CN115270263A - Method for quickly generating dome prestressed steel beam - Google Patents
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Abstract
The invention discloses a method for quickly generating a dome prestressed steel beam, which comprises the following steps of: determining geometric parameters according to the plane and elevation projection drawings of the steel beam; establishing a target function based on the least square thought to solve the circle center coordinates of three sections of curves of the plane projection when the curves are tangent at the same time, solving the intersection point coordinates and the curve equation of the three sections of curves according to the geometric relation equation of the circle center coordinates and the intersection point coordinates between the curves, and calculating the coordinates of each point on the plane projection surface according to certain interval increment; establishing a space equation set, substituting the plane projection coordinate point set into the space equation set, and determining a vertical coordinate corresponding to the projection coordinate point set, namely forming a three-dimensional space coordinate point set of the dome prestressed steel beam; and importing the space coordinate point set into a graph generation system to generate a three-dimensional model of the dome prestressed steel beam. The method can accurately and quickly model any type of reactor of the same type, and has great significance for the researches such as containment structure performance calculation, steel beam prestress loss analysis and the like.
Description
Technical Field
The invention belongs to the technical field of nuclear power, and particularly relates to a method for quickly generating a dome prestressed steel beam.
Background
The nuclear power safety is the central importance of nuclear power development, advanced nuclear power technology and nuclear power operation life prolonging put higher requirements on the service performance of a nuclear power plant structural facility during service, and the reliability of the structural performance of a containment serving as the most important barrier protection structure is very important. The structural mechanical properties of the containment vessel under various load working conditions are usually analyzed by adopting a finite element system, and the dome prestressed steel beam is time-consuming and tedious in the generation process due to the complexity of the form, and the change point cannot be accurately determined, so that the structural calculation accuracy is influenced.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method for quickly generating dome prestressed steel beams, which can accurately and quickly model any form of the same type of reactor and has great significance for the researches such as containment structure performance calculation, steel beam prestress loss analysis and the like.
In order to achieve the above purposes, the invention adopts the technical scheme that: the method for quickly generating the dome prestressed steel beam comprises the following steps:
1) Determining geometric parameters according to the plane and elevation projection drawings of the steel beam;
2) Establishing a target function based on the least square idea, establishing a plane projection curve equation set, and calculating a plane projection coordinate point set;
3) Establishing a space equation set, substituting the plane projection coordinate point set into the space equation set, and calculating a vertical coordinate corresponding to the plane projection coordinate point set, namely constructing a dome prestressed steel beam three-dimensional space coordinate point set;
4) And importing the three-dimensional space coordinate point set into a graph generation system to generate a dome prestressed steel beam three-dimensional model.
Further, in the method for quickly generating a dome prestressed steel beam as described above, in step 1), the geometric parameters to be determined are as follows:
11 From the horizontal projection view, determining the horizontal projection exit angle θ of the prestressed steel beam 1 Angle of deflection theta 2 The cylindrical surface radius R;
12 According to the vertical projection drawing, determining the radius R of the dome top part of the prestressed steel beam dome 1 The top part of the prestressed steel beam is divided into circle centers (0, z) 0 ) The inclination angle alpha of the prestressed steel beam and the maximum radius R of the prestressed steel beam distribution max Circle center (x) of second section of vertical face rotating reference steel beam 6 ，z 6 ) And radius R 2 And the exit angle theta of the vertical plane rotating reference steel beam 8 Vertical face rotating reference steel bundle section intersection point coordinate (x) 5 ，z 5 )、(x 7 ，z 7 )、(x 8 ，z 8 )。
Further, in the method for rapidly generating a dome prestressed steel beam as described above, in step 2), the method for calculating the plane projection coordinate point set includes:
21 Taking the center of the containment cylinder as the origin 0 of a space coordinate system, and establishing the space coordinate system xyz;
22 According to the position relation of tangency of the three-segment curves at the intersection point in the horizontal projection drawing, the coordinate of the intersection point of the first segment and the second segment is set as (x) 1 ，y 1 ) (ii) a The center of the second segment is (x) 0 ，y 0 ) (ii) a The coordinates of the intersection point of the second segment and the third segment are (x) 2 ，y 2 ) (ii) a The coordinates of the exit point of the third segment are (x) 3 ，y 3 )；
23 Establishing an objective function based on least square idea, and solving the circle center coordinate (x) when three curves are tangent at the same time 0 ，y 0 )；
24 According to the center coordinates (x) 0 ，y 0 ) Solving a three-section curve equation by using a geometric relation equation of the intersection point coordinates;
25 Starting from the initial coordinate, respectively calculating the y coordinate corresponding to the x coordinate at intervals of a certain preset value, and obtaining a plane projection coordinate point set.
Further, according to the method for quickly generating the dome prestressed steel beam, in the step 3), the radius R of the dome top part of the dome is determined according to the radius R of the dome top part 1 Vertical surface rotating second section radius R 2 The vertical face rotates the second circle center (x) 6 ，z 6 ) A third section of vertical rotation outlet angle theta 8 Coordinate of intersection (x) 5 ，z 5 )、(x 7 ，z 7 )、(x 8 ，z 8 ) And determining a vertical surface rotation space positioning equation of the prestressed steel beam.
Further, in the method for rapidly generating a dome prestressed steel beam as described above, in step 4), the graph generation system includes a CAD system.
The invention has the beneficial technical effects that:
1. the method for quickly generating the dome prestressed steel beam has great significance for the researches such as calculation of containment structure performance, analysis of steel beam prestress loss and the like by accurately and quickly modeling any reactor type of the same type by using plane and elevation projection drawings.
2. The method for quickly generating the dome prestressed steel beam is a method for solving a point cloud space coordinate set based on geometric information, and is convenient to use and strong in operability by programming and automating a calculation method and realizing accurate results.
3. According to the method, the accuracy and the calculation performance of the method are verified through designing the simulation model, and the feasibility of the method in the engineering environment is verified.
Drawings
FIG. 1 is a flow chart of a method for rapidly generating a dome prestressed steel beam according to the present invention;
FIG. 2 is a plan view of the dome prestressed steel beam of the present invention;
FIG. 3 is a plan view of the dome prestressed steel beam deflection angle positioning of the present invention;
FIG. 4 is a view of the dome prestressing steel beam elevation rotation datum line positioning of the present invention;
FIG. 5 is a view of the dome prestressed steel beam elevation rotation angle positioning of the present invention;
FIG. 6 shows a dome-shaped prestressed steel beam model in an embodiment of the method for rapidly generating dome-shaped prestressed steel beams according to the present invention;
FIG. 7 is a set of dome prestressed steel beam models in an embodiment of the method for rapidly generating dome prestressed steel beams according to the present invention;
fig. 8 shows a dome prestressed steel beam model in an embodiment of the method for rapidly generating a dome prestressed steel beam.
Detailed Description
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
The dome prestressed steel beams are divided into three groups, and each group of dome prestressed steel beam plane projection surface comprises three sections of curves, and each section of curve is an intersecting line of a steel beam forming surface. The first section is an intersection line of a plane which forms a certain inclination angle through the spherical center and the vertical plane of the dome top part and the steel bundle forming surface of the group, and the plane is parallel to the axis of the steel bundle group; the second section is an intersection line of a cylindrical surface with a certain radius and a steel bundle forming surface; the third section is an intersecting line of a cylinder axis of the safety shell or a vertical plane which does not pass through the cylinder axis and a steel beam forming plane. The intersection point of the first section of curve of each group of steel bundles and the horizontal plane is on a circle.
Each steel beam in each group of dome prestressed steel beams is on the same rotating surface, the vertical surface rotating datum line is composed of three sections of curves, and the sections are tangent at the intersection point. The first section is an arc section which takes the sphere center of the dome top as the center of a circle and takes the radius of the dome top as the radius; the second section is an arc section with a certain point as the center of a circle and a certain radius; the third segment is an oblique straight line segment tangent to the second segment at the point of intersection.
As shown in fig. 1, the method for rapidly generating the dome prestressed steel beam of the invention comprises the following steps:
1) Receiving a drawing; determining geometric parameters according to the plane and elevation projection drawings;
2) Establishing a target function based on the least square thought, establishing a plane projection curve equation set, and calculating a projection coordinate point set (establishing a circle center coordinate when the target function is established to solve three sections of curves of plane projection and are tangent at the same time based on the least square thought, solving an intersection point coordinate and a curve equation of the three sections of curves according to a geometric relation equation of the circle center coordinate and the intersection point coordinate between the curves, and calculating the coordinate of each point on a plane projection plane according to a certain interval increment);
3) Establishing a space equation set, and calculating a vertical coordinate corresponding to the projection coordinate point set, (substituting the projection coordinate point set into the space equation, and determining the vertical coordinate corresponding to the projection coordinate point set, namely forming a three-dimensional space coordinate point set of the dome prestressed steel beam);
4) And (3) introducing the space coordinate point set into a CAD system (not limited to the CAD system, but other systems can also be used) to generate a three-dimensional model of the dome prestressed steel beam.
In step 1), the geometric parameters to be determined are as follows:
11 Based on the plane projection, determining the plane projection exit angle theta of the prestressed steel beam 1 Angle of deflection theta 2 Cylinder radius R, as shown in fig. 2 and 3;
12 Determining the radius R1 of the top part of the prestressed steel beam sphere and the center (0, Z) of the top part of the prestressed steel beam sphere according to the elevation projection drawing 0 ) The inclination angle alpha of the prestressed steel beam and the maximum radius R of the prestressed steel beam distribution max Circle center (x) of second section of vertical face rotating reference steel beam 6 ，z 6 ) And radius R 2 And the exit angle theta of the vertical plane rotating reference steel beam 8 Vertical face rotating reference steel bundle section intersection point coordinate (x) 5 ，z 5 )、(x 7 ，z 7 )、(x 8 ，z 8 ) As shown in fig. 4 and 5.
In step 2), a specific calculation method for calculating the projection coordinates is as follows:
21 Taking the circle center of the containment cylinder as the origin 0 of a space coordinate system, and establishing a space coordinate system xyz;
22 According to the plane projection diagram, the position relation of tangency of the three sections of curves at the intersection point is added with an auxiliary line and a reference point, and the coordinate of the intersection point of the first section and the second section is set as (x) 1 ，y 1 ) The tangent at this point is L0, and L3 is perpendicular to L0 at this point; the center of the second segment is (x) 0 ，y 0 ) Any straight line passing through the circle center is L2; the coordinate of the intersection point of the second segment and the third segment is (x) 2 ，y 2 ) L4 is perpendicular to the tangent at that point; l1 is the straight line in which the third segment is located, and is also the point (x) at which the third segment is located 2 ，y 2 ) The coordinates of the exit point of the third segment are (x) 3 ，y 3 ) As shown in fig. 2.
23 Based on the least square idea, the specific calculation method for solving the center coordinates when three curves are tangent at the same time is as follows:
according to the distribution of the prestressed steel beam, the maximum radius R max Angle of exit theta 1 Denotes the coordinates (x) of the exit point 3 ，y 3 )；
And the third deflection angle of the prestressed steel beam is theta 2 According to theta 1 And theta 2 Determining the slope k of the straight line L1 1 ；
Assume that the equation for the straight line L1 is y = k 1 x+m 1 And point (x) 3 ，y 3 ) On a straight line, then: m is 1 ＝y 3 -k 1 x 3 ；
According to the point (x) 0 ，y 0 ) The distance from the straight line L1 is R, and y is obtained by combining the expression of the straight line L1 0 The expression of (1);
and point (x) 0 ，y 0 ) Located on the straight line L2: y = k 2 x+m 2 To obtain k 2 And k is 1 Relation of (1), m 2 And m 1 The relational expression of (1);
let the first section of curveThe ellipse equation of (a) is:
wherein, a t 、b t Are all R max Is represented by the formula (1);
the straight line L0 is the point (x) on the ellipse 1 ，y 1 ) Perpendicular to the line L3, and point (x) 1 ，y 1 ) On the arc segment, the straight line L3 passes through the center of the circle (x) 0 ，y 0 ). Obtaining a parameterized expression by combining an elliptic equation according to the relationship between the slopes of mutually perpendicular lines, so that the slope of the line L3 is a t /b t tanθ；
Let (x) 1 ，y 1 )＝(a t cosθ，b t sin θ) from the line L3 and the center (x) 0 ，y 0 ) Is solved for (x) 0 ，y 0 ) The expression of (1);
point (x) 0 ，y 0 ) The distance to the ellipse is:
in order to determine the coordinates of the circle center when the circular arc section with the radius R and the elliptical section are tangent to the straight line section at the same time, the following objective function is defined: minf (theta) = (d) 2 -R 2 ) 2 The constraint condition is 0-pi/2;
after theta is solved according to the objective function, the circle center coordinate (x) can be determined 0 ，y 0 ) The tangent point coordinate (x) of the first segment 1 ，y 1 )。
24 The specific calculation method for solving the three-segment curve equation according to the geometric relation equation of the center coordinates and the intersection coordinates is as follows:
is perpendicular to the straight line L1 according to the straight line L4, and the straight line L4 passes through the circle center (x) 0 ，y 0 ) Point (x) 2 ，y 2 ) On the straight line L4 and the straight line L1, simultaneous equations are solved to obtain a point (x) 2 ，y 2 ) The expression of (1);
to sum up, the plane orientation equation of the prestressed steel beam is shown as follows:
25 Starting from the initial coordinate, respectively calculating the y coordinate corresponding to the x coordinate at intervals (x-direction coordinate increment) of a certain preset value, and obtaining a plane projection coordinate point set.
In step 3), the specific calculation method of the three-dimensional space coordinate is as follows:
31 The specific calculation method for establishing the space equation is as follows:
according to the radius R of the dome part 1 A second vertical rotation radius R 2 The vertical surface rotates the second section circle center (x) 6 ，z 6 ) Vertical surface rotating third section outlet angle theta 8 Coordinate of intersection (x) 5 ，z 5 )、(x 7 ，z 7 )、(x 8 ，z 8 ) The vertical surface rotation space positioning equation of the prestressed steel beam is shown as the following formula:
wherein k is 8 ＝-tanθ 8 ，m 8 ＝z 8 -k 8 x 8
32 Substituting the projection coordinate point set obtained by calculation in the step two into the space equation of the A to solve the corresponding z coordinate, and obtaining the space coordinate point set of the dome prestressed steel beam.
The following will describe the steps of rapidly forming the dome prestressed steel bundle in detail with reference to fig. 1-5, taking one steel bundle of a group of (29) dome prestressed steel bundles as an example:
a. in step 1), the geometric parameters are determined: from fig. 2-3, the exit angle θ is determined 1 =54.375 ° and deflection angle θ 2 =13.5 °, cylinder radius R =6000; according to fig. 4-5, the radius R of the dome portion is determined 1 =2451, the center of the spherical top part (0, 31880), the bevel angle α =35.91 °, and the maximum radius R of the prestressed steel beam distribution max =19700 vertical face rotating referenceCenter of circle (x) of second segment of steel bundle 6 ，z 6 ) = (9755, 42621) and radius R 2 =10000, exit angle θ of vertical plane rotation reference steel bundle 8 =49.306 degrees and vertical plane rotating reference steel bundle intersection point coordinates (x) 5 ，z 5 )＝(16478，50024)、(x 7 ，z 7 )＝(17337，49141)、(x 8 ，z 8 )＝(19700，46390)。
b. In step 2), a circle center coordinate of the objective function when three curves are tangent at the same time is established based on the least square idea:
according to the distribution of the prestressed steel beam, the maximum radius R max Angle of exit theta 1 Determining the coordinates (x) of the exit point 3 ，y 3 )；
The third deflection angle of the prestressed steel beam is theta 2 According to theta 1 And theta 2 Determining the slope k of the straight line L1 1 ；
Assume that the straight line L1 equation is y = k 1 x+m 1 And point (x) 3 ，y 3 ) On a straight line, then: m is 1 ＝6082.05；
According to the point (x) 0 ，y 0 ) The distance from the straight line L1 is R, and y is obtained by combining the expression of the straight line L1 0 The expression of (1);
and point (x) 0 ，y 0 ) On the straight line L2: y = k 2 x+m 2 And (3) obtaining: k is a radical of 2 ＝0.8655，m 2 ＝14017.24；
The elliptic equation of the first section of curve is set as:
wherein, a t ＝19700，b t ＝14375.45；
Obtaining a parameterized expression, point (x), in combination with an elliptic equation 0 ，y 0 ) The distance to the ellipse is:
theta is more than or equal to 0 and less than or equal to pi/2Solving an objective function minf (theta) = (d) 2 -R 2 ) 2 To obtain the following solution: θ =1.327;
thereby obtaining the center coordinates (x) 0 ，y 0 ) And the tangent point coordinate (x) of the first segment 1 ，y 1 )；
Is perpendicular to the straight line L1 according to the straight line L4, and the straight line L4 passes through the circle center (x) 0 ，y 0 ) After obtaining the expression of the straight line L4, the (x) is obtained 2 ，y 2 )＝(10709，15351)；
In summary, the plane orientation equation of the dome prestressed steel beam is shown as follows:
and (3) solving a corresponding y coordinate by taking x =0 as a starting coordinate and 100 as an x-direction coordinate increment according to the equation set to obtain a plane projection plane coordinate point set.
c. In step 3), solving a prestressed steel beam vertical surface rotation space positioning equation according to the geometric parameters obtained in step 1), as shown in the following formula:
substituting the coordinate set (x, y) obtained in the step 2) into the equation set, and solving a corresponding z coordinate, namely forming a three-dimensional space coordinate point set (x, y, z) of the dome prestressed steel beam.
d. In step 4), the spatial coordinate point set (x, y, z) obtained in step 3) is imported into a CAD system, so as to generate a three-dimensional model of the single dome prestressed steel beam as shown in fig. 6.
The rapid generation method of the dome prestressed steel beam provided by the invention realizes program automation, takes a group of (29) steel beams as an example, and automatically generates a group of dome prestressed steel beam models, as shown in fig. 7. And assembling the three groups of steel beams to automatically generate the whole dome prestressed steel beam model, as shown in fig. 8.
The above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto. The technical solutions disclosed in the present invention and the inventive concept thereof are equivalent or changed by those skilled in the art, and the obtained technical solutions should be covered by the protection scope of the present invention.
Claims (5)
1. A method for quickly generating dome prestressed steel beams comprises the following steps:
1) Determining geometric parameters according to the plane and elevation projection drawings of the steel beam;
2) Establishing a target function based on the least square idea, establishing a plane projection curve equation set, and calculating a plane projection coordinate point set;
3) Establishing a space equation set, substituting the plane projection coordinate point set into the space equation set, and calculating a vertical coordinate corresponding to the plane projection coordinate point set, namely constructing a dome prestressed steel beam three-dimensional space coordinate point set;
4) And (4) importing the three-dimensional space coordinate point set into a graph generation system to generate a dome prestressed steel beam three-dimensional model.
2. The method for rapidly generating the dome prestressed steel beam as claimed in claim 1, wherein: in step 1), the geometric parameters to be determined are as follows:
11 From the horizontal projection view, determining the horizontal projection exit angle θ of the prestressed steel beam 1 Angle of deflection theta 2 A cylindrical surface radius R;
12 According to the vertical projection drawing, determining the radius R of the dome top part of the prestressed steel beam dome 1 The center of circle of the top part of the prestressed steel beam ball is (0, z) 0 ) The inclination angle alpha of the prestressed steel beam and the maximum radius R of the prestressed steel beam distribution max Circle center (x) of second section of vertical face rotating reference steel beam 6 ，z 6 ) And radius R 2 And the exit angle theta of the vertical-face rotating reference steel bundle 8 And the intersection point coordinates (x) of each section of the vertical face rotating reference steel bundle 5 ，z 5 )、(x 7 ，z 7 )、(x 8 ，z 8 )。
3. The method for rapidly generating the dome prestressed steel beam as claimed in claim 1, wherein: in step 2), the calculation method of the plane projection coordinate point set is as follows:
21 Taking the center of the containment cylinder as the origin 0 of a space coordinate system, and establishing the space coordinate system xyz;
22 The coordinate of the intersection point of the first and second segments is set as (x) according to the position relation of the tangency of the three segments of curves at the intersection point in the horizontal projection drawing 1 ，y 1 ) (ii) a The circle center of the second section is (x) 0 ，y 0 ) (ii) a The coordinates of the intersection point of the second segment and the third segment are (x) 2 ，y 2 ) (ii) a The coordinates of the exit point of the third stage are (x) 3 ，y 3 )；
23 Establishing an objective function based on least square thought, and solving the circle center coordinate (x) when three curves are tangent at the same time 0 ，y 0 )；
24 According to the centre coordinates (x) 0 ，y 0 ) Solving a three-section curve equation by using a geometric relation equation of the intersection point coordinates;
25 Starting from the initial coordinate, respectively calculating the y coordinate corresponding to the x coordinate at intervals of a certain preset value, and obtaining a plane projection coordinate point set.
4. A method for rapidly forming a dome prestressed steel strand as claimed in claim 1, wherein: in step 3), according to the radius R of the dome top part 1 Vertical surface rotating second section radius R 2 The vertical surface rotates the second section circle center (x) 6 ，z 6 ) Vertical surface rotating third section outlet angle theta 8 Coordinate of intersection point (x) 5 ，z 5 )、(x 7 ，z 7 )、(x 8 ，z 8 ) And determining a vertical surface rotation space positioning equation of the prestressed steel beam.
5. A method for rapidly forming a dome prestressed steel strand as claimed in claim 1, wherein: in step 4), the graph generation system comprises a CAD system.
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