooth block and the anchoring plane F as σ. According to the structural requirements, σ ≥ 90°;

[0019] (5) Rotate the Y-axis around the Z-axis by an angle θ, where θ = σ - 90°, to obtain the normal vector Y1-axis of the anchoring top inclined plane G. Y1 = (X Y , Y Y , Z Y ) × M (Z,θ) , M (Z,θ) is the rotation matrix around the Z-axis.

[0020]

[0021] (6) Construct the anchoring top inclined plane G with point P 1 and the normal vector Y1-axis of the anchoring top inclined plane G. At this time, the anchoring top inclined plane G is an infinite plane passing through point P 1 ;

[0022] (7) Calculate the intersection point of the anchoring top inclined plane G and the prestressed steel bundle C, defined as point P 4 ;

[0023] (8) With P 4 as the center, move a distance L 1 along the negative direction of the Z-axis, marked as point P 5 , and move a distance L 2 along the positive direction of the Z-axis, marked as point P 6 ;

[0024] (9) Find the tangent T of the prestressed steel bundle through point P 4 . Take the cross product of the tangent T and the direction vector of the Z-axis to obtain the normal vector Y2-axis of the anchoring bottom plane H;

[0025] (10) Determine the anchoring bottom plane H according to point P 4 and the Y2-axis. At this time, the anchoring bottom plane H is an infinite plane passing through point P 4 ;

[0026] (11) Construct a ray R1(X R1 , Y R1 , Z R1 ) passing through point P 2 and along the negative direction of the local coordinate system Y-axis. Rotate the ray R1 around the X-axis by an angle α 2 with point P 1 as the center to obtain another ray R2 passing through point P 2 . is the rotation matrix around the X-axis.

[0027]

[0028] (12) The structure passes through point P 3 and along the ray R3 in the negative Y-axis direction of the local coordinate system (X R3 , Y R3 , Z R3 ), and rotates the ray R3 around the X-axis of the coordinate system by an angle α with point P 3 as the center to obtain another ray R4 passing through point P 2 . 3 point. is the rotation matrix around the X-axis.

[0029]

[0030] (13) Respectively obtain the intersection points of rays R3 and R4 with the anchoring bottom plane H, defined as points P 7 and P 8 ;

[0031] (14) According to the foregoing calculation results of points, connect the point set {P2, P7, P8, P3} counterclockwise to form the anchoring plane F, connect the point set {P2, P3, P6, P5} counterclockwise to form the anchoring top inclined plane G, connect the point set {P5, P7, P8, P6} counterclockwise to form the anchoring bottom plane H, connect the point set {P2, P7, P5} counterclockwise to form the anchoring side surface K1, connect the point set {P3, P8, P9} counterclockwise to form the anchoring side surface K2, and stitch the surface set {F, G, H, K1, K2} into a body to construct the initial wedge V of the concrete anchoring block.

[0032] The final model of the anchoring block is obtained by scanning the surrounding concrete body according to the AABB bounding box of the initial wedge of the anchoring block and performing a Boolean subtraction operation. The steps of the algorithm are as follows:

[0033] (1) Respectively obtain the AABB bounding boxes (i.e., Axially Aligned Bounding Boxes arranged according to the coordinate axes) of the initial wedge of the anchoring block and the surrounding concrete body. If the AABB bounding box of the concrete body intersects with the AABB bounding box of the initial wedge of the anchoring block, it is included in the concrete set {T1, T2,...};

[0034] (2) Respectively traverse the concrete set {T1, T2,...} obtained in step 1, and perform a Boolean subtraction operation with the anchoring block in turn to obtain the final body model of the anchoring block.

[0035] The beneficial technical effects of the present invention are:

[0036] (1) A three-dimensional modeling method for concrete anchorage teeth blocks of the present invention, by defining the geometric parameters of the anchorage teeth blocks, creatively using the mathematical principle of spatial vectors, accurately deriving and obtaining all the faces included in the initial wedge of the anchorage teeth blocks, and then using a collision detection algorithm AABB bounding box to scan the surrounding concrete body to perform a Boolean subtraction operation to obtain the final model of the anchorage teeth blocks.

[0037] (2) A three-dimensional modeling method for concrete anchorage teeth blocks of the present invention can automatically draw the spatial shape of the concrete anchorage teeth blocks by inputting key parameters, intuitively presenting the three-dimensional shape of the anchorage teeth blocks, which can greatly improve the design efficiency and ensure the accuracy of the teeth block structure.

[0038] (3) A three-dimensional modeling method for concrete anchorage teeth blocks of the present invention simplifies the drawing process of the anchorage teeth blocks, is convenient for designers to use, and at the same time improves the three-dimensional design efficiency of bridges, which is conducive to promoting the development of bridge three-dimensional design. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings;

[0040] Figure 1 is a schematic diagram of the initial wedge structure of the anchorage teeth block of the present invention;

[0041] Figure 2 is a schematic diagram of the key parameters of the anchorage teeth block of the present invention;

[0042] Figure 3 is a schematic diagram of the final model of the anchorage teeth block of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0043] In order to make the technical means, creative features, achieved purposes and effects of the present invention easy to understand, the present invention will be further clarified below with reference to specific embodiments.

[0044] Embodiment

[0045] A three-dimensional modeling method for concrete anchorage teeth blocks first defines a general initial wedge of the concrete anchorage teeth blocks, then uses a digital integration algorithm to calculate and construct the initial wedge, and finally performs a Boolean subtraction operation on the surrounding concrete body according to the AABB bounding box of the initial wedge to obtain the final model of the anchorage teeth blocks.

[0046] As Figure 1 shown, the initial wedge of the concrete anchorage teeth block, marked as V, is defined as as Figure 1As shown, i.e., V = {F, G, H, K1, K2}:

[0047] f) Anchoring plane F;

[0048] g) Anchoring top inclined plane G;

[0049] h) Anchoring bottom plane H;

[0050] i) Anchoring side surface K1;

[0051] j) Anchoring side surface K2.

[0052] Calculate and construct the initial wedge body through digital integration algorithm. The specific steps are as follows:

[0053] (1) Define the geometric parameters of the anchoring tooth block, including the included angle σ = 92° between the anchoring plane F and the anchoring top inclined plane, the anchoring surface size S 1 = 0.3m, the top length L 1 = 0.25m and L 2 = 0.25m, the spatial curve equation C of the prestressed steel strand;

[0054] (2) As Figure 1 shown, define the direction of the local coordinate system. According to the alignment of the prestressed steel strand, define the tangential direction of the end point O of the prestressed steel strand as the X-axis direction of the local coordinate system, that is, the normal direction of the anchoring plane F. The coordinate axes perpendicular to the X-axis of the local coordinate system are the Y-axis and the Z-axis respectively. Assume the direction vector of the X-axis is (X X , Y X , Z X ), the direction vector of the Y-axis is (X Y , Y Y , Z Y ), and the direction vector of the Z-axis is (X Z , Y Z , Z Z );

[0055] (3) As Figure 1 shown, determine the anchoring plane F according to the normal direction X of the anchoring plane F. The anchoring plane F is perpendicular to the X-axis, and the anchoring surface size is the dimension along the Y-axis direction of the local coordinate system. With the steel strand end point O as the center in the anchoring plane, move a distance S 1 = 0.3m along the positive Y-axis direction and mark it as point P 1 . With point P 1 as the center, move a distance L 1 = 0.25m along the negative Z-axis direction and mark it as point P 2 . Move a distance L 2 = 0.25m along the positive Z-axis direction and mark it as point P 3 ;

[0056] (4) Define the included angle between the top inclined plane G of the tooth block and the anchoring plane F as σ = 92°, meeting the structural requirement of σ ≥ 90°;

[0057] (5) Rotate the Y-axis around the Z-axis by an angle θ, where θ = σ - 90° = 92° - 90° = 2°, to obtain the normal vector Y1-axis of the anchoring top inclined plane G, and Y1 = (X Y , Y Y , Z Y ) × M (Z,θ) , where M (Z,θ) is the rotation matrix around the Z-axis, cos2° = 0.999, and sin 2° = 0.035

[0058]

[0059] (6) Construct the anchoring top inclined plane G with point P 1 and the normal vector Y1-axis of the anchoring top inclined plane G. At this time, the anchoring top inclined plane G is an infinite plane passing through point P 1 ;

[0060] (7) Calculate the intersection point of the anchoring top inclined plane G and the prestressed steel bundle C, defined as point P 4 ;

[0061] (8) With P 4 as the center, move along the negative Z-axis by a distance L 1 = 0.25m, marked as point P 5 , and move along the positive Z-axis by a distance L 2 = 0.25m, marked as point P 6 ;

[0062] (9) Find the tangent T of the prestressed steel bundle through point P 4 . Take the cross product of the tangent T and the direction vector of the Z-axis to obtain the normal vector Y2-axis of the anchoring bottom plane H;

[0063] (10) Determine the anchoring bottom plane H based on point P 4 and the Y2-axis. At this time, the anchoring bottom plane H is an infinite plane passing through point P 4 ;

[0064] (11) Construct a ray R1(X 2 , Y R1 , Z R1 ) passing through point P R1 and along the negative Y-axis of the local coordinate system. Rotate the ray R1 around the X-axis of the coordinate system by an angle α 2 = 1° with point P 1 as the center to obtain another ray R2 passing through point P 2 ; is the rotation matrix about the X-axis, cos 1° = 0.9998, sin 1° = 0.017,

[0065] (12) Construct a ray R3(X 3 , Y R3 , Z R3 ) passing through point P and along the negative Y-axis direction of the local coordinate system, and rotate the ray R3 about the X-axis of the coordinate system by an angle α R3 = 1° with point P as the center to obtain another ray R4 passing through point P 3 . 2 (13) Respectively obtain the intersection points of rays R3 and R4 with the anchoring bottom plane H, and define them as points P 3 and P is the rotation matrix about the X-axis, cos 1° = 0.9998, sin 1° = 0.017,

[0066] (14) According to the aforementioned calculation results of points, connect the point set {P2, P7, P8, P3} counterclockwise to form the anchoring plane F, connect the point set {P2, P3, P6, P5} counterclockwise to form the anchoring top inclined plane G, connect the point set {P5, P7, P8, P6} counterclockwise to form the anchoring bottom plane H, connect the point set {P2, P7, P5} counterclockwise to form the anchoring side K1, connect the point set {P3, P8, P9} counterclockwise to form the anchoring side K2, and sew the surface set {F, G, H, K1, K2} together to form a solid to construct the initial wedge V of the concrete anchoring tooth block. 7 and P 8 points;

[0067] (14) According to the aforementioned calculation results of points, connect the point set {P2, P7, P8, P3} counterclockwise to form the anchoring plane F, connect the point set {P2, P3, P6, P5} counterclockwise to form the anchoring top inclined plane G, connect the point set {P5, P7, P8, P6} counterclockwise to form the anchoring bottom plane H, connect the point set {P2, P7, P5} counterclockwise to form the anchoring side K1, connect the point set {P3, P8, P9} counterclockwise to form the anchoring side K2, and sew the surface set {F, G, H, K1, K2} together to form a solid to construct the initial wedge V of the concrete anchoring tooth block.

[0068] The final model of the anchoring tooth block is obtained by scanning the surrounding concrete body according to the AABB bounding box of the initial wedge of the anchoring tooth block and performing a Boolean subtraction operation. The steps of the algorithm are as follows:

[0069] (1) Respectively obtain the AABB bounding boxes (i.e., Axially Aligned Bounding Boxes arranged according to the coordinate axes) of the initial wedge of the anchoring tooth block and the surrounding concrete body. If the AABB bounding box of the concrete body intersects with the AABB bounding box of the initial wedge of the anchoring tooth block, include it in the concrete set {T1, T2,...};

[0070] (2) Traverse the concrete set {T1, T2,...} obtained in step 1 respectively, and perform a Boolean subtraction operation with the anchoring tooth block in turn to obtain the final solid model of the anchoring tooth block, as shown in Figure 3 .

[0071] The foregoing has shown and described the basic principles, main features and characteristics of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments, and what is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. A three-dimensional modeling method for concrete anchoring tooth blocks, characterized in that: firstly, a general initial wedge body of the concrete anchoring tooth block is defined, then the initial wedge body is calculated and constructed by using a digital integration algorithm, and finally, the final model of the anchoring tooth block is obtained by scanning the surrounding concrete body with the AABB bounding box of the initial wedge body and performing a Boolean subtraction operation; A general initial wedge body of the concrete anchoring tooth block, denoted as V, is defined as V = {F, G, H, K1, K2}: a) The anchoring plane F; b) The anchoring top inclined plane G; c) The anchoring bottom plane H; d) The anchoring side surface K1; e) The anchoring side surface K2; The digital integration algorithm has the following steps: (1) Define the geometric parameters of the anchorage tooth block, including the angle α between the anchorage plane F and the anchorage top inclined plane, where α≥90°, the anchorage surface size S 1 , the length L of the top of the tooth block 1 and L 2 , and the spatial curve equation C of the prestressed steel strand; (2) Define the direction of the local coordinate system. According to the alignment of the prestressed tendon, define the tangential direction of the end point O of the prestressed tendon as the X-axis direction of the local coordinate system, that is, the normal direction of the anchorage plane F. The coordinate axes perpendicular to the X-axis of the local coordinate system are the Y-axis and the Z-axis respectively. Assume that the direction vector of the X-axis is (X X , Y X , Z X ), the direction vector of the Y-axis is (X Y , Y Y , Z Y ), and the direction vector of the Z-axis is (X Z , Y Z , Z Z ); (3) Determine the anchoring plane F according to the normal X of the anchoring plane F. The anchoring plane F is perpendicular to the X-axis. The size of the anchoring surface is the dimension along the Y-axis of the local coordinate system. With the end point O of the steel strand as the center in the anchoring plane, move a distance S along the positive direction of the Y-axis 1 , and mark it as point P 1 . With point P 1 as the center, move a distance L along the negative direction of the Z-axis 1 , and mark it as point P 2 . Move a distance L along the positive direction of the Z-axis 2 , and mark it as point P 3 ; (4) Define the included angle between the anchoring top inclined plane G and the anchoring plane F as σ, where σ ≥ 90°; (5) Rotate the Y-axis around the Z-axis by an angle θ, where θ = σ - 90°, to obtain the normal vector Y1-axis of the anchoring top inclined plane G, and Y1 = (X Y , Y Y , Z Y ) × M (Z,θ) , where M (Z,θ) is the rotation matrix around the Z-axis. (6) With point P 1 Construct the anchoring top inclined plane G using the normal vector Y1 axis of point P and the anchoring top inclined plane G. At this time, the anchoring top inclined plane G is an infinite plane passing through point P 1 point; (7) Calculate the intersection point of the anchorage top inclined plane G and the prestressed steel bundle C, and define it as point P 4 Point; (8) Move a distance L in the negative Z-axis direction with P as the center 4 and mark it as point P 1 5 Move a distance L in the positive Z-axis direction 2 6 and mark it as point P 6 ; (9) Pass through point P 4 Find the tangent line T of the prestressed steel tendon passing through point P. Take the cross product of the direction vector of the tangent line T and the Z-axis to obtain the normal vector Y2-axis of the anchorage bottom plane H; (10) Determine the anchoring bottom plane H according to point P 4 Determine the anchoring bottom plane H with point P and the Y2 axis. At this time, the anchoring bottom plane H is an infinite plane passing through point P 4 and is an infinite plane (11) The structure passes through point P 2 and along the ray R1(X R1 , Y R1 , Z R1 ) in the negative Y-axis direction of the local coordinate system. Rotate the ray R1 around the X-axis of the coordinate system by an angle α 2 with point P as the center to obtain another ray R2 passing through point P 1 . 2 is the rotation matrix around the X-axis, ​ (12) The structure passes through point P 3 and along the ray R3(X R3 , Y R3 , Z R3 ) in the negative Y-axis direction of the local coordinate system. Rotate the ray R3 around the X-axis of the coordinate system by an angle α 3 with point P as the center to obtain another ray R4 passing through point P 2 . 3 is the rotation matrix around the X-axis. (13) Find the intersection points of rays R3 and R4 with the anchoring bottom plane H respectively, and define them as point P 7 and P 8 points; (14) According to the results of the aforementioned calculated points, connect the point set {P2, P7, P8, P3} counterclockwise to form the anchoring plane F, connect the point set {P2, P3, P6, P5} counterclockwise to form the anchoring top inclined plane G, connect the point set {P5, P7, P8, P6} counterclockwise to form the anchoring bottom plane H, connect the point set {P2, P7, P5} counterclockwise to form the anchoring side surface K1, connect the point set {P3, P8, P9} counterclockwise to form the anchoring side surface K2, and stitch the surface set {F, G, H, K1, K2} into a body to construct the initial wedge body V of the concrete anchoring tooth block.

2. The three-dimensional modeling method for concrete anchoring tooth blocks according to claim 1, characterized in that: The final model of the anchoring tooth block is obtained by scanning the surrounding concrete body with the AABB bounding box of the initial wedge body and performing a Boolean subtraction operation, and the steps are as follows: (1) Respectively obtain the AABB bounding boxes of the initial wedge body of the anchoring tooth block and the surrounding concrete body. If the AABB bounding box of the concrete body intersects with the AABB bounding box of the initial wedge body of the anchoring tooth block, it is included in the concrete set {T1, T2,...}; (2) Traverse the concrete set {T1, T2,...} obtained in step 1 respectively, and perform a Boolean subtraction operation with the anchoring tooth block in turn to obtain the final body model of the anchoring tooth block.

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