CN117313208A - Modeling method of multi-layer spherical space grid structure system - Google Patents

Modeling method of multi-layer spherical space grid structure system Download PDF

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CN117313208A
CN117313208A CN202311296500.XA CN202311296500A CN117313208A CN 117313208 A CN117313208 A CN 117313208A CN 202311296500 A CN202311296500 A CN 202311296500A CN 117313208 A CN117313208 A CN 117313208A
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rod
ring
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radial
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陈伟刚
周观根
陈庆剑
俞春杰
钱伟江
陶志山
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Zhejiang Southeast Space Frame Co Ltd
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    • G06—COMPUTING; CALCULATING OR COUNTING
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Abstract

The invention relates to a modeling method of a multi-layer spherical space grid structure system, which belongs to the technical field of architecture and comprises the following operation steps: 1. firstly, inputting span, sagittal height and reticulated shell thickness parameters 2, calculating the spherical center position and spherical radius of the spherical reticulated shell through the parameters, and determining an upper chord plane and a lower chord plane. 3. The number of rings of the first-stage reticulated shell net is input, then the split forms of the radial rod pieces of the subsequent stages are input, and the number of each split form is input. 4. The edge number sequence of the ring-shaped polygons is obtained in a radial rod piece splitting mode, and the total number of the rings, the number of the polygons of each ring number and the like are calculated according to the edge number sequence. 5. And sequentially generating a vertical web member, an upper chord member, a lower chord member, a circumferential diagonal web member and a radial diagonal web member. 6. The rods at different positions are automatically divided into different layers. 7. Each rod is rotated through an angle to align the rod surface with the reticulated shell surface. 8. The result is output as a graphic or model file. The workload of generating the adjustment grids is saved, and the attractive appearance and the symmetry of grid division are considered.

Description

Modeling method of multi-layer spherical space grid structure system
Technical Field
The invention relates to the technical field of architecture, in particular to a modeling method of a multi-layer spherical space grid structure system.
Background
With the improvement of technology and the improvement of economy consciousness, the steel structure building with beautiful shape, reasonable stress and environmental protection is rapidly developed in the structural design field. The space grid structure has the characteristics of large span, light dead weight, strong flexibility, high strength, complex construction and the like, so that the space structure can create an open and wide internal space in building and engineering design, and a stable and efficient solution is provided.
The spherical space grid structure is a commonly used space grid structure type, and many design software and tools can provide a convenient generation mode of the spherical space grid structure. However, the grid division of the spherical space grid structure generated by the traditional software is not uniform, and the grid division is embodied in that the central area grid tends to be radially long and circumferentially short, and the peripheral area grid tends to be radially short and circumferentially long. After the spherical space grid structure is generated using conventional software, in order to make the grid size of each region uniform and the aspect ratio tends to be 1, it is often necessary to manually adjust the positions of grid nodes, merge and split the grid. This greatly affects the quality and efficiency of grid generation and further limits the applicability of spherical spatial grid structures. There is currently no spherical spatial grid structure generation tool suitable for generating a homogenized grid.
Disclosure of Invention
The invention mainly solves the defects existing in the prior art, and provides a modeling method of a multi-layer spherical space grid structure system, which has the characteristics of full-automatic grid generation, good grid uniformity, consistent rod length and no need of subsequent editing. And the chord layers and the web layer members are divided into different layers, so that the workload of generating an adjustment grid is saved, the attractive appearance and the symmetry of grid division are considered, and the processing and the production are facilitated.
The technical problems of the invention are mainly solved by the following technical proposal:
a modeling method of a multi-layer spherical space grid structure system comprises the following operation steps:
the first step: setting model control parameters of the spherical space grid structure, and controlling the positions (x 0, y0, z 0) of the centers of the spheres and the radius (R) of the spheres, wherein the positions of the centers of the spheres are x0, y0 and z0, so as to carry out coordinate values.
And a second step of: by the sphere center position and sphere radius, the sphere equation can be listed:
(x-x0) 2 +(y-y0) 2 +(z-z0) 2 ＝R 2 。
and a third step of: setting a span (L), chord layer thickness sequences (D1, D2, D3) of the space grid structure to be generated and a target value (S) of the rod length, wherein the target value of the rod length is the ideal rod length which is expected to be generated, and the target value is used as a target value for grid size adjustment.
Fourth step: initializing the number of segments (N1) =1 of radial meshing, and calculating a length representative value (L1) of the radial rod piece according to the number of segments (N1) of radial meshing, the spherical equation generated in the step 2 and the span input in the step 3 by the following formula:
fifth step: calculating the difference value (delta 1) between the length representative value (L1) of the rod piece and the rod length target value input in the third step, starting to iterate the radial grid division segment number (N1), and increasing the radial grid division segment number (N1) by 1 each time until the radial grid division segment number (N1) corresponding to the minimum delta 1 is found:
Δ1＝|L1-S|。
sixth step: initializing the number of segments (N2) =4 of the annular first ring network grid division, calculating a length representative value (L2) of the annular first ring rod piece according to the number of segments (N2) of the annular first ring network grid division, the number of segments (N1) of the optimal radial grid division obtained in the fifth step, the spherical equation generated in the step 2 and the span input in the third step, wherein the number of segments (N2) of the annular first ring network grid division is initialized to 4 by the following formula, and the generated grids are ensured to be symmetrical along the X axis and the Y axis:
seventh step: calculating the difference value (delta 2) between the length representative value (L2) of the rod piece and the rod length target value input in the third step, and starting to iterate the number (N2) of segments divided into the first ring network grid by the ring network:
Δ2＝|L2-S|。
eighth step: the number of segments (N2) divided by the first ring network grid in the ring direction expands the grid outwards according to 3 forms;
ninth step: according to the three split forms of the eighth step, the three calculation formulas of the length representative value (LI) of the ring rod of the ring are obtained by the ring serial Number (NI) and the number of segments (NIL) divided by the ring grid of the last ring:
tenth step: the difference (Δi) between the rod length representative value (LI) and the rod length target value input in step 3 is calculated by the following formula, preferably the minimum Δi corresponds to the grid split form:
ΔI＝|LI-S|。
eleventh step: repeating the eighth step to the tenth step, and continuously expanding the grid outwards until ni=n1 to obtain a complete grid of the chord layer 1 (see fig. 2) of the spherical space grid structure.
Twelfth step: calculating grid node coordinates (xN, yN, zN) corresponding to the chord layer N according to the node coordinates (x 1, y1, z 1) of the grid of the chord layer 1, the spherical center position (x 0, y0, z 0) input in the first step, the spherical radius (R) and the chord layer thickness sequence (D1, D2, D3) input in the third step:
thirteenth step: and generating web layer vertical rods, web layer annular rod members and web layer radial rod members according to the corresponding relation between each chord layer grid node and each chord layer grid node obtained in the twelfth step.
Fourteenth step: each chord layer rod piece (chord layer 1, chord layer 2, & chord layer N & gtchord layer), each web layer vertical rod, each web layer circumferential rod piece and each web layer radial rod piece are automatically divided into different layers.
Fifteenth step: and (3) automatically adjusting the azimuth of each rod piece to enable the plane formed by the 1 axis and the 2 axis of each rod piece to pass through the sphere center, and finally outputting the result as a graph or a model file.
Preferably, the span of the input should be smaller than the radius of the sphere, if the span of the input is larger than the radius of the sphere, this will result in no solution to the equation.
Preferably, the input target rod length is an ideal rod length, and the generated grid rod length is compared with the target rod length to determine the size and uniformity of grid division.
Preferably, the three forms expand the grid outwards, the corresponding rod splitting forms are not split, "1 part 2" and "2 part 3", and under the non-splitting form, the number of the annular rod pieces is the same as that of the previous annular rod piece, and the rod pieces at the node parts are in a cross shape. Under the form of '1 branch 2', the number of the annular rod pieces is 2 times of that of the annular rod pieces of the previous ring, each node of the previous ring is connected with 3 nodes of the ring, and the expansion diagram shows a 'wood' -shaped bifurcation. In the form of '2 min 3', the number of the annular rod pieces is 1.5 times of that of the annular rod pieces of the previous ring, half nodes of the previous ring are connected with two nodes of the previous ring, and a 'large' bifurcation is shown on an unfolding diagram; the other half nodes are connected with 1 node of the ring, and are in a ten-shaped bifurcation on the expansion diagram.
Preferably, in order to ensure that the grid generated after iteration is still symmetrical along the X axis and the Y axis, the number of segments (N2) divided into the first ring network grid is increased by 4 each time of iteration until the number of segments (N2) divided into the first ring network grid corresponding to the minimum Δ2 is found.
Preferably, the web side vertical rods are formed by connecting upper grid nodes and lower grid corresponding nodes; the web layer circumferential rod member is formed by connecting upper layer grid nodes and lower layer grid nodes with same ring adjacent nodes; the web layer radial rod member is formed by connecting an upper layer grid node and a lower layer grid outer ring with the same radial node.
The invention can achieve the following effects:
compared with the prior art, the modeling method of the multi-layer spherical space grid structure system has the characteristics of full-automatic grid generation, good grid uniformity, consistent rod length and no need of subsequent editing. And the chord layers and the web layer members are divided into different layers, so that the workload of generating an adjustment grid is saved, the attractive appearance and the symmetry of grid division are considered, and the processing and the production are facilitated.
Drawings
FIG. 1 is a schematic diagram of the modeling flow of the present invention.
Fig. 2 is a cross-sectional view of the structure of the spatial grid structure system produced by the present invention.
Fig. 3 is a schematic plan view of a spatial grid architecture generated by the present invention.
Fig. 4 is a schematic view of a partial planar mesh of the spatial mesh architecture of the present invention.
Fig. 5 is a schematic view of a "ten" bifurcation of the non-split version of the radial stem of the present invention.
Fig. 6 is a schematic view of a "wood" type bifurcation of the radial bar "1:2" split version of the present invention.
FIG. 7 is a schematic view of a "large" bifurcation of the radial rod member "2 split" split version of the present invention.
Fig. 8 is a complete grid schematic of the generated chord layer 1 of the present invention.
Fig. 9 is a schematic view of the structure of the web vertical rod, web circumferential rod and web radial rod of the present invention.
Fig. 10 is a schematic diagram of an axial structure of the present invention.
Fig. 11 is a schematic top view of the present invention.
Detailed Description
The technical scheme of the invention is further specifically described below through examples and with reference to the accompanying drawings.
Examples: as shown in fig. 1-11, a modeling method of a multi-layer spherical space grid structure system includes the following operation steps:
the first step: setting model control parameters of the spherical space grid structure, and controlling the positions (x 0, y0, z 0) of the centers of the spheres and the radius (R) of the spheres, wherein the positions of the centers of the spheres are x0, y0 and z0, so as to carry out coordinate values.
And a second step of: by the sphere center position and sphere radius, the sphere equation can be listed:
(x-x0) 2 +(y-y0) 2 +(z-z0) 2 ＝R 2 。
and a third step of: the span (L), chord layer thickness sequence (D1, D2, D3 …) and target rod length (S) of the space grid structure to be generated are set, and the target rod length is the ideal rod length which is expected to be generated and is used as the target value of grid size adjustment.
The span of the input should be less than the radius of the sphere, if the span of the input is greater than the radius of the sphere, this will result in an equation that is unresolved. The input target length of the rod is the ideal length of the rod, and the size and uniformity of the grid division are judged by comparing the generated grid length with the target length of the rod.
Fourth step: initializing the number of segments (N1) =1 of radial meshing, and calculating a length representative value (L1) of the radial rod piece according to the number of segments (N1) of radial meshing, the spherical equation generated in the step 2 and the span input in the step 3 by the following formula:
fifth step: calculating the difference value (delta 1) between the length representative value (L1) of the rod piece and the rod length target value input in the third step, starting to iterate the radial grid division segment number (N1), and increasing the radial grid division segment number (N1) by 1 each time until the radial grid division segment number (N1) corresponding to the minimum delta 1 is found:
Δ1＝|L1-S|。
sixth step: initializing the number of segments (N2) =4 of the annular first ring network grid division, calculating a length representative value (L2) of the annular first ring rod piece according to the number of segments (N2) of the annular first ring network grid division, the number of segments (N1) of the optimal radial grid division obtained in the fifth step, the spherical equation generated in the step 2 and the span input in the third step, wherein the number of segments (N2) of the annular first ring network grid division is initialized to 4 by the following formula, and the generated grids are ensured to be symmetrical along an X axis and a Y axis:
seventh step: calculating the difference value (delta 2) between the length representative value (L2) of the rod piece and the rod length target value input in the third step, and starting to iterate the number (N2) of segments divided into the first ring network grid by the ring network:
Δ2＝|L2-S|。
in order to ensure that the grids generated after iteration are still symmetrical along the X axis and the Y axis, the number of segments (N2) divided into the first ring network grids is increased by 4 in each iteration until the number of segments (N2) divided into the first ring network grids corresponding to the minimum delta 2 is found out.
Eighth step: the number of segments (N2) divided by the first ring network grid in the ring direction expands the grid outwards according to 3 forms; the three forms expand the grid outwards, the corresponding rod splitting forms are not split, "1 min 2" and "2 min 3", and under the non-splitting form, the number of the annular rod pieces is the same as that of the previous annular rod piece, and the rod pieces at the node parts are in a cross shape. Under the form of '1 branch 2', the number of the annular rod pieces is 2 times of that of the annular rod pieces of the previous ring, each node of the previous ring is connected with 3 nodes of the ring, and the expansion diagram shows a 'wood' -shaped bifurcation. In the form of '2 min 3', the number of the annular rod pieces is 1.5 times of that of the annular rod pieces of the previous ring, half nodes of the previous ring are connected with two nodes of the previous ring, and a 'large' bifurcation is shown on an unfolding diagram; the other half nodes are connected with 1 node of the ring, and are in a ten-shaped bifurcation on the expansion diagram.
Ninth step: according to the three split forms of the eighth step, the three calculation formulas of the length representative value (LI) of the ring rod of the ring are obtained by the ring serial Number (NI) and the number of segments (NIL) divided by the ring grid of the last ring:
tenth step: the difference (Δi) between the rod length representative value (LI) and the rod length target value input in step 3 is calculated by the following formula, preferably the minimum Δi corresponds to the grid split form:
ΔI＝|LI-S|。
eleventh step: repeating the eighth step to the tenth step, and continuously expanding the grid outwards until ni=n1 to obtain a complete grid of the chord layer 1 (see fig. 2) of the spherical space grid structure.
Twelfth step: calculating grid node coordinates (xN, yN, zN) corresponding to a chord layer N according to node coordinates (x 1, y1, z 1) of the grid of the chord layer 1, the spherical center position (x 0, y0, z 0) input in the first step, the spherical radius (R) and the chord layer thickness sequence (D1, D2, D3 …) input in the third step:
thirteenth step: and generating web layer vertical rods, web layer annular rod members and web layer radial rod members according to the corresponding relation between each chord layer grid node and each chord layer grid node obtained in the twelfth step. The web layer vertical rods are formed by connecting upper grid nodes and lower grid corresponding nodes; the web layer circumferential rod member is formed by connecting upper layer grid nodes and lower layer grid nodes with same ring adjacent nodes; the web layer radial rod member is formed by connecting an upper layer grid node and a lower layer grid outer ring with the same radial node.
Fourteenth step: each chord layer rod member (chord layer 1, chord layer 2 and … chord layer N …), each web layer vertical rod, each web layer circumferential rod member and each web layer radial rod member are automatically divided into different layers.
Fifteenth step: and (3) automatically adjusting the azimuth of each rod piece to enable the plane formed by the 1 axis and the 2 axis of each rod piece to pass through the sphere center, and finally outputting the result as a graph or a model file.
The specific flow steps of inputting specific parameters are as follows:
1) First, the center of sphere position (0, -40000) and sphere radius (60000) are entered.
2) And calculating a spherical equation by the parameters.
3) The span of the space grid structure to be generated (80000), the chord layer thickness sequence (0, -1600) and the target value of the pole length (3000) are input.
4) Initializing the number of segments (N1) =1 of radial meshing, calculating a length representative value (L1) of the radial rod, and calculating a difference value (Δ1) of the rod length target value. The number of radial meshing segments (N1) is iterated, and 1 is increased each time until the radial meshing segment number (N1) corresponding to the minimum delta 1 is found. This example n1=15 is finally obtained.
5) Initializing the number of segments (N2) =4 of the first ring network grid division, calculating a length representative value (L2) of the first ring rod member, and calculating a difference value (Δ2) of the rod length target value. And iterating the number of segments (N2) divided into the first ring network grids, and increasing by 4 each time until the number of segments (N2) divided into the first ring network grids corresponding to the minimum delta 2 is found out. This example n2=8 is finally obtained.
6) The mesh is further extended outwards according to the 3 mesh extension forms until ni=n1. Finally, the ring number sequences of 8, 12, 24, 36 are obtained 36, 72 72, 72.
7) And calculating grid nodes corresponding to the chord layer N according to the grid nodes of the chord layer 1.
8) Sequentially generating a web layer vertical rod, a web layer annular rod piece and a web layer radial rod piece.
9) The rods at different positions are automatically divided into different layers.
10 Rotating each rod member by an angle that aligns the rod member surface with the net shell surface.
11 Outputting the result as a graphic or model file.
In conclusion, the modeling method of the multi-layer spherical space grid structure system has the characteristics of full-automatic grid generation, good grid uniformity, consistent rod length and no need of subsequent editing. And the chord layers and the web layer members are divided into different layers, so that the workload of generating an adjustment grid is saved, the attractive appearance and the symmetry of grid division are considered, and the processing and the production are facilitated.
The above embodiments are merely examples of the present invention, but the present invention is not limited thereto, and any changes or modifications made by those skilled in the art are included in the scope of the present invention.

Claims (6)

1. The modeling method of the multi-layer spherical space grid structure system is characterized by comprising the following operation steps:
the first step: setting model control parameters of a spherical space grid structure, wherein the model control parameters are used for controlling the position (x 0, y0, z 0) of a sphere center and the radius (R) of the sphere, and the position of the sphere center is x0, y0 and z0 for coordinate values;
and a second step of: by the sphere center position and sphere radius, the sphere equation can be listed:
(x-x0) 2 +(y-y0) 2 +(z-z0) 2 ＝R 2 ；
and a third step of: setting a span (L), a chord layer thickness sequence (D1, D2, D3) and a target value (S) of a rod length of a space grid structure to be generated, wherein the target value of the rod length is the ideal rod length which is expected to be generated, and the target value is used as a target value for grid size adjustment;
fourth step: initializing the number of segments (N1) =1 of radial meshing, and calculating a length representative value (L1) of the radial rod piece according to the number of segments (N1) of radial meshing, the spherical equation generated in the step 2 and the span input in the step 3 by the following formula:
fifth step: calculating the difference value (delta 1) between the length representative value (L1) of the rod piece and the rod length target value input in the third step, starting to iterate the radial grid division segment number (N1), and increasing the radial grid division segment number (N1) by 1 each time until the radial grid division segment number (N1) corresponding to the minimum delta 1 is found:
Δ1＝|L1-S|；
sixth step: initializing the number of segments (N2) =4 of the annular first ring network grid division, calculating a length representative value (L2) of the annular first ring rod piece according to the number of segments (N2) of the annular first ring network grid division, the number of segments (N1) of the optimal radial grid division obtained in the fifth step, the spherical equation generated in the step 2 and the span input in the third step, wherein the number of segments (N2) of the annular first ring network grid division is initialized to 4 by the following formula, and the generated grids are ensured to be symmetrical along the X axis and the Y axis:
seventh step: calculating the difference value (delta 2) between the length representative value (L2) of the rod piece and the rod length target value input in the third step, and starting to iterate the number (N2) of segments divided into the first ring network grid by the ring network:
Δ2＝|L2-S|；
eighth step: the number of segments (N2) divided by the first ring network grid in the ring direction expands the grid outwards according to 3 forms;
ninth step: according to the three split forms of the eighth step, the three calculation formulas of the length representative value (LI) of the ring rod of the ring are obtained by the ring serial Number (NI) and the number of segments (NIL) divided by the ring grid of the last ring:
tenth step: the difference (Δi) between the rod length representative value (LI) and the rod length target value input in step 3 is calculated by the following formula, preferably the minimum Δi corresponds to the grid split form:
ΔI＝|LI-s|；
eleventh step: repeating the eighth step to the tenth step, and continuously expanding the grid outwards until ni=n1 to obtain a complete grid of the chord layer 1 (see fig. 2) of the spherical space grid structure;
twelfth step: calculating grid node coordinates (xN, yN, zN) corresponding to a chord layer N according to node coordinates (x 1, y1, z 1) of the grid of the chord layer 1, the spherical center position (x 0, y0, z 0) input in the first step, the spherical radius (R) and the chord layer thickness sequence (D1, D2, D3 …) input in the third step:
thirteenth step: generating web layer vertical rods, web layer circumferential rod members and web layer radial rod members according to the corresponding relation between each chord layer grid node and each chord layer grid node obtained in the twelfth step;
fourteenth step: dividing each chord layer member (chord layer 1, chord layer 2 and … chord layer N …), each web layer vertical rod, each web layer circumferential member and each web layer radial member into different layers automatically;
fifteenth step: and (3) automatically adjusting the azimuth of each rod piece to enable the plane formed by the 1 axis and the 2 axis of each rod piece to pass through the sphere center, and finally outputting the result as a graph or a model file.
2. The modeling method of a multi-layer spherical space grid structure system according to claim 1, wherein: the span of the input should be less than the radius of the sphere, if the span of the input is greater than the radius of the sphere, this will result in an equation that is unresolved.
3. The modeling method of a multi-layer spherical space grid structure system according to claim 1 or 2, characterized in that: the input target length of the rod is the ideal length of the rod, and the size and uniformity of the grid division are judged by comparing the generated grid length with the target length of the rod.
4. The modeling method of a multi-layer spherical space grid structure system according to claim 1, wherein: the three forms expand the grid outwards, the corresponding rod splitting forms are not split, "1 min 2" and "2 min 3", and under the non-splitting form, the number of the annular rod pieces is the same as that of the previous annular rod piece, and the rod pieces at the node parts are in a cross shape. Under the form of '1 branch 2', the number of the annular rod pieces is 2 times of that of the annular rod pieces of the previous ring, each node of the previous ring is connected with 3 nodes of the ring, and the expansion diagram shows a 'wood' -shaped bifurcation. In the form of '2 min 3', the number of the annular rod pieces is 1.5 times of that of the annular rod pieces of the previous ring, half nodes of the previous ring are connected with two nodes of the previous ring, and a 'large' bifurcation is shown on an unfolding diagram; the other half nodes are connected with 1 node of the ring, and are in a ten-shaped bifurcation on the expansion diagram.
5. The method according to claim 1, wherein: in order to ensure that the grids generated after iteration are still symmetrical along the X axis and the Y axis, the number of segments (N2) divided into the first ring network grids is increased by 4 in each iteration until the number of segments (N2) divided into the first ring network grids corresponding to the minimum delta 2 is found out.
6. The modeling method of a multi-layer spherical space grid structure system according to claim 1, wherein: the web layer vertical rods are formed by connecting upper grid nodes and lower grid corresponding nodes; the web layer circumferential rod member is formed by connecting upper layer grid nodes and lower layer grid nodes with same ring adjacent nodes; the web layer radial rod member is formed by connecting an upper layer grid node and a lower layer grid outer ring with the same radial node.
CN202311296500.XA 2023-10-08 2023-10-08 Modeling method of multi-layer spherical space grid structure system Pending CN117313208A (en)

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