Containment prestressed steel beam parametric modeling method based on B-spline interpolation

Abstract

The invention belongs to the technical field of data processing and parameterized modeling, and particularly relates to a containment prestressed steel beam parameterized modeling method based on B-spline interpolation, which comprises the following steps of: determining position information and shape parameters of each steel beam on an expanded drawing according to a design drawing of a containment prestressed steel beam; nodes of complex prestressed steel beams near an equipment gate and a hole opening are calculated; calculating a B spline primary function based on the nodes of the complex prestressed steel beam; coordinate interpolation of a vertical curve section part in the complex prestressed steel beam is achieved through a B-spline primary function, space coordinates are calculated, and a three-dimensional space coordinate point set of the prestressed steel beam is generated; based on a secondary development function of the ABAQUS, a Python script is compiled to realize parametric modeling and automatic numbering of the prestressed steel beam, so that a three-dimensional model of the prestressed steel beam is established. According to the method, coordinate interpolation of the prestressed steel beam is achieved through a B-spline interpolation function, and secondary development of ABAQUS and parameterized modeling of the prestressed steel beam are achieved based on Python.

Description

Technical Field

[0001] The invention belongs to the technical field of data processing and parametric modeling, and in particular relates to a parametric modeling method for prestressed steel bundles of a containment shell based on B-spline interpolation. Background Art

[0002] Traditional modeling methods have certain limitations. In the traditional structural design and modeling process, structural engineers need to manually model according to the structural design plan. For some complex structures, or structures with a lot of repetitive work in the modeling process, manual modeling is inefficient. If the structural plan changes during the design process, it will lead to a large workload for modifying the model, a longer design cycle, and it is easy to make mistakes.

[0003] ABAQUS secondary development based on Python has superior modeling efficiency. ABAQUS / CAE is a finite element processing application of ABAQUS. It not only provides a graphical modeling and analysis platform, but also allows users to create scripts and graphical interfaces through Python-based secondary development to achieve automated pre- and post-processing and operation flow of finite element analysis. ABAQUS / CAE can convert user operations in the graphical interface into internal commands for execution, and write operations that need to be repeated as program scripts. Users can realize automated processing of the program by executing the script and setting and adjusting parameters.

[0004] There is a need for parametric modeling of the prestressed steel strands of the containment. The parametric design and modeling method can take all design elements as function variables, associate different variables through algorithms, and automatically establish a structural model after inputting parameters and debugging. Compared with traditional modeling methods, the parametric modeling method can significantly improve modeling efficiency and facilitate modification and adjustment of the model. Summary of the invention

[0005] The purpose of the present invention is to provide a parametric modeling method for prestressed steel bundles of a containment shell based on B-spline interpolation. The method utilizes B-spline interpolation function to realize coordinate interpolation of prestressed steel bundles, and realizes secondary development of ABAQUS and parametric modeling of prestressed steel bundles based on Python.

[0006] The technical solution to achieve the purpose of the present invention is:

[0007] A parametric modeling method for containment prestressed steel strands based on B-spline interpolation, the method comprising:

[0008] Step (1) determining the position information and shape parameters of each steel bundle on the development drawing according to the design drawing of the containment prestressed steel bundle;

[0009] Step (2) for the complex prestressed steel strands near the equipment gate and opening, calculate their nodes;

[0010] Step (3) calculating B-spline basis functions based on nodes of the complex prestressed steel tendons;

[0011] Step (4) uses B-spline basis functions to interpolate the coordinates of the vertical curve segment in the complex prestressed steel tendon, calculates the spatial coordinates, and generates a three-dimensional spatial coordinate point set of the prestressed steel tendon;

[0012] Step (5) Based on the secondary development function of ABAQUS, a Python script is written to realize the parametric modeling and automatic numbering of the prestressed steel strands, thereby establishing a three-dimensional model of the prestressed steel strands.

[0013] In the step (1), the position information and shape parameters are specifically as follows: for each prestressed steel strand, determine its elevation h and the angle θ at the two end points of the steel strand; for a complex prestressed steel strand, determine its bending circle radius r and arc length l, and then calculate the center angle α corresponding to the arc length.

[0014] The calculation formula of the central angle α is:

[0015]

[0016] In the step (2), the node calculation method is as follows: determine the starting node coordinates, intermediate node coordinates and end node coordinates of the complex prestressed steel strand according to the unfolded diagram; calculate the angle difference Δθ and elevation difference Δh of adjacent nodes according to the steel strand unfolding radius R, the circle radius r of each arc and the center angle α, and then calculate the coordinates of the intermediate nodes.

[0017] The calculation formula of the angle difference of the adjacent nodes is:

[0018]

[0019] The calculation formula of the elevation difference between adjacent nodes is:

[0020] Δh=r×(1-cosα).

[0021] In step (3), the calculation formula of the B-spline basis function is:

[0022]

[0023]

[0024]

[0025] Where S(x) is a univariate spline under the B-spline basis, B i,0(x) represents the i-th 0th degree B-spline basis function, B i,k (x) represents the i-th k-order B-spline basis function, c j represents the i-th node, t represents the node, t i represents the i-th node, t i+k Represents the i+kth node.

[0026] The step (4) is specifically as follows: using the B-spline basis function, after setting a reasonable k parameter value, the node vector is calculated; for the complex prestressed steel strand on the unfolded diagram, coordinate points are selected at a certain interval on the curve within the range from the starting node to the end node, and a point array of a smooth spline is calculated based on the B-spline basis function to realize the coordinate interpolation of the curve; for all nodes and insertion points, their spatial coordinates (Rcosθ, Rsinθ, h) are calculated, and then a three-dimensional spatial coordinate point set of the prestressed steel strand is created.

[0027] In the step (5), parametric modeling and automatic numbering of prestressed steel strands are realized, and the specific implementation steps are as follows:

[0028] Step (5.1) Import ABAQUS related packages and libraries into the Python script;

[0029] Step (5.2) Create a new model, viewport and assembly in the database and set the necessary parameters;

[0030] Step (5.3) analyzing the characteristics of the steel bundles and classifying the steel bundles;

[0031] Step (5.4) records the information such as the steel bundle number, endpoint coordinates, elevation, etc. in an Excel table and exports it to a csv format file;

[0032] In step (5.5), import the csv file in the script and create sketch and part;

[0033] Step (5.6) creates arcs and straight lines on the corresponding sketch according to the endpoint coordinates of each steel strand;

[0034] Step (5.7) According to the elevation information of each steel strand, select the corresponding sketch and perform translation operation to create an instance;

[0035] Step (5.8) merges all instances into one part and instance, and creates the vertical curve segment of the complex prestressed tendon;

[0036] Step (5.9) merges all instances into one instance, and deletes all instances other than the merged instance as well as sketches and parts that are no longer needed in the subsequent modeling process.

[0037] The beneficial technical effects of the present invention are:

[0038] 1. The present invention provides a parametric modeling method for prestressed steel bundles of a containment based on B-spline interpolation, which realizes rapid and accurate modeling of prestressed steel bundles of containments of similar reactor types according to the unfolded diagram of the prestressed steel bundles, which is of great significance for the calculation of containment structure performance, analysis of prestress loss of steel bundles, etc.

[0039] 2. A parametric modeling method for prestressed steel bundles of a containment shell based on B-spline interpolation is provided in the present invention. A Python script is written based on the secondary development function of ABAQUS, which realizes the parametric modeling and automatic numbering of prestressed steel bundles, significantly reduces the probability of modeling errors, and improves the modeling quality.

[0040] 3. The parametric modeling method of the containment prestressed steel bundle based on B-spline interpolation provided by the present invention verifies the feasibility, calculation performance and accuracy of the method by designing numerical simulation tests, proving that the method has good application value in practical engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A flow chart of a method for parameterized modeling of containment prestressed steel strands based on B-spline interpolation provided by the present invention;

[0042] Figure 2 A top view of a prestressed steel strand in a parameterized modeling method for prestressed steel strands for containment based on B-spline interpolation provided by the present invention;

[0043] Figure 3 A schematic diagram of a B-spline curve of a vertical curve segment in a complex prestressed steel bundle in a parametric modeling method for prestressed steel bundles of a containment shell based on B-spline interpolation provided by the present invention.

[0044] Figure 4 The figure is an effect diagram of parametric modeling of prestressed steel bundles for containment using a parametric modeling method of prestressed steel bundles for containment based on B-spline interpolation provided by the present invention. DETAILED DESCRIPTION

[0045] The present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0046] The present invention provides a parametric modeling method for containment prestressed steel bundles based on B-spline interpolation, which can be applied to the rapid generation of a group of horizontal prestressed steel bundles. The horizontal prestressed steel bundles include steel bundles composed of arcs and straight lines and located at the same elevation, and also include complex steel bundles with vertical curve segments and points that are not at the same elevation. Each steel bundle is composed of an anchoring straight line segment in the buttress column and an arc segment in the cylinder body, wherein the complex prestressed steel bundle also includes a curve segment. To facilitate parameter setting when creating a steel bundle, the point at the center of the containment cylinder with an elevation of 0 is set as the origin O of the spatial coordinate system, and the clockwise direction (looking from top to bottom) is set as the positive direction to establish a cylindrical coordinate system. The expanded radius of the steel bundle plane is denoted as R.

[0047] like Figure 1 As shown, the parameterized modeling method of containment prestressed steel strands based on B-spline interpolation of the present invention comprises the following steps:

[0048] Step (1) Determine the position information and shape parameters of each steel strand on the development drawing according to the design drawing of the containment prestressed steel strand

[0049] In step (1), the position information and shape parameters that need to be determined mainly include: the elevation h of each prestressed steel strand, the starting angle θ start 、End point angle θ end ,like Figure 2 For complex prestressed steel tendons, such as Figure 3 As shown, the coordinates of the endpoints of the arc segment and the straight line segment can be calculated first, and then the bending circle radius r and arc length l of each vertical curve portion can be determined, and the central angle α of each curve segment can be calculated by the following formula:.

[0050]

[0051] Step (2) Calculate the nodes of the complex prestressed steel strands near the equipment gate and opening.

[0052] In step (2), the calculation method of the nodes is as follows: To calculate the node coordinates of the vertical curve part of the complex prestressed steel tendon, first determine the coordinates of the starting node (tangent point) (θ1, h1), the coordinates of the middle node (i.e., the lowest point) (θ4, h4), and the coordinates of the end node (tangent point) (θ7, h7) according to the unfolded diagram. Then, the angle difference Δθ and the elevation difference Δh of the adjacent nodes are calculated according to the unfolded radius R of the steel tendon, the radius r of each arc, and the center angle α, and then the coordinates of the middle node (θ2, h2); (θ3, h3); (θ5, h5); (θ6, h6) are calculated according to the following formula, as follows: Figure 3 shown.

[0053] The calculation formula for the angle difference between adjacent nodes is:

[0054]

[0055] The calculation formula for the elevation difference between adjacent nodes is:

[0056] Δh=r×(1-cosα).

[0057] Step (3) Calculate the B-spline basis function based on the nodes of the complex prestressed steel tendon

[0058] In step (3), the B-spline basis function is calculated by the following formula:

[0059]

[0060]

[0061]

[0062] Where S(x) is a univariate spline under the B-spline basis, B i,0 (x) represents the i-th 0th degree B-spline basis function, B i,k (x) represents the i-th k-order B-spline basis function, c j represents the i-th node, t represents the node, t i represents the i-th node, t i+k Represents the i+kth node.

[0063] Step (4) uses the B-spline basis function to interpolate the coordinates of the vertical curve segment in the complex prestressed steel tendon, calculates the spatial coordinates, and generates a three-dimensional spatial coordinate point set of the prestressed steel tendon.

[0064] In step (4), the B-spline basis function is used to realize the coordinate interpolation of the vertical curve segment in the complex prestressed steel strand, and the spatial coordinates are calculated to generate the three-dimensional spatial coordinate point set of the prestressed steel strand. The specific steps are as follows: for a given node, after setting a reasonable k parameter value, the basis function is calculated. Among them, k represents the degree of spline fitting, and a larger k value can obtain a relatively smoother curve. The size of k can be adjusted according to actual needs. For the complex prestressed steel strand on the unfolded diagram, coordinate points are selected at a certain interval on the curve within the range from the starting node to the end node as the nodes of the B-spline basis function, and the smooth spline of the steel strand is calculated based on the B-spline basis function. To facilitate subsequent modeling, coordinate interpolation is realized based on the B-spline curve to obtain the insertion point set on the curve. For all nodes and insertion points, their spatial coordinates (Rcosθ, Rsinθ, h) are calculated to create a three-dimensional spatial coordinate point set of the prestressed steel strand.

[0065] Step (5) Based on the secondary development function of ABAQUS, write a Python script to realize the parametric modeling and automatic numbering of the prestressed steel tendons, thereby establishing a three-dimensional model of the prestressed steel tendons.

[0066] In step (5), parametric modeling and automatic numbering of prestressed steel tendons are realized. The specific implementation steps are as follows:

[0067] Step (5.1) imports ABAQUS related packages and libraries in the Python script.

[0068] Step (5.2) creates a new model, viewport and assembly in the database, and sets the necessary parameters: create a new model through the mdb.Model(name) method, where name defines the name of the model; create a new viewport using the session.Viewport(name, origin) method, where name and origin define the name and origin of the Viewport respectively, where origin is (0, 0); create an assembly through myModel.rootAssembly.

[0069] Step (5.3) Analyze the characteristics of the steel strands and classify them: In this step, they can be divided into two parts according to whether there are vertical curve segments in the steel strands - ordinary prestressed steel strands and complex prestressed steel strands. The former has all points at the same elevation, while the latter has some curve segments and its points are at different elevations. For ordinary prestressed steel strands, they can be classified according to their projections on the horizontal plane. The shape parameters of the same type of steel strands are the same but the elevations are different, so different instances can be created based on the same sketch. For complex prestressed steel strands, their arc segments and straight line segments can be created in the sketch, and the complex curve segments can be interpolated based on the B-spline basis function to create a spline.

[0070] Step (5.4) records the information such as the steel bundle number, endpoint coordinates, and elevation in an Excel table and exports it to a csv format file. In this step, the steel bundle is disassembled into different segments and recorded in different Excel sub-tables:

[0071] a.Arcs subtable: records the sketch name of the steel tendon and the horizontal coordinates of the nodes of the arc segment;

[0072] b. Lines subtable: records the sketch name of the steel strand and the horizontal coordinates of the nodes of the straight line segment;

[0073] c.Instances subtable: records the instance name (i.e., the steel bundle number), sketch name, and elevation information of the steel bundle;

[0074] d.Splines subtable: records the instance name of the steel tendon (i.e. the steel tendon number) and the three-dimensional spatial coordinates of the complex prestressed steel tendon.

[0075] Import the csv file in the script of step (5.5), and create sketch and part according to the recorded steel strand sketch name: Based on the created model, the ConstrainedSketch(name,sheetSize) method can be used to create a sketch, where name and sheetSize are used to define the name and size of the sketch respectively; the Part(name,dimensionality,type) method can be used to create a part, where name, dimensionality and type are used to define the name, dimension and type of the part respectively. It is worth noting that for ordinary prestressed steel strands, different instances of the same type of steel strand can be created based on the same sketch and part.

[0076] Step (5.6) Create arcs and lines on the corresponding sketch according to the horizontal coordinates of the nodes of each steel strand: Since the projections of all arcs on the plane have the same center, the ArcByCenterEnds(center, point1, point2) method can be used to create arcs, where center is the point (0,0), and point1 and point2 are the two end points of the arc (horizontal coordinates of the nodes). Line(point1, point2) method can be used to create a line, where point1 and point2 are the two end points of the line (horizontal coordinates of the nodes). After completing the creation of arcs and lines, use the BaseWire(sketch) method to create a plane wire for the part in the database using the given ConstrainedSketch object.

[0077] Step (5.7) According to the elevation information of each steel strand, select the corresponding sketch to perform the translation operation to create an instance: In this step, use Instance(name, part) to create a new instance based on the built assembly, where name and part are used to define the name and the part referenced when creating the instance. Use the translate(instanceList, vector) method to translate the created instance, where instanceList and vector define the instance name list and translation vector to be translated.

[0078] Step (5.8) merges all instances into one part and instance, and creates the vertical curve segment of the complex prestressed steel strand using the WireSpline(points) method based on the merged part, where points is the three-dimensional space coordinate point set of the vertical curve segment.

[0079] Step (5.9) merges all instances into one instance, and deletes all instances other than the merged instance, as well as sketches and parts that are no longer needed in the subsequent modeling process. The InstanceFromBooleanMerge(name, instances) method is used to merge instances, where name and instances define the name of the merged instance and the instances used for merging, respectively.

[0080] The method for parameterized modeling of containment prestressed steel strands based on B-spline interpolation provided by the present invention has realized program automation and rapidly generated the results of the horizontal prestressed steel strand partial model. Figure 4 shown.

[0081] The present invention is described in detail above with reference to the accompanying drawings and embodiments, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of ordinary technicians in the field without departing from the purpose of the present invention. The contents not described in detail in the present invention can adopt the existing technology.

Claims

1. A parametric modeling method for containment prestressed steel strands based on B-spline interpolation, characterized in that: The method comprises: Step (1) determining the position information and shape parameters of each steel bundle on the development drawing according to the design drawing of the containment prestressed steel bundle; Step (2) for the complex prestressed steel strands near the equipment gate and opening, calculate their nodes; Step (3) calculating B-spline basis functions based on nodes of the complex prestressed steel tendons; Step (4) uses B-spline basis functions to interpolate the coordinates of the vertical curve segment in the complex prestressed steel tendon, calculates the spatial coordinates, and generates a three-dimensional spatial coordinate point set of the prestressed steel tendon; Step (5) Based on the secondary development function of ABAQUS, a Python script is written to realize the parametric modeling and automatic numbering of the prestressed steel strands, thereby establishing a three-dimensional model of the prestressed steel strands.

2. A method for parameterized modeling of containment prestressed steel strands based on B-spline interpolation according to claim 1, characterized in that: In the step (1), the position information and shape parameters are specifically as follows: for each prestressed steel strand, determine its elevation h and the angle θ at the two end points of the steel strand; for a complex prestressed steel strand, determine its bending circle radius r and arc length l, and then calculate the center angle α corresponding to the arc length.

3. The method for parameterized modeling of containment prestressed steel strands based on B-spline interpolation according to claim 2 is characterized in that: The calculation formula of the central angle α is:

4. The method for parameterized modeling of containment prestressed steel strands based on B-spline interpolation according to claim 1 is characterized in that: In the step (2), the node calculation method is as follows: determine the starting node coordinates, intermediate node coordinates and end node coordinates of the complex prestressed steel strand according to the unfolded diagram; calculate the angle difference Δθ and elevation difference Δh of adjacent nodes according to the steel strand unfolding radius R, the circle radius r of each arc and the center angle α, and then calculate the coordinates of the intermediate nodes.

5. The method for parameterized modeling of containment prestressed steel strands based on B-spline interpolation according to claim 4 is characterized in that: The calculation formula of the angle difference of the adjacent nodes is:

6. The method for parameterized modeling of containment prestressed steel strands based on B-spline interpolation according to claim 4 is characterized in that: The calculation formula of the elevation difference between adjacent nodes is: Δh=r×(1-cosα).

7. The method for parameterized modeling of containment prestressed steel strands based on B-spline interpolation according to claim 1 is characterized in that: In step (3), the calculation formula of the B-spline basis function is: Where S(x) is a univariate spline under the B-spline basis, B i,0 (x) represents the i-th 0th degree B-spline basis function, B i,k (x) represents the i-th k-order B-spline basis function, c j represents the i-th node, t represents the node, t i represents the i-th node, t i+k Represents the i+kth node.

8. The method for parameterized modeling of containment prestressed steel strands based on B-spline interpolation according to claim 1 is characterized in that: The step (4) is specifically as follows: using the B-spline basis function, after setting a reasonable k parameter value, the node vector is calculated; for the complex prestressed steel strand on the unfolded diagram, coordinate points are selected at a certain interval on the curve within the range from the starting node to the end node, and a point array of a smooth spline is calculated based on the B-spline basis function to realize the coordinate interpolation of the curve; for all nodes and insertion points, their spatial coordinates (Rcosθ, Rsinθ, h) are calculated, and then a three-dimensional spatial coordinate point set of the prestressed steel strand is created.

9. The method for parameterized modeling of containment prestressed steel strands based on B-spline interpolation according to claim 1 is characterized in that: In the step (5), parametric modeling and automatic numbering of prestressed steel strands are realized, and the specific implementation steps are as follows: Step (5.1) Import ABAQUS related packages and libraries into the Python script; Step (5.2) Create a new model, viewport and assembly in the database and set the necessary parameters; Step (5.3) analyzing the characteristics of the steel bundles and classifying the steel bundles; Step (5.4) records the information such as the steel bundle number, endpoint coordinates, elevation, etc. in an Excel table and exports it to a csv format file; In step (5.5), import the csv file in the script and create sketch and part; Step (5.6) creates arcs and straight lines on the corresponding sketch according to the endpoint coordinates of each steel strand; Step (5.7) According to the elevation information of each steel strand, select the corresponding sketch and perform translation operation to create an instance; Step (5.8) merges all instances into one part and instance, and creates the vertical curve segment of the complex prestressed tendon; Step (5.9) merges all instances into one instance, and deletes all instances other than the merged instance as well as sketches and parts that are no longer needed in the subsequent modeling process.

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