A closed-loop optimization method for building structure design and construction

Abstract

The application discloses a kind of closed-loop optimization methods of building structure design and construction, comprising the following steps: S1: building design surface is converted into structure analysis model;S2: the rotation angle β of each secondary direction beam and main direction beam is calculated, structure analysis model and bar information are imported into finite element analysis software, and initial space net shell model is established;S3: iteration optimization is carried out to model using "passive" form finding method, and initial geometric model is obtained;S4: initial geometric model is decomposed into the construction step with explicit sequence;S5: step-by-step construction simulation is carried out by finite element analysis software, and iteration optimization is carried out again, and geometric model with initial pre-adjusted shape is obtained.The application is accurately simulated and high-fidelity reverse solution to the whole construction path, which converts complex uncontrollable site construction problems into accurate controllable digital prefabrication processing problems, greatly improving the construction accuracy and quality of complex buildings.

Description

Technical Field

[0001] This invention relates to the technical field of architectural design, and in particular to a closed-loop optimization method for architectural structural design and construction. Background Technology

[0002] With the increasing demand for architectural expressiveness and large-span spatial functions in urban construction, large public buildings with complex geometric configurations (such as theaters and exhibition halls) are becoming more common. The roof systems of these buildings often employ unconventional, irregularly shaped curved surfaces, exhibiting significant characteristics such as large spans, complex forms, and variable load-bearing states. In realizing such complex designs, the nonlinear deformation of the structure under its own weight and dynamic disturbances during construction often lead to a significant deviation between the completed physical form and the architect's initial geometric vision.

[0003] Taking the cultural and arts center project as an example, its roof outline features non-standard designs such as single-ridge anti-curve and dynamic streamlines, making construction extremely difficult. Due to the lack of effective closed-loop optimization methods, traditional static design methods cannot predict and offset the cumulative displacement generated throughout the construction process, thus affecting the overall visual effect and structural accuracy of the building. Therefore, how to deeply integrate stress deformation and construction impact into the design stage through scientific calculation methods to ensure the high-precision reproduction of complex irregular structures is the problem addressed in this application. Summary of the Invention

[0004] To address the above problems, this invention provides a closed-loop optimization method for building structure design and construction.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] The closed-loop optimization method for building structure design and construction of this invention includes the following steps:

[0007] S1: Transform the architectural design surface into a structural analysis model;

[0008] S2: Calculate the rotation angle β between each secondary direction beam and the main direction beam, import the structural analysis model and member information into the finite element analysis software, and establish the initial spatial reticulated shell model;

[0009] S3: The model is iteratively optimized using the "passive" form-finding method to find an "equilibrium form" with minimal deformation under constant load, thus obtaining the initial geometric model;

[0010] S4: Decompose the initial geometric model into construction steps with a clear sequence;

[0011] S5: The construction process is simulated step by step using finite element analysis software. After each construction step is completed, the cumulative displacement of all nodes under the current state is accurately recorded.

[0012] By integrating and vector-superimposing the incremental displacements generated at each construction step, a final displacement that reflects the overall impact of the entire process is obtained. Then, the node coordinates and β angle of the initial design model are reverse-corrected to obtain a geometric model with the initial pre-adjusted shape.

[0013] S6: Final design output.

[0014] The closed-loop optimization method for building structure design and construction of this invention further includes the following specific calculation steps in step S5:

[0015] Initial stage:

[0016] The goal of this stage is to calculate the initial model and obtain... These three benchmark values;

[0017] Select a representative node: usually the node at the mid-span of the structure or the node with the most significant deformation, i.e., "observation point P". ”;

[0018] Create three new load cases:

[0019] Condition 1 (Force_X): A unit force in the X direction is applied at observation point P;

[0020] Condition 2 (Force_Y): A unit force in the Y direction is applied at observation point P;

[0021] Case 3 (Force_Z): A unit force in the Z direction is applied at observation point P;

[0022] Run a linear static analysis, analyze three working conditions, and read the displacement results:

[0023] Under the Force_X condition, read the X-direction displacement of observation point P. ;

[0024] Under the Force_Y condition, read the Y-direction displacement of observation point P. ;

[0025] Under the Force_Z condition, read the Z-direction displacement of observation point P. ;

[0026] Calculate initial stiffness :

[0027]

[0028] (9)

[0029]

[0030] Enter the iteration loop

[0031] Step 1: Main Analysis

[0032] The construction simulation was run in stages to obtain the final node coordinates considering the construction simulation, as well as the "observation point P". "

[0033] Therefore, the residual error is:

[0034] ,

[0035] (10)

[0036]

[0037] Step 2: Calculate tangential stiffness

[0038] Run incremental analysis: Solve the three load cases Force_X, Force_Y, and Force_Z created earlier linearly again;

[0039] Since the model is already in a deformed state, the displacement obtained in this solution is an incremental displacement based on the "tangential stiffness".

[0040] Read incremental displacement:

[0041] Under the Force_X condition, read the X-direction displacement of observation point P. ;

[0042] Under the Force_Y condition, read the Y-direction displacement of observation point P. ;

[0043] Under the Force_Z condition, read the Z-direction displacement of observation point P. ;

[0044] Calculate tangential stiffness :

[0045]

[0046] (11)

[0047]

[0048] Step 3: Calculate the equivalent stiffness:

[0049] equivalent stiffness :

[0050]

[0051] Therefore, we can obtain:

[0052]

[0053] Step 4: Solving for the trimming factor

[0054] The correction factor is expressed as the ratio of the equivalent stiffness to the tangential stiffness. :

[0055]

[0056] To prevent computational divergence, a nonlinear factor is introduced. Therefore, the above formula can be rewritten as:

[0057]

[0058] Calculate the new machining coordinates:

[0059]

[0060]

[0061]

[0062] Step 3: Participate in error termination judgment

[0063] The loop can be terminated if it is stopped; otherwise, the iteration loop continues.

[0064] In the closed-loop optimization method for building structure design and construction of the present invention, in step S4, the construction process of temporary support installation, component installation and unloading is decomposed into construction steps with a clear sequence.

[0065] In the closed-loop optimization method for building structure design and construction of the present invention, further, in step S5, when running the construction simulation for "step-by-step construction", the internal force state of the component in each construction step is recorded, and an "internal force envelope diagram" is generated for each component that runs through the entire process from installation to use; the maximum value of the internal force in this "internal force envelope diagram" is used to check the cross section, and if it does not meet the requirements, the cross section size of the component needs to be adjusted.

[0066] In the closed-loop optimization method for building structure design and construction of this invention, further, in step S3, a target load is applied to the current model, static analysis is performed, and the displacements of all nodes in the current state are obtained. Then, the maximum displacement at the nodes after the structure's first equilibrium is utilized. After proportionally reversing the spatial node coordinates and recalculating and updating the β angle of the secondary direction beam, the structure reaches its second equilibrium, at which point the maximum displacement at the node is determined. again according to Proportional reverse correction of spatial node coordinates and updating of components After the angle, the analysis shows that the maximum displacement at the control point after the third equilibrium of the structure is This process continues until the structural deformation, calculated iteratively, meets the design requirements under the target load.

[0067] The closed-loop optimization method for building structure design and construction of this invention further... The value is between 10mm and 15mm.

[0068] In the closed-loop optimization method for building structure design and construction of the present invention, in step 1, the building design surface is projected onto a plane, and the main direction beams and secondary direction beams are meshed on the plane projection. Then, the meshes are mapped to the construction design surface to complete the transformation from the construction design surface to the structural analysis model.

[0069] The closed-loop optimization method for building structure design and construction of this invention further includes adjustments to the correction coefficients. Set an upper limit to prevent calculations from diverging.

[0070] The closed-loop optimization method for building structure design and construction of this invention further calculates the β angle of each secondary beam direction. Specifically, after selecting a suitable target surface in Rhino and importing it into the Grasshopper plugin, the surface is subdivided in the u and v directions using the slide lever, generating the coordinates (x0, y0, z0) of the subdivision points, which are recorded as target points. Line segments in the u and v directions of the surface are generated simultaneously through the subdivision points, and the coordinates (x1, y1, z1) of the two ends of the line segments are generated. In the Grasshopper plugin, the normal vector of each point on the target surface is automatically generated by inputting the beam end coordinates and the target surface. Based on the normal vector corresponding to each endpoint of the beam element, the β angle at both ends of the beam element is calculated using a battery pack composed of the β angle solution formula. The average of the two angles is taken as the rotation angle β of each beam segment.

[0071] The closed-loop optimization method for building structure design and construction of this invention further includes detailed design and delivery: by fine-tuning the cross-sectional height of the secondary beam and rotating it at a small angle around its own axis, the misaligned edge is completely "enclosed" within the web height range of the main beam.

[0072] Compared with the prior art, the present invention has the following beneficial effects:

[0073] 1. The parametric design and iterative optimization design method and system for building structural form proposed in this application has a clear and advanced overall logic; it accurately grasps the core pain points of modern complex curved surface buildings in design and construction: that is, there is a difference between the architect's initial design (ideal form) and the actual form after the structure is built (after deformation under stress), as well as the huge influence of the construction process itself on the final form.

[0074] 2. This application employs a dual-iterative design and construction cycle. The first cycle aims to resist the loads during the service phase, while the second cycle counteracts the deformations during the construction phase, elevating the static "reverse calculation" to a dynamic "construction process decoding and reconstruction." It no longer treats the structure as a simple linear superposition but as a complex system with memory effects and path dependencies. Through detailed simulation and high-fidelity reverse solving of the entire construction path, the final output is no longer a simple pre-camber value but a "unified digital twin precursor" containing multiple objectives and encoding construction process information. This precursor precisely defines the geometric shape of the component when it leaves the factory, thereby transforming the complex and uncontrollable on-site construction problem into a precise and controllable digital prefabrication problem, greatly improving the construction accuracy and quality of complex buildings. This represents a major innovation and advancement over existing construction simulation and pre-adjustment technologies.

[0075] 3. A "passive" force-finding design method for precisely matching architectural curved surfaces;

[0076] 4. In order to ensure a smooth and uniform transition between the main beam and the secondary beam, avoid the occurrence of bending and twisting components, and ensure the construction accuracy and quality of the building, the β angle and its fast and accurate calculation method are introduced in the design form finding to ensure that the form finding is closer to the on-site construction.

[0077] 5. By recording the internal force state at each construction step, an "internal force envelope diagram" is generated for each component, spanning its entire installation and use process. The maximum internal force value in this "internal force envelope diagram" is used to check the cross-section. If the requirements are not met, the cross-section size needs to be adjusted. This ensures that the component is safe not only during the use stage but also has sufficient safety reserves during the construction stage, which is full of uncertainties, thereby achieving the most efficient use of materials while ensuring safety.

[0078] The invention will now be further described with reference to the accompanying drawings. Attached Figure Description

[0079] Figure 1 This is a schematic diagram of the process of the present invention;

[0080] Figure 2 This is a coordinate diagram for calculating the β angle in this invention;

[0081] Figure 3 Schematic diagram of the projection of the main direction beam and the secondary direction beam;

[0082] Figure 4 Schematic diagram of detailed design adjustments for main direction beams and secondary direction beams;

[0083] Figure 5 A schematic diagram showing the selection of locations for typical members;

[0084] Figure 6 This is the maximum value of axial force in the construction simulation.

[0085] Figure 7 This represents the maximum value of the bending moment My during construction simulation.

[0086] Figure 8 The maximum value of the bending moment Mz in the construction simulation;

[0087] Figure 9 This represents the minimum value of axial force during construction simulation.

[0088] Figure 10 This is the minimum value of the bending moment My during construction simulation;

[0089] Figure 11 This represents the minimum value of the bending moment Mz during construction simulation.

[0090] Figure 12 To take into account the stress ratio of construction simulation and design conditions.

[0091] Figure label:

[0092] , Tangents to beams in adjacent main directions; Two tangents and The normal angle bisector; Let be the rotation angle of the rod. Detailed Implementation

[0093] See Figures 1-12 This invention discloses a closed-loop optimization method for building structure design and construction, comprising the following steps:

[0094] S1: Discretization and Parametricization of Architectural Form: The continuous architectural design surface is transformed into a discretized structural analysis model. Since the architectural design surface of this project is a single-ridged, inverted, double-glazed profile, it is customary to divide each side into equal parts for ease of modeling, with curves connecting the division points. However, due to the single-ridged, inverted, double-glazed design of this project, the curvature and arc length of each division point are different. The connecting lines between the surfaces will inevitably present irregular spatial curves, making it easy for components to form spatially twisted components. To ensure that the visually uniform and smooth transition of the rhomboid oblique grid is achieved, in this application, after projecting the architectural design surface onto a plane, two diagonals are connected. This process forms bidirectional intersecting ridge lines. The common side of two spatial curved triangles is designated as the primary ridge line, and the other as the secondary ridge line. The primary ridge line is divided into equal parts along its central intersection point on both sides of the plane projection. A grid is then created through the division points parallel to the secondary ridge line direction, forming the primary directional beam line of the curved surface. Similarly, the secondary ridge line is divided into equal parts according to the plane projection, and a grid is created through the division points parallel to the primary ridge line direction, forming the secondary directional beam line of the spatial curved surface. This results in an oblique rhomboid grid on the plane projection. This oblique rhomboid grid is then mapped onto the architectural design surface, generating a series of spatial longitudinal and transverse curves. The intersection points of the primary and secondary directional beams are precisely extracted as the three-dimensional coordinates of the structural nodes. This completes the transformation of architectural design surfaces into structural analysis models.

[0095] S2: Intelligent Determination of the Principal Axis Direction of Members: To optimize the stress performance of members, it is necessary to rationally define the placement direction of member sections. At each node, normal planes are established for the intersecting longitudinal and transverse curves (i.e., primary direction beams and secondary direction beams). and normal plane and The intersection line defines the direction vector of the principal axis section of the component at that node. , direction vector The direction of the vector follows the right-hand rule. The strong axis of the component section is usually aligned.

[0096] S3: Establishment of the benchmark analysis model and calibration of the β angle of the secondary direction beam: For complex structural surfaces, there are generally two methods. One is to subdivide the complex two-way surface into smaller mesh sizes and rotate the main and secondary direction members by angle B in the node region to adapt to a higher level of architectural profile. The other is to simplify the complex two-way surface into a single-direction surface to avoid bending and twisting members, and use a straight line to approximate the curve in the other direction. This simplification method simplifies the construction difficulty and is usually suitable for architectural profiles with lower levels of architectural profile. Specifically, the main direction beam is made with a vertical web on the ground, simulating a circular arc steel beam along the curve. The secondary direction beam is broken into multiple straight segments by the main direction beam, thus forming an approximate bending arc effect by using straight lines to approximate the curve. The secondary direction beam is arranged at an angle to match the curvature of the main direction beam. The β angle defines the rotation angle of the secondary direction beam section in the plane perpendicular to its axis. It is the rotation relationship between the local coordinate system of the member and the global coordinate system. It determines the precise "posture" of the member in three-dimensional space. Without the precise calibration of the β angle, the model will not be able to truly reflect the spatial stress state of the member. It is worth noting that if the curvature of the surface is not large, the entire component can be rotated. However, if the curvature is large, the component needs to be divided into several segments.

[0097] The β angle is solved by using different reference datums based on the relative relationship between the x-axis of the local coordinate system and the z-axis of the global coordinate system.

[0098] When the x-axis of the local coordinate system of the element is not parallel to the z-axis of the global coordinate system; in this case, the correction vector of the z-axis of the global coordinate system is used. For reference, calculate Compared to The included angle, therefore:

[0099]

[0100]

[0101] The calculation of the β angle requires a correction vector through the Z-axis of the global coordinate system. and the principal axis correction vector of the cross section The dot product and cross product determine the direction, therefore:

[0102] like Then:

[0103]

[0104] like Then:

[0105]

[0106] like Then:

[0107]

[0108] When the x-axis of the unit's local coordinate system is parallel to the z-axis of the global coordinate system, i.e., it is a vertical component, the z-axis projection becomes invalid. Therefore, the x-axis of the global coordinate system is used as the reference datum. Angle is the principal axis correction vector of the cross section ,at this time Located in the XY plane, the angle between the X-axis and the global coordinate system is:

[0109] like Then:

[0110]

[0111] like Then:

[0112]

[0113] like Then:

[0114]

[0115] in, and These are the unit vectors for the X and Z axes of the global coordinate system, respectively. and These are the unit vector along the x-axis of the local coordinate system and the unit vector along the principal axis section, respectively. The global coordinate system Z-axis unit vector is the projection correction vector onto the local x-axis of the element; it is also called the global coordinate system Z-axis correction vector. It is the principal axis section direction vector, and the projection correction vector onto the local x-axis of the element, also known as the section principal axis correction vector.

[0116] The calculation of the β angle for each secondary beam direction is as follows: After selecting a suitable target surface in Rhino and importing it into the Grasshopper plugin, the surface is subdivided in the u and v directions using the slide lever, generating the coordinates (x0, y0, z0) of the subdivision points, which are denoted as target points. Simultaneously, line segments in the u and v directions of the surface are generated from these subdivision points, along with the coordinates (x1, y1, z1) of the two ends of each segment. In the Grasshopper plugin, the normal vector of each point on the target surface is automatically generated by inputting the beam end coordinates and the target surface. Based on the normal vectors corresponding to each endpoint of the beam element, the β angle at both ends of the beam element is calculated using a battery pack composed of the β angle calculation formula. The average of the two angles is taken as the rotation angle β of each beam segment. Through the above operations, the rotation angle β can be quickly calculated in Rhino software, facilitating subsequent design use.

[0117] Since the Grasshopper plugin cannot directly calculate the angle between the normal vector and the plane, the Z-axis of the coordinate system is projected onto the x'-z' plane, and then the angle between the two vectors is calculated. The sign of the angle between the vector and the plane is determined by whether the angle between the z-axis and the x'-axis is acute.

[0118] The structural analysis model and member information are imported into the finite element analysis software to establish an initial spatial reticulated shell model. The member information includes data such as the cross-sectional shape, dimensions, node coordinates, and β angle of the members.

[0119] S4: Iterative optimization based on inverse displacement: First, apply the target load to the current model, perform static analysis, and obtain the displacement of all nodes in the current state. Then, the maximum displacement at the nodes after the structure's first equilibrium is utilized. After proportionally reversing the spatial node coordinates and recalculating and updating the β angle of the secondary direction beam, the structure reaches its second equilibrium, at which point the maximum displacement at the node is determined. again according to Proportional reverse correction of spatial node coordinates and updating of components After the angle, the analysis shows that the maximum displacement at the control point after the third equilibrium of the structure is This process continues until the structural deformation is minimized under the target load, and the final form is the one that most closely approximates the architectural design outline. The minimum structural deformation can be determined based on the acceptable tolerance of the project, either the tolerance set by the architect or the allowable deformation amount specified in the steel structure design code.

[0120] S5: Initial Design Output: The initial geometric model is obtained through iterative calculations, with node coordinates as follows: The design process, including the spatial positioning of the components at angle β, completes the first phase of design. This phase of forward design and optimization involves iterative calculations to find the structural solution with the least deformation and greatest stability under a given load for a free-form architectural silhouette. Its core is to transform the artistic architectural form into an engineering model with optimal mechanical performance.

[0121] S6: Construction Simulation Analysis Iteration: The spatial curved single-layer shell structure is a deformation-sensitive structure, which varies with different construction methods and procedures. Therefore, the construction process of temporary support installation, component installation and unloading is decomposed into construction steps with a clear sequence, such as main ridge hoisting, partitioned main beam installation, secondary beam connection, and roof panel laying.

[0122] S7: High-precision initial state inverse solution based on construction steps: For deformation-sensitive structures such as spatial curved surfaces, the final forming state depends not only on the total load, but also on the order of load application and the path of component installation. Traditional construction inverse calculations often simplify the construction process into a final state, while this method regards construction as a dynamic, nonlinear, time-varying process, thereby achieving an accurate "portrait" of the initial manufacturing form of the structure.

[0123] 1) Decomposition and state recording of time-varying construction stage: Step-by-step construction simulation is carried out using finite element analysis software. After each construction step is completed, the cumulative displacement of all nodes and the peak internal force of the components under the current state are accurately recorded. This process fully considers the time-varying nonlinear behaviors such as material creep, shrinkage and the "birth and death" of temporary support system.

[0124] 2) Inverse correction based on the "pre-adjustment" of the full-path displacement field: Integrating and vector-superimposing the incremental displacements generated at each construction step, a more realistic final displacement that reflects the influence of the entire process is obtained. Subsequently, the node coordinates and β angle of the initial design model are reverse-corrected; the correction coefficients here... It is an adjustment factor that takes into account the influence of stress redistribution in construction simulation, where It can also be obtained through experimental data. The "initial pre-adjusted form" obtained in this way can "absorb" and "counteract" harmful deformations introduced during the entire dynamic construction process to the greatest extent, ensuring that the structure can achieve the design form expected by the architect after "unloading", that is, after the construction is completed and the temporary supports are removed.

[0125] The specific calculation steps are as follows:

[0126] Initial stage:

[0127] The goal of this stage is to calculate the initial model and obtain... These three benchmark values.

[0128] Select a representative node: usually the node at the mid-span of the structure or the node with the most significant deformation, i.e., "observation point P". ".

[0129] Create three new load cases:

[0130] Condition 1 (Force_X): At observation point P, a unit force in the X direction, for example 1 kN, is applied.

[0131] Condition 2 (Force_Y): Apply a unit force in the Y direction, for example, 1 kN, at observation point P.

[0132] Condition 3 (Force_Z): Apply a unit force in the Z direction, for example, -1 kN, at observation point P.

[0133] Run a linear static analysis, analyze three working conditions, and read the displacement results:

[0134] Under the Force_X condition, read the X-direction displacement of observation point P. .

[0135] Under the Force_Y condition, read the Y-direction displacement of observation point P. .

[0136] Under the Force_Z condition, read the Z-direction displacement of observation point P. .

[0137] Calculate initial stiffness :

[0138]

[0139] (9)

[0140]

[0141] Enter the iteration loop

[0142] Step 1: Main Analysis

[0143] The construction simulation was run in stages to obtain the final node coordinates considering the construction simulation, as well as the "observation point P". "

[0144] Therefore, the residual error is:

[0145] ,

[0146] (10)

[0147]

[0148] Step 2: Calculate tangential stiffness

[0149] Run incremental analysis: Solve the three load cases Force_X, Force_Y, and Force_Z created earlier linearly again.

[0150] Since the model is already in a deformed state, the displacement obtained in this solution is an incremental displacement based on the "tangential stiffness".

[0151] Read incremental displacement:

[0152] Under the Force_X condition, read the X-direction displacement of observation point P. .

[0153] Under the Force_Y condition, read the Y-direction displacement of observation point P. .

[0154] Under the Force_Z condition, read the Z-direction displacement of observation point P. .

[0155] Calculate tangential stiffness :

[0156]

[0157] (11)

[0158]

[0159] Step 3: Calculate the equivalent stiffness:

[0160] equivalent stiffness :

[0161]

[0162] Therefore, we can obtain:

[0163]

[0164] Step 4: Solving for the trimming factor

[0165] The correction factor is expressed as the ratio of the equivalent stiffness to the tangential stiffness. :

[0166]

[0167] To prevent computational divergence, a nonlinear factor is introduced. Therefore, the above formula can be rewritten as:

[0168]

[0169] Calculate the new machining coordinates:

[0170]

[0171]

[0172]

[0173] Step 3: Participate in error termination judgment

[0174] The loop can be terminated if it is stopped; otherwise, the iteration loop continues. The tolerance for this value is typically set between 10mm and 15mm in conventional steel structure projects. This value can be related to the span or length of the component, for example, not exceeding 1 / 1000 of the member's span, or it can be determined based on the minimum gap for building curtain wall installation.

[0175] 3) Generation and Verification of the Component's Full Life Cycle "Internal Force Envelope": Traditional methods typically only use the internal forces at the final state to verify the cross-section. However, during construction, the peak internal forces of some components may occur at an intermediate stage rather than the final stage. By recording the internal force state at each construction step, an "internal force envelope" diagram is generated for each component, spanning its entire installation and use process. The maximum internal force value in this "internal force envelope diagram" is used for cross-section verification; if the requirements are not met, the cross-section size needs to be adjusted. This ensures that the component is safe not only during the service stage but also has sufficient safety reserves during the uncertain construction stage, thereby achieving the most efficient use of materials while ensuring safety.

[0176] The following example uses a local area of ​​the roof to solve for members L1-L4 at the intersection of the members. The key steps in calculating the angle and the results are detailed in Table 1. This table displays the unit vector of the x-axis in the element coordinate system. Used to calculate the principal axis correction vector of the cross section. And the discriminant used to determine the direction of rotation. The value of . It is worth mentioning that for the unit vector of the x-axis in the local coordinate system of the element. During the solution process, the direction is from the i-th end of the x-axis in the element coordinate system to the j-th end. This directional direction will affect subsequent steps. The size of the angle.

[0177] Table 1 Calculation results of β angle for L1-L4 components

[0178]

[0179] Note: Nodes at the intersection of the members:

[0180] P1(10535.793,50289.209,-4863.4623);

[0181] P2(12353.612,46135.892,-4910.0536);

[0182] P3(5706.5089,40052.98,-4035.6369);

[0183] P4(7524.3571,35899.596,-3996.8193);

[0184] Mid(9029.3704,43093.804,-4482.4852);

[0185] Unit vector in the direction of principal section (0.094043295, 0.040409087, 1);

[0186] Unit vector of the Z-axis of the global coordinate system (0,0,1).

[0187] The analysis results show that this method has achieved significant results in controlling the internal forces and deformations of components:

[0188] See Figure 5 The axial force (P) was significantly reduced: For the ridge beams (members 2 and 3), which are the main load-bearing components, the axial force was reduced by 35.3% and 28.7% respectively after iterative optimization. This proves that the method greatly improves the force transmission path of the structure through shape optimization, making it more reasonable, thereby effectively reducing the axial force level of the components and creating conditions for cross-section optimization and cost control.

[0189] Relative deformation was effectively controlled: the relative deformation of all selected members decreased to varying degrees. Among them, the relative deformation reduction rates of the main directional beam (member 4) and the ridge beam (member 1) were the most significant, reaching 5.95% and 5.17%, respectively. This indicates that iterative form-finding not only optimized the final completed state but also effectively controlled the excessive local deformation that may occur during construction, thereby improving the overall stiffness and stability of the structure.

[0190] The bending moments (My, Mz) exhibit varying characteristics, but overall tend towards optimization:

[0191] At the main beam (member 4) and the edge member of the opening (member 5), the bending moment in both directions decreased significantly, with Mz decreasing by as much as 15.2%. This indicates that in these areas where shape and precision requirements are high, this method effectively reduces the bending effect of the members, making them closer to the ideal axial stress state.

[0192] For the ridge beams (members 1, 2, and 3), the changes in My and Mz are small, and even show a slight negative increase. This is normal and reflects the redistribution of internal forces during the global optimization process. The sharp decrease in axial force, accompanied by a small adjustment in bending moment, means that the structure is shifting from a combined bending-compression stress state to a more efficient axial compression state, thus improving the overall stress performance.

[0193] In summary, through quantitative analysis of the internal forces and deformations of typical members before and after iteration, it can be confirmed that the proposed closed-loop form-finding optimization method for the design and construction of the outer steel structure with a spatial curved surface can significantly optimize the key mechanical performance indicators of the structure. This method not only effectively controls the relative deformation of the members, but more importantly, it fundamentally improves the overall force transmission mechanism of the structure by significantly reducing the axial force of the main components; at the same time, it achieves ultra-high precision characterization of the initial manufacturing form of the structure.

[0194] The table below shows a comparison of iterative internal forces in typical components.

[0195] Generation and verification of the "internal force envelope" throughout the entire life cycle of a component:

[0196] Traditional methods typically use only the final internal forces to verify cross-sections. However, during construction, the peak internal forces of some components may occur at some intermediate stage, rather than the final stage. This method generates an "internal force envelope" for each component by recording the internal force state at each construction step, spanning its entire lifecycle from installation to use. When verifying the cross-section, the maximum value within this "internal force envelope" is used, rather than a single final internal force value. This is a more rigorous and safer design principle, ensuring that the component is safe not only during the service phase but also has sufficient safety reserves during the uncertain construction phase, thereby achieving the most efficient use of materials while ensuring safety.

[0197] Figures 6-11 To take into account the maximum and minimum values ​​of axial force and bending moment at each construction stage after construction simulation, the envelope value is used as the internal force of the original design self-weight condition and combined with other conditions. Figure 12 To ultimately consider the internal force state of each construction step and the maximum stress ratio of other design conditions, the ratio is 0.89.

[0198] S8: The initial alignment is determined by the form-finding logic of the continuing structural design. Based on the determined component dimensions, coordinates, and β angle information, the alignment principle of the continuing design is determined, and the detailed content is prepared (mainly referring to industry standards, processing and installation conditions, welding process qualification, and other core data). At the same time, it is necessary to be familiar with the structural drawings, check whether there are any conflicts between the design form-finding and detailed form-finding logic, and prepare for the detailed design of steel structure nodes.

[0199] S9: Detailed Design and Delivery

[0200] The practice of vertically positioning the web of the main directional beam inevitably results in its cross-section not always being perpendicular to the roof. Consequently, geometric misalignment (i.e., misalignment) occurs at the intersection with the secondary directional beam, causing welding difficulties. The solution proposed in this application does not forcibly eliminate the misalignment, but rather finely adjusts the cross-sectional height of the secondary beam and rotates it around its own axis at a small angle, so that the misalignment is completely "enclosed" within the web height range of the main directional beam. This allows workers to perform high-quality bevel welding on the sidewall of the main directional beam, cleverly resolving this construction problem.

[0201] See Figure 3 and Figure 4 The following section uses a specific project as an example to detail the specific procedures for steel structure detailed layout:

[0202] 1) Each member of the main directional beam has a different curvature, and it also needs to meet the requirements of the building's curved surface. If a folded beam is used instead, the segments will be too small and the welds will be too dense, increasing the structural safety risks. Therefore, the main directional beam cannot be made into a folded line. However, in order to avoid box-shaped bending and torsion members, it is necessary to ensure that the main directional beam is a straight line when projected horizontally on the curved surface, and that the web is perpendicular to the ground, so as to ensure that the main directional beam is a single-plane curve. Finally, through the simulation of a plane circular arc curve, the main directional beam is realized to be a plane arc beam composed of multiple curvature circular arcs.

[0203] 2) The secondary direction beams are arranged at an angle to match the curvature of the primary direction beams. Specifically, tangents are drawn along the adjacent primary direction beams at the grid nodes. and Then projection is performed.

[0204] Two tangents and normal angle bisector The angle formed with the Y-axis of the global coordinate system is the rotation angle of the rod. Utilizing the rotation angle of the rod Rotate the secondary directional beam at the node to minimize the misalignment between it and the primary directional beam. Originally, the primary and secondary directional beams were at the same height. Considering the misalignment issue, the design phase appropriately increases the cross-sectional height of the primary directional beam. Simultaneously, the secondary directional beam is moved within the yz plane to ensure that the highest point at the corner is within the height range of the primary directional beam's sidewall.

[0205] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A closed-loop optimization method for building structure design and construction, characterized in that, Includes the following steps: S1: Transform the architectural design surface into a structural analysis model; S2: Calculate the rotation angle β between each secondary direction beam and the primary direction beam, import the structural analysis model and member information into the finite element analysis software, and establish the initial spatial reticulated shell model; the member information includes the cross-sectional shape, size, node coordinates, and β angle of the member. S3: The model is iteratively optimized using the "passive" form-finding method to find an "equilibrium form" with minimal deformation under constant load, thus obtaining the initial geometric model; S4: Decompose the initial geometric model into construction steps with a clear sequence; S5: The construction process is simulated step by step using finite element analysis software. After each construction step is completed, the cumulative displacement of all nodes under the current state is accurately recorded. By integrating and vector-superimposing the incremental displacements generated at each construction step, a final displacement that reflects the overall impact of the entire process is obtained. Then, the node coordinates and β angle of the initial geometric model are reverse-corrected to obtain a geometric model with the initial pre-adjusted shape. The specific calculation steps are as follows: Initial stage: The goal of this stage is to calculate the initial model and obtain... These three benchmark values; Select a representative node: the node at the mid-span of the structure or the node with the most significant deformation, which is the "observation point". ”; Create three new load cases: Condition 1, Force_X: Apply a unit force in the X direction at observation point P; Condition 2, Force_Y: Apply a unit force in the Y direction at observation point P; Condition 3, Force_Z: Apply a unit force in the Z direction at observation point P; Run a linear static analysis, analyze three working conditions, and read the displacement results: Under the Force_X condition, read the X-direction displacement of observation point P. ; Under the Force_Y condition, read the Y-direction displacement of observation point P. ; Under the Force_Z condition, read the Z-direction displacement of observation point P. ; Calculate initial stiffness : （9） Enter the iteration loop Step 1: Main Analysis The construction simulation was run in stages to obtain the final node coordinates considering the construction simulation, as well as the "observation point P". Therefore, the residual error is: , （10） Step 2: Calculate tangential stiffness Run incremental analysis: Solve the three load cases Force_X, Force_Y, and Force_Z created earlier linearly again; Since the model is already in a deformed state, the displacement obtained in this solution is an incremental displacement based on the "tangential stiffness". Read incremental displacement: Under the Force_X condition, read the X-direction displacement of observation point P. ; Under the Force_Y condition, read the Y-direction displacement of observation point P. ; Under the Force_Z condition, read the Z-direction displacement of observation point P. ; Calculate tangential stiffness : （11） Step 3: Calculate the equivalent stiffness: equivalent stiffness : Therefore, we obtain: Step 4: Solving for the correction coefficient: The correction factor is expressed as the ratio of the equivalent stiffness to the tangential stiffness. : To prevent computational divergence, a nonlinear factor is introduced. Therefore, the above formula can be rewritten as: Calculate the new machining coordinates: Where (x0, y0, z0) are the node coordinates of the initial geometric model; Step 5: Termination Judgment Based on Residual Error The loop will terminate if the loop is terminated; otherwise, the iteration loop will continue. S6: Final design output.

2. The closed-loop optimization method for building structure design and construction according to claim 1, characterized in that, In step S4, the construction process of temporary support installation, component installation and unloading is broken down into construction steps with a clear sequence.

3. The closed-loop optimization method for building structure design and construction according to claim 1, characterized in that, In step S5, when running the construction simulation for "step-by-step construction", the internal force state of the components in each construction step is recorded, and an "internal force envelope diagram" is generated for each component that runs through the entire process from installation to use. The maximum value of the internal force in this "internal force envelope diagram" is used to check the cross section. If the requirements are not met, the cross section size of the component needs to be adjusted.

4. The closed-loop optimization method for building structure design and construction according to claim 1, characterized in that, In step S3, the target load is applied to the current model, static analysis is performed, and the displacements of all nodes in the current state are obtained. Then, the maximum displacement at the nodes after the structure's first equilibrium is utilized. After proportionally reversing the spatial node coordinates and recalculating and updating the β angle of the secondary direction beam, the structure reaches its second equilibrium, at which point the maximum displacement at the node is determined. again according to Proportional reverse correction of spatial node coordinates and updating of components After the angle, the analysis shows that the maximum displacement at the control point after the third equilibrium of the structure is This process continues until the structural deformation, calculated iteratively, meets the design requirements under the target load.

5. The closed-loop optimization method for building structure design and construction according to claim 1, characterized in that, The value is between 10mm and 15mm.

6. The closed-loop optimization method for building structure design and construction according to claim 1, characterized in that, In step 1, the architectural design surface is projected onto a plane, and the main direction beams and secondary direction beams are meshed on the plane projection. Then, the mesh is mapped onto the architectural design surface to complete the transformation from the architectural design surface to the structural analysis model.

7. The closed-loop optimization method for building structure design and construction according to claim 1, characterized in that, For correction coefficients Set an upper limit to prevent calculations from diverging.

8. The closed-loop optimization method for building structure design and construction according to claim 1, characterized in that, The calculation of the β angle for each sub-direction beam is as follows: After picking the target surface in Rhino into the Grasshopper plugin, the surface is subdivided in the u and v directions using the slide lever as needed, and the coordinates of the subdivision points (x0, y0, z0) are generated, which are recorded as the target points. Line segments in the u and v directions of the surface are generated from the subdivision points, and the coordinates of the two ends of the line segments (x1, y1, z1) are generated. In the Grasshopper plugin, the normal vector of each point on the target surface is automatically generated by inputting the beam end coordinates and the target surface. Based on the normal vector corresponding to each endpoint of the beam element, the β angle at both ends of the beam element is calculated using the encapsulated battery pack composed of the β angle solution formula. The average of the two angles is taken as the rotation angle β of each beam segment.

9. The closed-loop optimization method for building structure design and construction according to claim 1, characterized in that, It also includes detailed design and delivery: by fine-tuning the cross-sectional height of the secondary beam and rotating it at a small angle around its own axis, the misaligned edge is completely "enclosed" within the web height range of the main beam.

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