A metal roof deformation analysis method based on linear interpolation

Abstract

The present invention discloses a metal roof deformation analysis method based on linear interpolation. The method uses the node coordinates, node deformation and node coordinates of the roof steel structure and the metal roof component as main input parameters, and quickly calculates the possible deformation and component stress conditions of the metal roof system during the construction process through the corresponding conversion algorithm, greatly reducing repetitive manual modeling and analysis work, and can provide guidance for the design, scheme preparation and on-site construction process of the metal roof system.

Description

Technical Field

[0001] The invention relates to the technical field of building steel structure construction, and more specifically to a metal roof deformation analysis method based on linear interpolation. Background Art

[0002] In the context of the continuous advancement of urban infrastructure and economic development, steel structures are widely used in the construction of urban infrastructure, sports stadiums, and cultural and entertainment facilities with their unique light weight, high strength, excellent mechanical properties and high degree of industrialization, and have become one of the main forms of large-span spatial structures. Such large-span spatial steel structures include a relatively complex roof steel structure system and a metal roof structure system covering it to meet the needs of building appearance and functional use.

[0003] Since metal roofs are very sensitive to deformation of steel structures, in most projects at present, large-span steel structures and metal roofs can only be constructed conservatively in a sequential manner. This is relatively safer and can reduce the risk of deformation and damage to the metal roof system to a certain extent. However, from the overall perspective of the project, sequential construction has problems such as long waiting periods between professionals and late water shut-off times, which increases construction period and labor costs. Its disadvantages are more obvious in projects with large scale and in rainy climates in the south.

[0004] In view of the above problems, more and more large-span space structures have begun to adopt the integrated construction method of metal roof + steel structure. When the main roof steel structure is assembled on the ground, the construction of the metal roof is interspersed. Then the metal roof system is hoisted / lifted to the designed height together with the main steel structure, which helps to control costs, ensure construction period and reduce construction difficulty.

[0005] However, for the roof steel structure, there are several temporary supporting states during the construction process. When the boundary conditions change, it will produce large deformation, which will affect the metal roof that has been constructed, and may cause deformation or connection damage of the metal roof. When designing the roof steel structure and metal roof, the steel structure and metal roof professionals generally do not consider the adverse effects of changes in boundary conditions on the metal roof system, which will eventually lead to the metal roof facing higher safety risks in the subsequent load-bearing process. Summary of the invention

[0006] The present invention provides a prediction calculation method for metal roof unit deformation based on linear interpolation. Based on the node coordinate table and plane layout diagram of the metal roof component, and the node deformation of the roof steel structure component obtained by finite element model analysis, the node deformation and unit deformation of the metal roof component are obtained by linear interpolation method. The entire calculation process does not require component modeling of the metal roof system in the finite element model, avoiding the cumbersome modeling process, improving work efficiency, and also reducing human errors caused by manual modeling.

[0007] To achieve the above object, the present invention adopts the following technical solution: a metal roof deformation analysis method based on linear interpolation, comprising the following steps:

[0008] 1) Obtain the node coordinates of the roof steel structure and the node deformation of the roof steel structure under specific working conditions;

[0009] 2) Based on the obtained node coordinates on the upper surface of the roof steel structure, triangulation is performed to generate a triangle set for the point set;

[0010] 3) Extract the node coordinates of metal roof components according to the metal roof design drawing;

[0011] 4) The nodes of the metal roof components are projected onto the interior of the triangulation corresponding to the upper surface of the roof steel structure;

[0012] 5) According to the projection point coordinates of the metal roof component node, as well as the coordinates and deformations of the three corner points of the triangulation, the deformation of the metal roof component node is calculated based on the linear interpolation method;

[0013] 6) Based on the deformation calculation results of all metal roof component nodes, further calculate the key data such as strain and stress of the metal roof components.

[0014] Furthermore, the Delaunay triangulation method is used in step 2) to ensure the quality of the generated triangulation and the calculation accuracy of the subsequent linear interpolation.

[0015] Furthermore, in the step 4), a projection method in a vertical direction perpendicular to the ground is adopted.

[0016] Furthermore, during the implementation of step 5), since the upper surface of the roof steel structure is generally not parallel to the ground, when interpolating, the coordinates of the nodes in the global coordinate system must first be converted to the local coordinate system corresponding to each triangulation.

[0017] Furthermore, in the implementation process of step 5), the interpolation calculation matrix used for linear interpolation is obtained by calculating the node coordinates of the metal roof component whose deformation is to be calculated, the triangulation corner point coordinates of the upper surface node set of the roof steel structure, and the triangulation corner point deformation.

[0018] Furthermore, during the implementation of step 5), the linear interpolation calculation process in the local coordinate system is completed, and after the deformation of the metal roof component node in the local coordinate system is obtained, it is converted into the node deformation in the global coordinate system, and the deformation and stress of the metal roof component unit are further calculated.

[0019] Furthermore, during the implementation process in step 5), the calculation process of the metal roof component nodes inside each triangulation is the same.

[0020] Compared with the prior art, the present invention provides a metal roof deformation analysis method based on plane projection and linear interpolation. This method uses the node coordinates, node deformation and node coordinates of the roof steel structure and the metal roof component as the main input parameters, and through the corresponding conversion algorithm program, quickly calculates the possible deformation level of the metal roof system during the construction process, greatly reducing the repetitive manual modeling and analysis work, and can provide guidance for the design, scheme preparation and on-site construction process of the metal roof system. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0022] Figure 2 A finite element calculation model diagram of a simulation analysis of a large-span steel structure roof during the construction phase of an embodiment of the present invention;

[0023] Figure 3 This is an example of a metal roof bar arrangement diagram;

[0024] Figure 4 It is a schematic diagram of Delaunay triangulation of the upper surface nodes of the long-span steel structure roof according to an embodiment of the present invention, and a schematic diagram of projection of the nodes of the metal roof components;

[0025] Figure 5 It is a schematic diagram of the calculation of node coordinate transformation between the global coordinate system and the local coordinate system;

[0026] Figure 6 It is a schematic diagram of calculating the node deformation by linear interpolation based on the vertical projection point of the metal roof member node in the local coordinate system;

[0027] Figure 7 Schematic diagram of linear interpolation calculation of internal node deformation of triangulation in local coordinate system. DETAILED DESCRIPTION

[0028] The following is combined with Figures 1 to 7 The specific implementation of the method for predicting and calculating the deformation of a metal roof unit based on linear interpolation of the present invention is further described in detail.

[0029] A metal roof deformation analysis method based on linear interpolation. The specific implementation process is as follows: Figure 1 As shown, it mainly includes the following steps:

[0030] 1) During the construction simulation analysis, finite element calculation software was used to calculate the deformation of the large-span steel structure roof. The metal roof system was not modeled in the calculation model, and the metal roof system was directly simplified to a constant load applied to the roof steel structure;

[0031] 2) Extract the node coordinates of the upper surface components of the long-span steel roof in the finite element calculation model and complete the Delaunay triangulation;

[0032] 3) Extract the node coordinates of metal roof components according to the metal roof structure design plan and plan layout drawing;

[0033] 4) Vertically project the extracted node coordinates of the metal roof components to the interior of the triangulation of the upper surface of the long-span steel roof;

[0034] 5) According to the deformation of the three corner points of each triangulation, the deformation of the metal roofing component nodes is obtained based on the linear interpolation method;

[0035] 6) Based on the obtained deformation of the metal roof component nodes, the deformation and stress conditions of the metal roof component units are reversed.

[0036] In particular, in the process of implementing step 4), since the upper surface of the large-span roof is not completely parallel to the ground, a coordinate system transformation process is required before linear interpolation to adjust the xy plane of the local coordinate system to be consistent with the planes of each triangulation.

[0037] The finite element model of the roof steel structure used for construction process simulation analysis is as follows: Figure 2 As shown in (a), examples of node coordinates are shown in Table 1 below. Table 1 is an example of some node coordinates in the finite element calculation model of the large-span steel structure roof according to the embodiment of the present invention, where the first column is the node number, and the second to fourth columns are the X, Y, and Z coordinates of the nodes, respectively. Based on this model, a specific construction condition (such as the self-weight condition of the structure) is selected to calculate the deformation of the component nodes of the roof steel structure under this condition. The derived node deformation cloud diagram is shown in Figure 2 As shown in (b), an example of a node deformation table is shown in Table 2 below. Table 2 is an example of deformation of some nodes of the finite element calculation model of the large-span steel structure roof under the action of deadweight according to an embodiment of the present invention, wherein the first column is the node number, the second column is the load condition corresponding to the calculation, the third to fifth columns are the displacement deformation components of the node along the X, Y, and Z axes, respectively, and the sixth to eighth columns are the rotation deformation components of the node around the X, Y, and Z axes, respectively.

[0038] Table 1 (node ​​coordinate examples)

[0039] Node Number X (mm) Y (mm) Z (mm) 1 -149372.0 15393.6 29257.8 2 -161028.9 15534.5 24513.3 3 -161028.9 15534.5 27568.2 4 -159448.4 18773.0 28392.1 5 -177697.2 24611.2 26534.3 6 -149372.1 59809.5 27537.7 7 -176117.3 27848.7 27447.5 8 -198195.7 65294.2 28581.6 9 -145772.1 17451.0 26453.3 10 -197383.4 68712.2 26066.2 11 -197383.4 68712.2 28545.3 12 -193977.8 68337.6 28701.4 13 -149372.1 63431.2 27465.4 14 -145772.1 59897.5 27641.9 15 -149372.1 19571.9 26330.9

[0040] Table 2 (Node deformation table example)

[0041] Node Number Load Cases DX (mm) DY (mm) DZ (mm) RX (rad) RY (rad) RZ (rad) 1 Deadweight 0.000 0.000 0.000 0.000941 0.000766 0.000178 2 Deadweight -0.737 2.171 -2.586 0.001793 -0.001052 0.000156 3 Deadweight -1.051 -3.385 -3.631 0.001412 -0.001126 0.000119 4 Deadweight 0.074 1.724 -2.752 -0.000889 -0.000580 -0.000186 5 Deadweight 0.000 0.000 0.000 0.002574 -0.001002 0.000215 6 Deadweight -0.236 2.882 -4.026 0.001235 -0.000101 0.000083 7 Deadweight 0.000 0.000 0.000 -0.001308 0.001021 -0.000214 8 Deadweight 0.000 0.000 0.000 0.002961 0.001648 0.000360 9 Deadweight -4.142 1.524 -2.134 0.000988 0.001414 0.000140 10 Deadweight -6.558 -6.508 -0.281 -0.002896 0.003440 0.000138 11 Deadweight 0.000 0.000 0.000 -0.002853 0.003864 -0.000271 12 Deadweight 0.524 0.372 -13.799 -0.001217 0.003469 0.000061 13 Deadweight -0.239 2.300 -0.411 0.000749 -0.000342 0.000061 14 Deadweight -1.055 3.434 -4.961 0.001621 0.000750 0.000019 15 Deadweight -3.106 1.152 -1.257 -0.000380 0.000649 -0.000084

[0042] like Figure 3As shown in the figure, based on the node coordinates of the upper surface of the roof steel structure, the Delaunay triangulation method is used to generate a triangle set based on the point set. In particular, the generated triangle set should also meet the following conditions:

[0043] (1) The endpoints of all triangles constitute the set of all nodes;

[0044] (2) The sides of any two triangles do not intersect (they can overlap);

[0045] (3) The union of all triangles forms the convex hull of the point set formed by all nodes.

[0046] like Figure 4 As shown, the node coordinates of the metal roof system component units are determined according to the design drawings or structural models of the metal roof. Figure 4 Taking the corrugated steel plate bottom plate component in the metal roof as an example, an example diagram of the component layout of the corrugated steel plate bottom plate in the metal roof is given. Based on this, the node coordinates of the corrugated steel plate bottom plate component unit in the metal roof can be further extracted.

[0047] like Figure 5 As shown in the figure, the nodes of the metal roof components to be solved are projected vertically into each Delaunay triangulation of the upper surface of the roof steel structure. The example selects three corner points (numbered 1, 2, and 3) of one of the triangulations of the upper surface of the roof steel structure and a metal roof component node (numbered P) inside.

[0048] like Figure 6 As shown in the figure, since the upper surface of the steel structure roof is not parallel to the ground, in order to facilitate the linear interpolation calculation, the interpolation calculation needs to be converted from the global coordinate system XYZ to the local coordinate system xyz. The direction of the xy plane of this local coordinate system is Figure 5 The planes formed by the three corner points 1, 2, and 3 in the example triangulation are consistent. Furthermore, the node coordinates in the local coordinate system are converted and calculated using the formula {x}=[R]{X}, where {x}={x, y, z, 1} T , {x, y, z} are the node coordinates in the local coordinate system; {X}={X, Y, Z, 1} T , {X, Y, Z} are the node coordinates in the global coordinate system; [R] is the coordinate transformation matrix, which can be obtained by the basis vectors in the global coordinate system , , , and the basis vectors in the local coordinate system , , Obtained by calculation.

[0049] In particular, the solution of the coordinate transformation matrix [R] can be calculated based on the transformation relationship between the basis vectors in the local coordinate system and the global coordinate system. , , , the following formula can be used to pass the basis vectors in the global coordinate system , , express:

[0050]

[0051] Furthermore, the coordinate transformation matrix [R] can be obtained as

[0052]

[0053] in , , They are the coordinates of the origin O' of the local coordinate system in the global coordinate system.

[0054] like Figure 7 As shown in the figure, in the transformed local coordinate system, after deformation, the triangulation corner points 1, 2, 3 and the internal point P are deformed to positions 1', 2', 3' and P' respectively. The linear interpolation method is used to calculate the node deformation {u1, v1, w1} of the known triangulation corner points 1, 2 and 3 in the local coordinate system. T , {u2, v2, w2} T , {u3, v3, w3} T , calculate the deformation of point P in the local coordinate system {u}={u, v, w} T Furthermore, the node deformation in the local coordinate system is given by the formula {u}=[N]{u c} is calculated, where {u c}={u1, v1, w1, u2, v2, w2, u3, v3, w3} T , [N] is the interpolation matrix, which can be obtained by triangulating the coordinates of each corner point {x1, y1, z1} T , {x2, y2, z2} T , {x3, y3, z3} T , and the coordinates of node P {x, y,z} T Obtained by calculation.

[0055] Based on linear interpolation methods, such as Figure 7 The deformation of the internal node P of the triangulation shown in the local coordinate system can be set as

[0056]

[0057] in , , , , , , , , They are all interpolation parameters and can be obtained by deforming each corner point of the triangulation.

[0058] Furthermore, taking the calculation of the deformation u of the node P along the local coordinate axis x-axis as an example, it can be expressed as

[0059]

[0060] Further, the interpolation calculation matrix [N] can be calculated as

[0061]

[0062] Using a similar method, the deformation of node P along the local coordinate axis y and z can be further obtained. Repeating the above process, the deformation of all metal roof component nodes in a triangulation in the local coordinate system can be obtained, and the inverse matrix [R] of the coordinate transformation matrix [R] can be further applied. -1 , the deformation of all metal roof component nodes inside this triangulation in the global coordinate system can be obtained.

[0063] For each triangulation, repeat Figure 5~Figure 7 The calculation process shown completes the deformation calculation of all metal roof component nodes.

[0064] Furthermore, through the node coordinates and unit definitions of the metal roof components, combined with the component node deformation obtained by interpolation calculation, the unit deformation of the metal roof components can be calculated, and the strain and stress data of each component unit of the metal roof can be further derived.

[0065] This process can be automated through programming, thereby completing a rapid estimate of the deformation and stress conditions of metal roof components without relying on tedious human modeling and calculation processes.

[0066] The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. A metal roof deformation analysis method based on linear interpolation, characterized in that: The steps include: 1) Obtain the node coordinates of the roof steel structure and the node deformation of the roof steel structure under specific working conditions; 2) Based on the obtained node coordinates on the upper surface of the roof steel structure, triangulation is performed to generate a triangle set for the point set; 3) Extract the node coordinates of metal roof components according to the metal roof design drawing; 4) The nodes of the metal roof components are projected onto the interior of the triangulation corresponding to the upper surface of the roof steel structure; 5) According to the projection point coordinates of the metal roof component node, as well as the coordinates and deformations of the three corner points of the triangulation, the deformation of the metal roof component node is calculated based on the linear interpolation method; 6) Based on the deformation calculation results of all metal roof component nodes, the key data of strain and stress of metal roof components are further calculated.

2. The metal roof deformation analysis method based on linear interpolation according to claim 1 is characterized in that: In the step 2), the Delaunay triangulation method is used to ensure the quality of the generated triangulation and the calculation accuracy of the subsequent linear interpolation.

3. The metal roof deformation analysis method based on linear interpolation according to claim 1 is characterized in that: In the step 4), a projection method in a vertical direction perpendicular to the ground is adopted.

4. A metal roof analysis method based on linear interpolation according to claim 1, characterized in that: During the implementation of step 5), since the upper surface of the roof steel structure is generally not parallel to the ground, the coordinates of the nodes in the global coordinate system must first be converted to the local coordinate system corresponding to each triangulation when interpolating.

5. The metal roof analysis method based on linear interpolation according to claim 1, characterized in that: In the implementation process of step 5), the interpolation calculation matrix used for linear interpolation is obtained by calculating the node coordinates of the metal roof component whose deformation is to be calculated, the triangulation corner point coordinates of the upper surface node set of the roof steel structure, and the triangulation corner point deformation.

6. The metal roof analysis method based on linear interpolation according to claim 1, characterized in that: During the implementation process in step 5), the linear interpolation calculation process in the local coordinate system is completed, and after the deformation of the metal roof component node in the local coordinate system is obtained, it is converted into the node deformation in the global coordinate system, and the deformation and stress of the metal roof component unit are further calculated.

7. The metal roof analysis method based on linear interpolation according to claim 1, characterized in that: During the implementation process in step 5), the calculation process of the metal roof component nodes inside each triangulation is the same.

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