A method and system for installation adjustment of a curtain wall connection node

Abstract

The application provides a mounting adjustment method and system for a curtain wall connecting node, relates to the technical field of multi-curved surface curtain wall construction, and comprises the following steps: obtaining the space coordinates of four corner points of each plate block of a curtain wall model and calculating the buckling geometric characteristic parameters thereof; constructing a buckling stiffness tensor according to the buckling characteristic parameters and performing eigenvalue decomposition to obtain eigenvalues and eigenvectors; calculating the thermal drift angle of the plate block under simulated temperature difference; dividing the plate block into a quasi-plane coordination type or a strong torsional buckling type based on the buckling anisotropy index and the thermal drift angle; adopting a three-point leveling method to install the quasi-plane coordination type plate block; setting an initial pre-tightening force for the strong torsional buckling type plate block, constructing an attitude vector, and performing pre-tightening simulation of the connecting node, calculating an eccentric moment vector, and determining an optimal attitude vector through an optimization algorithm to realize the best mounting effect, and the long-term service safety and reliability of the curtain wall structure in a complex curved surface building are significantly improved.

Description

Technical Field

[0001] This invention relates to the field of multi-curved curtain wall construction technology, specifically to an installation and adjustment method and system for curtain wall connection nodes. Background Technology

[0002] Curtain wall structures, as an important component of building envelope systems, are widely used in large public buildings such as airport terminals, stadiums, and super high-rise buildings. With architectural designs increasingly pursuing curved shapes and visual transparency, the application of irregularly shaped curtain wall panels, such as hyperboloids, torsion panels, and spatially tilted panels, is becoming more common. During the processing and installation of these panels, their four corner points are often not on the same spatial plane, exhibiting inherent geometric warping characteristics. When fixing these warped panels to the main structure through connection nodes, the determination of the three-dimensional spatial orientation of the connection nodes directly determines the installation accuracy of the panels, the long-term safety performance of the connection nodes, and the service life of the sealing and waterproofing system.

[0003] In existing technologies, for the installation and adjustment of curtain wall connection nodes, the existing technologies generally adopt an assembly method that is uniformly applicable to all panels, with the theoretical spatial coordinates provided by the design blueprint as the sole reference. On this basis, some existing technologies have introduced finite element analysis to simulate the load on the overall curtain wall structure before installation, and to check the stress distribution of each connection node under wind load and self-weight. Based on this, the cross-sectional dimensions of the connectors or the strength grade of the bolts are uniformly adjusted or regionally reinforced.

[0004] However, existing technologies do not differentiate between panels with different postures within the same curtain wall, and the adjustment logic for all panels is completely consistent. This leads to a non-uniform spatial deviation between the actual and theoretical coordinates of the four corners of the warped panels during actual processing. Existing technologies forcibly align all connection nodes on the panels to the theoretical coordinates for locking, which essentially applies forced elastic flattening to the panels. The warping rebound strain energy generated during this flattening process cannot be released by existing adjustment methods, but is entirely converted into the initial assembly stress inside the connection nodes. At the same time, the adjustment process does not correct the adjustment posture based on force feedback, so it is impossible to identify or quantify the stress impact at the bolt roots caused by warping rebound. This results in a significant increase in the amplitude of alternating stress on the bolts at the panel connection points during their service life, accelerating the fretting wear process of the threaded pairs, leading to fatigue loosening of the connection nodes, and increasing the risk of construction.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide an installation and adjustment method and system for curtain wall connection nodes, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] Obtain the spatial coordinates of the four corner points of each panel in the curtain wall model to be installed, and calculate the warping geometric characteristic parameters of each panel based on them;

[0009] For any given plate, based on its warping geometric characteristic parameters, the warping stiffness tensor of the plate is constructed and eigenvalue decomposition is performed to obtain three eigenvalues ​​and corresponding eigenvectors.

[0010] For any given plate, calculate the angle between the direction of the eigenvector corresponding to the maximum eigenvalue under the simulated temperature difference and the eigenvector corresponding to the maximum eigenvalue before the temperature difference is applied, and use it as the thermal drift angle of the plate.

[0011] For any given panel, its warping anisotropy index is calculated based on its characteristic value. Based on the warping anisotropy index and thermal drift angle, all panels are classified into quasi-planar compatible type or strong torsional warping type. For panels belonging to the quasi-planar compatible type, the three-point leveling method is used for their installation.

[0012] For any plate belonging to the strong torsional warping type, an initial preload is set, and the horizontal rotation angle, vertical rotation angle, and screw extension / retraction of each connecting node are used as optimization objects to construct an attitude vector. Based on the initial preload, the preload simulation is performed on the connecting nodes in the plate under each attitude vector to obtain the strain value of each connecting node in the plate under different attitude vectors. Based on this, the eccentric moment vector of each connecting node in the plate under different attitude vectors is calculated. With minimizing the eccentric moment vector as the optimization objective, the optimal attitude vector of each connecting node in the plate is determined by the optimization algorithm, and installation is carried out based on it.

[0013] Furthermore, a spatial coordinate system is established for the curtain wall model to be installed, and each panel in the curtain wall model is mapped into the spatial coordinate system to determine the spatial coordinates of the four corner points of each panel in the curtain wall model to be installed.

[0014] The warping geometric feature parameters specifically include the shortest non-plane distance and the average Gaussian curvature.

[0015] Furthermore, for any given plate, the construction logic for its warpage stiffness tensor is as follows:

[0016] 1): The in-plane elastic modulus, moment of inertia, and Poisson's ratio of the plate material are used as the basic material constants;

[0017] 2) Divide the shortest skew distance of the plate by its projected area in the positive direction, and then take the square root to obtain the warpage of the plate;

[0018] 3) Using the identity matrix as the basis, the product between the average Gaussian curvature of the plate and its positive projected area is used as the curvature enhancement factor, and the constant 1 and 0.5 times the sum of the Poisson's ratio of the plate are used as the material enhancement factor. The curvature enhancement factor and the material enhancement factor are superimposed on the diagonal terms of the basis to form the stiffness basis matrix of the plate.

[0019] 4) The product of the warpage, in-plane elastic modulus and cross-sectional moment of inertia of the plate is used as a common scaling factor to scale the stiffness basis matrix of the plate as a whole, and construct its warpage stiffness tensor.

[0020] Furthermore, for any given plate, the calculation logic for its warpage anisotropy index is as follows:

[0021] The plate warping stiffness tensor of the plate is decomposed into three eigenvalues. The difference between the maximum and minimum values ​​of the three eigenvalues ​​is used as the numerator, and the arithmetic mean of the three eigenvalues ​​is used as the denominator. The ratio of the numerator to the denominator is used as the warping anisotropy index of the plate.

[0022] Furthermore, for any given plate, the calculation logic for its thermal drift angle is as follows: after adding a temperature correction coefficient that is negatively correlated with the simulated temperature difference value to the in-plane elastic modulus of the plate material, the construction and eigenvalue decomposition process of the warping stiffness tensor is re-executed to obtain the eigenvector corresponding to the maximum eigenvalue under the simulated temperature difference condition, and the angle between its direction and the eigenvector corresponding to the maximum eigenvalue before the temperature difference is applied is calculated, which is used as the thermal drift angle of the plate.

[0023] Furthermore, for any given plate, if the plate simultaneously meets the following conditions, then the plate is classified as quasi-planar conforming type; otherwise, the plate is classified as strongly torsional warping type.

[0024] Condition 1: The warpage anisotropy index of the plate is not greater than the preset stress concentration threshold;

[0025] Condition 2: The thermal drift angle of the plate is not greater than the preset swing amplitude threshold.

[0026] Furthermore, for any connection node, the calculation logic for its eccentric moment vector is as follows:

[0027] Subtract the initial zero-drift strain in the same direction from the strain values ​​of the connection node in the two orthogonal directions to obtain the actual strain increment of the connection node in the two orthogonal directions. First, sum the squares and then take the square root to obtain the resultant strain amplitude of the connection node. The initial zero-drift strain is the strain value calibrated by the connection node under completely unstressed conditions. Use the product of the elastic modulus of the bolt material at the connection node and the moment of inertia of the bolt shank section as the moment conversion factor. Divide the moment conversion factor by the bonding radius of the strain gauge at the connection node and multiply it by the resultant strain amplitude to obtain the eccentric moment vector of the bolt root at the connection node, which is the eccentric moment vector of the connection node.

[0028] Furthermore, for any plate belonging to the strong torsional warping type, its attitude vector includes the horizontal rotation angle, vertical rotation angle, and screw extension / retraction of each connecting node within it. With minimizing the eccentric moment vector as the optimization objective, the fitness function value of the plate under any attitude vector is calculated. The specific logic is as follows:

[0029] Using the maximum allowable eccentric moment of the bolts preset in the design specifications as the first normalized benchmark, the square of the ratio of the mean eccentric moment vector of all connection nodes in the plate under this attitude vector to the first normalized benchmark is calculated, and used as the mechanical off-center load evaluation item of the plate under this attitude vector.

[0030] The theoretical compression of the four sealant seams of the plate under this attitude vector is determined. The difference between the maximum and minimum values ​​of the four theoretical compression values ​​is taken as the sealant non-uniformity. The design standard sealant seam width is taken as the second normalization benchmark. The square of the ratio of the sealant non-uniformity to the second normalization benchmark is calculated. The product of the square of the ratio and the preset weighting coefficient is taken as the sealant uniformity evaluation item of the plate under this attitude vector.

[0031] The sum of the mechanical off-center load evaluation term and the sealant uniformity evaluation term of the plate under this attitude vector is calculated and its reciprocal is taken as the fitness function of the plate under this attitude vector.

[0032] Furthermore, the optimal attitude vector for any given segment is determined using a genetic algorithm. The specific logic is as follows: the attitude vector of the segment is taken as an individual, and the horizontal rotation angle, vertical rotation angle, and screw extension / retraction of all connected nodes within the attitude vector are taken as genes. Several attitude vectors of the segment are selected to form an initial population. Iterative operations of selection, crossover, and mutation are performed on the individuals in the initial population. The fitness function value of each individual is calculated during each iteration. When the preset maximum number of iterations is reached, the iteration operation is stopped, and the attitude vector with the maximum fitness function value in the iteration operation is selected as the optimal attitude vector for each connected node within the segment.

[0033] The present invention also provides an installation and adjustment system for curtain wall connection nodes, for performing the above-described installation and adjustment method for curtain wall connection nodes, comprising:

[0034] The feature acquisition module is used to acquire the spatial coordinates of the four corner points of each panel in the curtain wall model to be installed, and to calculate the warping geometric feature parameters of each panel based on them.

[0035] The eigenvalue decomposition module is used to construct the warping stiffness tensor of any given plate based on its warping geometric feature parameters and perform eigenvalue decomposition to obtain three eigenvalues ​​and corresponding eigenvectors.

[0036] The thermal drift detection module is used to calculate the angle between the eigenvector corresponding to the maximum eigenvalue under simulated temperature difference and the eigenvector corresponding to the maximum eigenvalue before the temperature difference is applied for any plate, and to use it as the thermal drift angle of the plate.

[0037] The panel classification module is used to calculate the warping anisotropy index of any panel based on its characteristic values, and classify all panels into quasi-planar compatible type or strong torsional warping type based on the warping anisotropy index and thermal drift angle. For panels belonging to the quasi-planar compatible type, the three-point leveling method is used for their installation.

[0038] The optimal attitude installation module is used to set an initial preload for any plate belonging to the strong torsional warping type. It constructs an attitude vector by using the horizontal and vertical rotation angles of each connection node and the screw extension / retraction amount as optimization objects. Based on the initial preload, it performs preload simulation on the connection nodes within the plate under each attitude vector to obtain the strain values ​​of each connection node under different attitude vectors. Based on this, it calculates the eccentric moment vector of each connection node under different attitude vectors. With minimizing the eccentric moment vector as the optimization objective, it determines the optimal attitude vector of each connection node within the plate through an optimization algorithm and performs installation based on it.

[0039] Compared with the prior art, the beneficial effects of the present invention are: by obtaining the spatial coordinates of the four corner points of each panel in the curtain wall model to be installed, the system can accurately calculate the warping geometric characteristic parameters of each panel; by introducing the warping stiffness tensor and its eigenvalue decomposition, the present invention achieves accurate quantification and directional characterization of the warping mechanical essence of the curtain wall panels.

[0040] In addition, this solution applies a preset simulated temperature difference to each panel and quantifies the deformation characteristics of the panels under the action of temperature difference by defining the thermal drift angle. Based on the thermal drift angle and the warping anisotropy index, the curtain wall panels are divided, which realizes more refined management and adjustment. Different installation methods are adopted for different types of panels, which improves the accuracy and efficiency of installation and enhances the safety and durability of the entire curtain wall structure.

[0041] This solution optimizes the horizontal and vertical rotation angles of the connection nodes and the extension and retraction of the bolts by constructing a fitness function with the minimization of the eccentric moment vector as the optimization objective. It also constructs a closed-loop optimization framework with the spatial attitude of the connection nodes as the optimization object, which fundamentally changes the stress state of the bolts, effectively reduces the risk of bolt loosening due to eccentric load and sealant leakage, and significantly improves the long-term service safety and reliability of the curtain wall structure in complex curved building. Attached Figure Description

[0042] Figure 1 This is a schematic flowchart of the overall method of the present invention;

[0043] Figure 2 The fitted curve of warpage anisotropy index versus thermal drift angle;

[0044] Figure 3 This is a schematic diagram of the overall system structure of the present invention. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0046] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0047] Example:

[0048] Please see Figures 1-2 This invention provides an installation and adjustment method for curtain wall connection nodes, comprising:

[0049] Step 1: Obtain the spatial coordinates of the four corner points of each panel in the curtain wall model to be installed, and calculate the warping geometric characteristic parameters of each panel based on them.

[0050] Establish a spatial coordinate system for the curtain wall model to be installed, and map each panel in the curtain wall model to be installed into the spatial coordinate system to determine the spatial coordinates of the four corner points of each panel in the curtain wall model to be installed.

[0051] The specific methods for establishing the spatial coordinate system of the curtain wall model to be installed include: selecting an origin to establish the coordinate system. Generally, a specific reference point of the curtain wall model to be installed is selected as the origin, such as the center point of the curtain wall model to be installed; the positive direction of the X-axis is from south to north, the positive direction of the Y-axis is from east to west, and the positive direction of the Z-axis is perpendicular to the ground upward.

[0052] By obtaining the design data or 3D model file of the curtain wall model to be installed, such as CAD file, BIM model, etc., the spatial coordinates of the four corner points of each panel are transformed into the set coordinate system. The specific method is to extract the spatial coordinate information of the four corner points of each panel from the model.

[0053] The warping geometric feature parameters specifically include the shortest non-plane distance and the average Gaussian curvature;

[0054] The specific method for determining the shortest skew distance is as follows: For any plate, based on the spatial coordinates of its four corner points, construct two spatial diagonals for the plate. Randomly select one endpoint of the diagonal as the starting point, determine the spatial vector of each diagonal based on the starting point, and calculate the skew distance between the two diagonals based on the cross product direction of the spatial vectors and the line vector connecting the starting points of the two diagonals. This distance is denoted as the shortest skew distance of the plate.

[0055] The formula used to calculate the shortest skew distance is as follows:

[0056]

[0057] In the formula, Let i be the shortest non-plane distance of the i-th plate. and Let be the spatial vectors of the main diagonal and secondary diagonal of the i-th segment, respectively. and These are the starting points of the main diagonal and secondary diagonal of the i-th panel, respectively, where i is the index of the panel within the curtain wall model to be installed;

[0058] It should be noted that the shortest skew distance Used to quantify the spatial warp of a plate, when The larger the value, the greater the skew distance between the two diagonals, which means that the degree of warping or deformation of the plate is relatively large;

[0059] Where cross product Calculate the normal vector between two vectors. The direction and magnitude of this normal vector reflect the spatial relationship between the two diagonals. The angle between the two vectors affects the magnitude of the cross product. The smaller the angle, the smaller the magnitude of the cross product, indicating that the two diagonals are closer to being collinear.

[0060] dot product Calculate the projected length between the normal vector and the vector connecting the starting points. This length reflects the perpendicular distance between the two diagonals. The cross product generates the normal vector, and the dot product projects the connecting vector onto the normal vector. Both together determine the skew distance. If the two diagonals are nearly parallel, the magnitude of the normal vector generated by the cross product will be smaller, and the calculated skew distance will be smaller. and Proportional;

[0061] denominator Used to normalize the results, mapping the distance to a unit length in the direction of the normal vectors of the two space vectors.

[0062] The specific method for determining the average Gaussian curvature is as follows: For any plate, fit its local quadratic surface to each of the four corner points of the plate, extract the absolute value of the principal curvature at each corner point of the plate, calculate the product between the absolute value of the principal curvature at each corner point of the plate and the area of ​​the corresponding Voronoi region, sum them up, and then divide by the positive projection area of ​​the plate to obtain the average Gaussian curvature of the plate.

[0063] The specific method for fitting the local quadratic surface at each corner point is as follows: For any one of the four corner points of the plate, a local coordinate system is constructed with that corner point as the origin. The three axes of the local coordinate system are determined as follows: The direction of the line connecting the corner point to the two adjacent corner points is taken as the initial direction of the local horizontal axis and the local vertical axis. Two orthogonal tangent plane basis vectors are obtained through Schmidt orthogonalization. The cross product direction of these two basis vectors is taken as the local normal vector.

[0064] In this local coordinate system, three points are taken: the corner point itself and two adjacent corner points along the two sides of the plate. The spatial coordinates of the three points constitute three data pairs, including local horizontal coordinates, local vertical coordinates, and local normal coordinates. Using the three data pairs as fitting samples, the construction coefficients of the standard surface equation are determined from the three data pairs. Based on the standard surface equation of the construction coefficients, the local fitted quadratic surface at the corner point is determined.

[0065] The absolute value of the principal curvature at each corner point of the plate is extracted as follows: For any corner point, the normal vector is extracted from the surface model using the constructed local quadratic surface. By analyzing the change of the normal vector, the principal curvature at the corner point is calculated. The absolute value of the obtained principal curvature is taken to obtain the absolute value of the principal curvature at the corner point. All corner points of the plate are traversed to determine the absolute value of the principal curvature at each corner point of the plate.

[0066] The specific method for obtaining the area of ​​the Voronoi region corresponding to each corner point is as follows:

[0067] For the plate formed by the four corner points, the actual space surface of the plate is divided into regions. The specific division operation is as follows: connect the two diagonals of the plate, and the intersection of the two diagonals is the centroid of the plate; connect the centroid of the plate to the midpoint of each edge of the plate in sequence to form four dividing line segments. These four dividing line segments divide the overall surface of the plate into four closed local regions, and each local region exactly surrounds one corner point of the plate.

[0068] For any given corner point, the local region is bounded by the following four vertices connected in sequence: the corner point itself, the midpoint of the first side where the corner point is located, the centroid of the plate, and the midpoint of the second side where the corner point is located. The coordinates of these four vertices in space are known values. The quadrilateral is divided into two spatial triangles along its diagonal. The spatial areas of the two triangles are calculated separately, and the sum of the areas of the two triangles is the actual spatial surface area of ​​the Voronoi region corresponding to the corner point.

[0069] The formula used to calculate the average Gaussian curvature of the plate is as follows:

[0070]

[0071] In the formula, Let be the average Gaussian curvature of the i-th plate. Let be the absolute value of the principal curvature at the j-th corner point within the i-th plate. Let V be the area of ​​the Voronoi region at the j-th corner point within the i-th plate. Let be the positive projection area of ​​the i-th plate; j is the index of the corner point inside the plate;

[0072] It should be noted that the mean Gaussian curvature The mean Gaussian curvature is used to reflect the overall curvature characteristics of the plate surface. It is used to assess the degree of warping of the plate and its response to external forces. The larger the value, the greater the degree of warping of the plate.

[0073] The principal curvature is obtained by fitting a local quadratic surface, reflecting the curvature of the surface in the two main directions at the corner point. The absolute value is used to represent the curvature of the plate surface without considering the warping direction, but rather focusing on the degree of warping of the plate surface.

[0074] Volonoi area Based on the plate geometry, the region surrounding each corner point is divided into a set of points closest to that corner point. The principal curvature at different corner points has an uneven impact on the overall plate curvature; corner points with a larger impact range contribute more to the overall curvature. This is achieved by introducing the area of ​​the Voronoi region. As a weight, it can more accurately reflect the impact of the local warping of each corner point on the entire plate;

[0075] The positive direction projected area refers to the area of ​​the curved panel block projected onto the plane along the normal vector direction. Since the actual surface area of ​​the warped panel block is usually larger than its projected area, the projected area is used as the denominator to normalize the entire panel and facilitate the comparison of the degree of warping.

[0076] Step 2: For any given plate, construct the warping stiffness tensor of the plate based on its warping geometric characteristic parameters and perform eigenvalue decomposition to obtain three eigenvalues ​​and their corresponding eigenvectors.

[0077] For any given plate, the construction logic for its warpage stiffness tensor is as follows:

[0078] 1): The in-plane elastic modulus, moment of inertia, and Poisson's ratio of the plate material are used as the basic material constants;

[0079] It should be noted that all basic material constants refer to mechanical characteristic parameters at a standard reference temperature, which is generally set to 25 degrees Celsius. The specific methods used to determine each basic material constant include: the in-plane elastic modulus describes the stiffness characteristics of a material in a plane; the in-plane elastic modulus is calculated by measuring the stress-strain curve of the material through standard tensile or compressive tests. For common materials, the known in-plane elastic modulus can be obtained by consulting material handbooks, technical standards, or literature. In this embodiment, the in-plane elastic modulus specifically refers to the equivalent elastic modulus of the plate. The flexural modulus of elasticity includes the flexural modulus of elasticity of the glass, structural adhesive, and aluminum frame components. The area-weighted arithmetic mean of the equivalent flexural modulus of elasticity of the components along the long and short sides is used as the input value for calculating the warpage stiffness tensor. The specific method for obtaining the area-weighted arithmetic mean is as follows: several continuous regions are selected on the surface of the component along the long side; based on these regions, several regions perpendicular to the long side are selected along the short side; and the area-weighted arithmetic mean is calculated based on the equivalent flexural modulus of elasticity of each region; and the areas of the regions are identical.

[0080] To address the viscoelastic response of the structural adhesive, this embodiment employs a short-term monotonic loading test that matches the timescale of the on-site installation and locking process. The specific test conditions are set as follows: ambient temperature controlled at 21-25°C. The relative humidity was controlled between 45% and 55%. The loading method was displacement control, with the loading rate set to ensure the specimen reached the design load from zero load within 25-35 seconds. This loading rate is comparable to the actual timescale of the preload applied by a servo-driven electric wrench on-site. Within this short timescale, the creep component in the viscoelastic response of the structural adhesive has not yet fully developed, and its mechanical behavior can be approximated as linear elastic. The load-deflection curve during the loading phase was recorded, and the slope of the linear segment of the curve was taken as the equivalent bending stiffness. The equivalent bending modulus was then calculated as the bending modulus of the plate.

[0081] The moment of inertia of a section is an important parameter describing the resistance of a cross-sectional shape to bending and warping. The moment of inertia of a section is calculated using the standard formula for the moment of inertia of a section, based on the geometry of the section.

[0082] Poisson's ratio is the ratio of the deformation perpendicular to a given direction to the deformation in that direction when a material is subjected to a force. It can be directly measured through tensile or compression tests. Like the in-plane modulus of elasticity, Poisson's ratio values ​​for many common materials, such as metals, concrete, and polymers, can be found in material handbooks or literature. In this embodiment, Poisson's ratio is measured through a uniaxial tensile test on a panel. Standard tensile specimens are taken from the same batch of curtain wall panels to be installed, and strain gauges are attached to the middle of the specimen along both the longitudinal and transverse directions. The specimens are mounted on a universal testing machine, and a uniaxial tensile load is applied. The loading rate is controlled so that the time for the specimen to reach the design load from zero load is within 20-35 seconds, and the ambient temperature is controlled at 20-25 degrees Celsius. The longitudinal and transverse strains are collected simultaneously, and the absolute value of the ratio of transverse strain to longitudinal strain is taken as the equivalent Poisson's ratio of the composite panel. The loading is repeated three times on the same specimen, and the arithmetic mean of the three measurements is taken as the final Poisson's ratio input value.

[0083] The reason for choosing a whole-plate tensile test instead of layered measurement and recombination is that the equivalent Poisson's ratio of the plate depends on the Poisson's ratio, thickness ratio, and interlayer bonding state of each layer material. The viscoelasticity of the structural adhesive layer causes its Poisson's ratio to change with the loading rate. Layered measurement and thickness weighting cannot reflect the constraint effect of interlayer shear coupling on lateral shrinkage. Directly measuring the lateral shrinkage response of the whole plate can obtain a Poisson's ratio that is consistent with the physical meaning of the warping stiffness tensor.

[0084] 2) Divide the shortest skew distance of the plate by its projected area in the positive direction, and then take the square root to obtain the warpage of the plate;

[0085] The warpage of the i-th plate Characterizing the relative severity of warpage amplitude with respect to plate size, its square root form originates from the quadratic relationship between strain energy and curvature in thin plate bending theory. The bigger, The smaller the value, the greater the warpage rate, which means that under the same material physical stiffness, the plate has a higher accumulated warpage strain energy.

[0086] 3) Using the identity matrix as the basis, the product between the average Gaussian curvature of the plate and its positive projected area is used as the curvature enhancement factor, and the constant 1 and 0.5 times the sum of the Poisson's ratio of the plate are used as the material enhancement factor. The curvature enhancement factor and the material enhancement factor are superimposed on the diagonal terms of the basis to form the stiffness basis matrix of the plate.

[0087] in, The core of this matrix is ​​the result of superimposing the dimensionless stiffness matrix of an isotropic linear elastic material under plane stress with a curvature enhancement factor; when the plate is warped, initial geometric defects have already accumulated inside, which cause the plate to have a spatial bending shape before being subjected to external forces; mean Gaussian curvature This characterizes the severity of the bending morphology across the entire plate, multiplied by the plate's projected area. The dimensionless total curvature contribution is then obtained; this contribution value is superimposed on the normal stress diagonal terms of the isotropic stiffness matrix to form... This indicates that, in the direction of normal stress within a plane, the stiffness of a plate against deformation includes not only the inherent elastic stiffness of the material but also an additional geometric stiffness increment contributed by the warping curvature. The greater the curvature of a plate, the greater the increase in stress required to resist further flattening.

[0088] off-diagonal terms The Poisson's ratio term is directly taken from the constitutive relation of isotropic materials to characterize the effect of normal strain in one direction on normal strain in another orthogonal direction. Meanwhile, the warping shape is mainly caused by out-of-plane bending deformation, while the in-plane shear stiffness is mainly determined by the material's inherent properties; therefore, the shear stiffness coefficient is retained. As the last diagonal term, during eigenvalue decomposition, this diagonal term ensures that the tensor has full rank, enabling stable eigenvector decomposition; physically, it is equivalent to the shear deformation component in the process of a plate resisting warping and torsion.

[0089] 4) The product of the warpage, in-plane elastic modulus, and moment of inertia of the plate is used as a common scaling factor to scale the stiffness basis matrix of the plate as a whole, and to construct its warpage stiffness tensor.

[0090] The specific formula used to construct its warpage stiffness tensor is as follows:

[0091]

[0092] In the formula, Let be the warping stiffness tensor of the i-th plate. Let be the in-plane elastic modulus of the i-th plate. Let be the moment of inertia of the i-th plate section. Let Poisson's ratio be the material of the i-th plate. That is, the warpage of the i-th segment; This is the curvature enhancement factor;

[0093] The warp stiffness tensor This follows the physical logic of the linear elastic thin plate small deflection bending theory and the constitutive relation of orthotropic materials; it should be noted that the warping stiffness tensor... It is used to establish a directional mapping relationship between geometric warping shape and mechanical resistance; therefore, the second-order symmetric tensor can fully characterize the severity of warping rebound in different directions, i.e., the magnitude of the corresponding eigenvalues, and the specific orientation of that direction in space through its three eigenvalues ​​and eigenvectors.

[0094] Flexural stiffness per unit width of the plate, representing the material's intrinsic ability to resist bending deformation; in-plane elastic modulus. The moment of inertia of a cross section is a characterizing property of a material to resist tension and compression. The geometric property that characterizes the cross-sectional shape's resistance to cross-sectional rotation, and the product of the two constitutes the bending stiffness, which is the basic stiffness dimension of beam and plate bending problems in elasticity. By combining it with the warpage, the overall value of the warpage stiffness tensor is reflected, that is, the severity of the stiffness rebound response against forced flattening.

[0095] Eigenvalue decomposition is performed on the warping stiffness tensor of the plate to obtain three eigenvalues ​​and corresponding eigenvectors. Numerical methods are usually used to calculate the eigenvalues ​​and eigenvectors; common numerical methods include the QR algorithm.

[0096] After performing eigenvalue decomposition on the two-dimensional warping stiffness tensor, three eigenvalues ​​are obtained by arranging them in descending order of numerical value. The largest and second largest eigenvalues ​​correspond to the stiffness amplitudes in two orthogonal directions in the plane, and the smallest eigenvalue corresponds to the in-plane shear stiffness component.

[0097] The maximum eigenvalue represents the bending stiffness amplitude of the plate in the main direction where the warping springback stress is most concentrated. The larger the value, the higher the warping strain energy density of the plate in this direction. That is, when the plate is forcibly flattened, the maximum resisting bending moment will be generated in this direction. This direction is the eigenvector direction corresponding to the maximum eigenvalue. It is the preferred direction when the warping strain energy inside the plate is released, and it is also the main contributing direction that causes the bolts at the connecting nodes to generate eccentric moments.

[0098] The second largest eigenvalue represents the bending stiffness amplitude of the plate in the secondary direction orthogonal to the direction of the eigenvector corresponding to the largest eigenvalue, indicating the degree of concentration of warping strain energy in the secondary direction;

[0099] The minimum eigenvalue represents the contribution amplitude of the in-plane shear stiffness of the plate. Under plane stress, the shear stiffness is usually significantly smaller than the stiffness in the normal stress direction. This value reflects the plate's ability to resist torsion when subjected to in-plane shear deformation. For connection nodes, the greater the shear stiffness, the greater the shear load component transmitted to the bolt when the plate is subjected to torque in the plane. The eigenvalue and the corresponding eigenvector represent the spatial orientation of each stress direction.

[0100] It should be noted that the calibration accuracy verification of the warping stiffness tensor adopts a four-point reverse loading comparison test. The specific operation steps are as follows: Select no less than three standard specimens from the same batch of curtain wall panels to be installed. Install the specimens on a rigid platform through ball joint supports at the four corner points. The three-dimensional coordinates of the four ball joint supports are consistent with the coordinates of the actual connection nodes on site. Displacement sensors are arranged at the four corners of the specimen to record the spatial displacement of each corner point during the forced flattening process. Then, a servo actuator applies a gradually increasing forced flattening displacement to the specimen, with each displacement increment controlled at 0.5 mm, until the four corner points are coplanar. Record the reaction force value under each displacement level. Compare the measured reaction force-displacement curve with the predicted reaction force-displacement curve calculated based on the warping stiffness tensor. The relative deviation of the reaction force values ​​of the two curves at the same displacement level is taken as the evaluation index of the tensor prediction accuracy.

[0101] The reaction force-displacement curve is predicted based on the warping stiffness tensor. Its physical basis is the moment-curvature relationship in the linear elastic thin plate bending theory. The physical function of the warping stiffness tensor is to map the curvature change of the plate into the section bending moment. Therefore, for any given forced flattening displacement level, the current residual warping geometry of the plate is first determined by the flattening displacement, then the curvature change is determined by the residual warping geometry, then the section bending moment is calculated by the curvature change through the warping stiffness tensor, and finally the section bending moment is converted into the corner reaction force.

[0102] For each flattening displacement level, the residual shortest skew distance is determined. Within the range where the displacement is less than or equal to twice the shortest skew distance, the relative deviation between the predicted and measured reactions must not exceed 15%; within the range where the displacement is greater than twice the shortest skew distance, the relative deviation must not exceed 25%. The assumption of linear tensor response holds true within the small displacement range, requiring stricter accuracy. Within the large displacement range, the composite plate enters a geometrically nonlinear state, naturally decreasing the accuracy of tensor prediction; therefore, the limits are appropriately relaxed.

[0103] Step 3: For any plate, calculate the angle between the direction of the eigenvector corresponding to the maximum eigenvalue under the simulated temperature difference and the eigenvector corresponding to the maximum eigenvalue before the temperature difference is applied, and use it as the thermal drift angle of the plate.

[0104] For any given plate, the calculation logic for its thermal drift angle is as follows: After adding a temperature correction coefficient that is negatively correlated with the simulated temperature difference value to the in-plane elastic modulus of the plate material, the construction and eigenvalue decomposition process of the warping stiffness tensor is re-executed to obtain the eigenvector corresponding to the maximum eigenvalue under the simulated temperature difference condition, and the angle between its direction and the eigenvector corresponding to the maximum eigenvalue before the temperature difference is applied is calculated as the thermal drift angle of the plate.

[0105] It should be noted that the simulated temperature difference value is generally set to a fixed value, which is typically the difference between the average summer temperature and the average winter temperature of the location where the curtain wall model to be installed is located, generally between 15 and 50 degrees Celsius; the specific formula used to calculate the temperature correction factor is as follows:

[0106]

[0107] In the formula, Let be the in-plane elastic modulus of the i-th plate under the simulated temperature difference. To simulate temperature difference values, It is a temperature proportionality constant;

[0108] It should be noted that in materials science, the elastic modulus of metallic materials decreases with increasing temperature, which is a physical law determined by their microstructure. When the temperature rises, the thermal vibration of lattice atoms intensifies, the bonding force between atoms weakens, and the material's ability to resist elastic deformation decreases. Since this application focuses on the warping and rebound stress of the plate, it does not consider the case where the elastic modulus increases with decreasing temperature, but only considers the case where the maximum warping and rebound stress is to ensure installation safety.

[0109] Therefore, set As the denominator, it is negatively correlated with the simulated temperature difference value, reflecting the decrease in elastic modulus as temperature increases; among which, the temperature proportionality constant... Based on the material of the plates, the temperature proportionality constant can be obtained by conducting thermal expansion tests on the corresponding materials and then performing linear fitting. Alternatively, typical values ​​from relevant materials in industry standards or literature can be used as initial values, and these values ​​are generally set between 0.0001 and 0.001.

[0110] The specific formula used to calculate the thermal drift angle is as follows:

[0111]

[0112] In the formula, Let be the thermal drift angle of the i-th plate. and These represent the eigenvectors corresponding to the maximum eigenvalues ​​before and under simulated temperature differences, respectively.

[0113] It should be noted that the thermal drift angle This indicates the extent to which the principal direction of the warping and rebound stress of the curtain wall panel changes spatially with temperature within the expected service temperature range. The larger the value, the greater the magnitude of the change in the direction of the warping and rebound stress of the panel with temperature. This may cause the panel installation alignment to fail due to temperature changes during the service life, and the stress state of the connection nodes to be unstable.

[0114] The warping stiffness tensor is related not only to the geometric warping shape of the plate but also to the elastic modulus of the material. The elastic modulus of the material decreases with increasing temperature, which changes the relative proportions of stiffness amplitudes in different directions of the tensor. This causes the direction of the largest eigenvector, i.e., the principal stress direction, to shift; this shift angle is the thermal drift angle.

[0115] Among molecules The denominator is used to represent the dot product of two vectors, which is equal to the cosine of the angle between them; The product of the magnitudes of two vectors is used to normalize the dot product and transform the inverse cosine function. Mapping the dot product back to the angle value yields the angle in radians between the two vectors. Convert the radian value to a numerical value in degrees.

[0116] Step 4: For any given panel, calculate its warping anisotropy index based on its characteristic value. Based on the warping anisotropy index and thermal drift angle, classify all panels into either quasi-planar compatible type or strong torsional warping type. For panels belonging to the quasi-planar compatible type, use the three-point leveling method to install them.

[0117] For any given plate, the calculation logic for its warpage anisotropy index is as follows:

[0118] The warpage stiffness tensor of the plate is decomposed into eigenvalues ​​to determine three eigenvalues. The difference between the maximum and minimum values ​​is taken as the numerator, and the arithmetic mean of the three eigenvalues ​​is taken as the denominator. The ratio of the numerator to the denominator is taken as the warpage anisotropy index of the plate. The specific formula for calculating the warpage anisotropy index is as follows:

[0119]

[0120] In the formula, Let be the warping anisotropy index of the i-th plate. Let i be the maximum eigenvalue of the i-th segment. Let be the second largest eigenvalue of the i-th segment. Let be the minimum eigenvalue of the i-th segment;

[0121] It should be noted that the warping anisotropy index of the plate It is used to represent the ratio of the concentration of the warping strain energy in the main bending direction to the average stiffness level in all directions, that is, the concentration or anisotropy of the warping energy in the spatial direction. The larger the value, the more the warping strain energy is concentrated in a single main bending direction, that is, the direction of the eigenvector corresponding to the maximum eigenvalue. During installation, the nodal internal force generated by forced flattening is highly concentrated in this direction, and the eccentric moment borne by the bolt will increase significantly.

[0122] in Characterized by the range between maximum bending stiffness and minimum shear stiffness, when the plate exhibits significant torsional warping, the stiffness in the principal bending direction is much greater than the shear stiffness. and The difference increased significantly, and this difference directly reflects the degree of concentration of the warp shape;

[0123] denominator The arithmetic mean of the three characteristic values ​​represents the average stiffness amplitude of the plate in each direction within the plane. Dividing the stiffness range represented by the numerator by the average stiffness amplitude aims to eliminate the difference in absolute stiffness caused by the difference in absolute size and material properties of the plate, in order to normalize the values.

[0124] For any given plate, if the plate simultaneously meets the following conditions, then the plate is classified as quasi-planar conforming type; otherwise, the plate is classified as strongly torsional warping type.

[0125] Condition 1: The warpage anisotropy index of the plate is not greater than the preset stress concentration threshold;

[0126] Condition 2: The thermal drift angle of this plate is not greater than the preset swing amplitude threshold; please refer to [link / reference] for details. Figure 2 ,Depend on Figure 2 The fitted curves show that the warping anisotropy index of the plate is correlated with the thermal drift angle, and the warping anisotropy index and the change of thermal drift angle are positively correlated. Therefore, the plate can be classified into different types by using the warping anisotropy index and thermal drift angle.

[0127] It should be noted that the warping anisotropy index characterizes the degree of concentration of warping strain energy in all directions of the plane, that is, whether the warping rebound stress tends to concentrate in a single direction; and by comparing the warping anisotropy indices of the same plate with and without simulated temperature difference, the largest warping anisotropy index is selected as the warping anisotropy index of the plate for judgment.

[0128] The thermal drift angle characterizes the swing amplitude of the principal direction of warpage and springback stress under temperature changes, that is, whether the principal direction deflects significantly with temperature changes;

[0129] When the warpage anisotropy index is not greater than the preset stress concentration threshold, it means that the three characteristic values ​​are close to each other, the warpage strain energy is nearly uniformly distributed in all directions of the plane and among all deformation modes, there is no obvious, prominent dominant direction, the warpage rebound stress borne by the connection node is approximately symmetrically distributed around the bolt, and the original basis for the generation of the eccentric moment is relatively weak.

[0130] The accuracy of the thermal drift angle calculation was verified using a temperature cycling test comparison method. The specific steps were as follows: The specimen, after warpage stiffness tensor calibration, was placed in a constant temperature and humidity chamber and installed with four-corner ball joint supports, maintaining the same boundary conditions as the warpage stiffness tensor calibration test. At least six temperature sensors and at least four triaxial strain gauges were evenly arranged on the specimen surface to record temperature distribution and strain response. The chamber temperature was increased from a reference temperature of 21 degrees Celsius to a reference temperature plus 35 degrees Celsius at a rate of 0.5 degrees Celsius per minute, held for one hour until the specimen temperature was uniform, and then the strain values ​​of each strain gauge were collected. The temperature was then decreased to the reference temperature at the same rate, held for one hour, and the strain values ​​were collected again. Based on the two collected strain values, the actual maximum principal strain direction of the specimen under the current temperature difference condition was calculated using strain rosette analysis. This direction was compared with the direction of the maximum eigenvector under the simulated temperature difference used in the thermal drift angle calculation; the spatial angle between the two is the thermal drift angle calculation error.

[0131] The allowable range for thermal drift angle calculation error is set at no more than 1.5 degrees. If the calculation error exceeds this critical value, it may lead to blurred boundaries in the classification results, causing plates that should be classified as strongly torsional warping to be misclassified as quasi-planar coordination plates, thus missing necessary node attitude optimization.

[0132] When the thermal drift angle is not greater than the preset swing amplitude threshold, it means that the main direction of warping stress remains highly stable within the temperature range throughout the year. Temperature changes only change the magnitude of stress in this direction, without changing the direction of stress. Under high or low temperature conditions, the angle between the actual warping stress direction and the alignment direction is always less than the swing amplitude threshold. The additional shear component generated is extremely small and not enough to have a substantial impact on the long-term fatigue life of the bolt, nor enough to cause the plate to be torn due to directional misalignment.

[0133] Therefore, panels that simultaneously meet conditions 1 and 2 are classified as quasi-planar coordination type; otherwise, they are classified as strong torsional warping type, indicating that they need to be optimized and adjusted to ensure the safety of curtain wall use.

[0134] The stress concentration threshold is set based on the material's elastic modulus and yield strength, and is generally set between 0.1 and 0.25, indicating that the local stress has a smaller concentration effect compared to the average stress. The sway amplitude threshold is generally set between 0.25 and 1.5 degrees. Within this range, the structure can be ensured to remain stable under thermal stress, while avoiding structural instability or failure.

[0135] For panels belonging to the quasi-planar coordination type, the three-point leveling method is used for node installation. The specific logic of the three-point leveling method for node installation is as follows: taking any three corner points of the panel as a reference, by adjusting the three-dimensional sliding groove of the connecting node, the three corner points are aligned with the corresponding three embedded parts positioning surfaces on the main structure of the curtain wall to be installed, and the connecting bolts at the three corner points are locked to complete the installation of the panel.

[0136] Step 5: For any plate belonging to the strong torsional warping type, set its initial preload, and use the horizontal rotation angle, vertical rotation angle and screw extension of each connection node as the optimization object to construct the attitude vector. Based on the initial preload, perform preload simulation on the connection nodes in the plate under each attitude vector to obtain the strain value of each connection node in the plate under different attitude vectors, and calculate the eccentric moment vector of each connection node in the plate under different attitude vectors. With minimizing the eccentric moment vector as the optimization objective, determine the optimal attitude vector of each connection node in the plate through the optimization algorithm, and install it based on it.

[0137] For any panel belonging to the strong torsional warping type, the specific method for setting its initial preload is as follows: the initial preload refers to the force applied to the connection node during panel installation. By consulting relevant building or mechanical design standards, such as ACI, ASCE, ISO, etc., the preload guidelines required for different materials and connection methods are obtained. Combined with expert experience, the preload used in this scheme is determined for panel installation.

[0138] The strain values ​​of each connecting node within the panel under different attitude vectors are obtained through finite element analysis. This process includes: constructing a finite element model of the curtain wall to be installed, clarifying the physical and mechanical properties of the panel material, including in-plane elastic modulus, Poisson's ratio, and density; creating a 3D geometric model using CAD software such as AutoCAD or SolidWorks based on the actual geometry of the panel; selecting appropriate finite element types based on the panel's geometric characteristics, such as triangles, quadrilaterals, and hexahedrons; and typically using shell or solid elements for torsion and warping problems. Finally, meshing is performed in the model, ensuring sufficient mesh density to capture variations in strain distribution. Finer meshes can be used in critical areas, such as connection nodes and stress concentration zones; boundary conditions can be set according to actual conditions to ensure that the model's degrees of freedom and constraints match the actual application; boundary conditions include fixed supports, simple supports, or sliding supports; initial preload is applied at the connection nodes, finite element analysis is run to solve the stress and strain distribution of the model under applied load and preload, and the strain values ​​at the connection nodes are extracted through post-processing software; finite element software such as ANSYS, Abaqus, and COMSOL provide functions for directly extracting strain, and the strain distribution can be viewed on specific nodes or elements;

[0139] The calculation logic for the eccentric moment vector acting on any connection node is as follows:

[0140] Subtract the initial zero-drift strain in the same direction from the strain values ​​of the connection node in the two orthogonal directions to obtain the actual strain increment of the connection node in the two orthogonal directions. First, sum the squares and then take the square root to obtain the resultant strain amplitude of the connection node. The initial zero-drift strain is the strain value calibrated by the connection node under completely unloaded conditions. Specifically, in an actual device or structure, without applying any external force, use strain gauges or other sensors to measure the connection node. Install strain gauges at the bolt root or other critical areas of the connection node. Record the output values ​​of the strain gauges under unloaded conditions. Perform multiple measurements to ensure the reliability and accuracy of the data. Take the average value as the initial zero-drift strain. Use the product of the elastic modulus of the bolt material at the connection node and the moment of inertia of the bolt shank section as the moment conversion factor. Divide this moment conversion factor by the strain gauge bonding radius at the connection node and multiply by the resultant strain amplitude to obtain the eccentric moment vector at the bolt root of the connection node, which is the eccentric moment vector of the connection node. The specific formula for calculating the eccentric moment vector is as follows:

[0141]

[0142] It should be noted that, Let be the eccentric moment vector at the bolt root of the i-th plate connection node. Let be the elastic modulus of the bolt steel at the i-th plate connection node. Let be the moment of inertia of the section of the bolt shank at the i-th plate connection node. and These are the strain values ​​of the i-th plate connection node in two orthogonal directions, where the orthogonal directions are the x and y directions in the spatial coordinate system; and These represent the initial zero-drift strains in two orthogonal directions; That is, the resultant strain amplitude. This is the torque conversion factor;

[0143] It should be noted that the eccentric moment vector This is used to represent the magnitude of the combined bending moment borne by the bolt root at the connection node in a plane perpendicular to the bolt axis. When a curtain wall panel with geometrically warped characteristics is installed to the main curtain wall structure through the connection node, the warping rebound strain energy accumulated inside the panel is transferred to the bolt at the connection node through the panel frame; therefore, a force component perpendicular to the axis is generated at the bolt root, and this force component forms a bending moment relative to the centroid of the bolt shank section; this bending moment is superimposed on the axial tensile stress of the bolt in the form of a coupling of shear and torsion, and the eccentric moment vector... It is the combined amplitude of this coupled bending moment; the larger the value, the larger the component of the plate warping rebound stress in the direction perpendicular to the bolt axis, the higher the proportion of the warping strain energy inside the plate converted into harmful eccentric load components, and the significantly reduced fatigue life of the plate.

[0144] Since the direction of the warp rebound stress applied to the bolt is arbitrary in space, simply reading the strain value in a single direction can only reflect the component in that direction and cannot characterize the overall bending deformation borne by the bolt. Therefore, the sum of the squares of the actual strain increments in two orthogonal directions is taken as the square root to obtain the resultant strain amplitude. As a scalar value, it specifically represents the total amplitude of the combined bending deformation experienced by the bolt root in a plane perpendicular to the axis. The larger this value, the greater the warping strain. and Proportional;

[0145] Based on the conversion relationship between surface strain and section bending moment, The bending moment value is obtained by multiplying the resultant strain amplitude by the conversion factor.

[0146] The fitness function is constructed with the goal of minimizing the eccentric moment vector. The specific logic behind this is as follows:

[0147] For any plate belonging to the strong torsional warping type, its attitude vector includes the horizontal rotation angle, vertical rotation angle, and screw extension / retraction of each connecting node within it. With minimizing the eccentric moment vector as the optimization objective, the fitness function value of the plate under any attitude vector is calculated. The specific logic is as follows:

[0148] Using the maximum allowable eccentric moment of the bolts preset in the design specifications as the first normalized benchmark, the square of the ratio of the mean eccentric moment vector of all connection nodes in the plate under this attitude vector to the first normalized benchmark is calculated, and used as the mechanical off-center load evaluation item of the plate under this attitude vector.

[0149] The theoretical compression of the four sealant seams of the plate under this attitude vector is determined. The difference between the maximum and minimum values ​​of the four theoretical compression values ​​is taken as the sealant non-uniformity. The design standard sealant seam width is taken as the second normalization benchmark. The square of the ratio of the sealant non-uniformity to the second normalization benchmark is calculated. The product of the square of the ratio and the preset weighting coefficient is taken as the sealant uniformity evaluation item of the plate under this attitude vector.

[0150] The sum of the mechanical off-center load evaluation term and the sealant uniformity evaluation term of the plate under this attitude vector is calculated and its reciprocal is taken as the fitness function of the plate under this attitude vector.

[0151] The fitness function is specifically expressed as follows:

[0152]

[0153] In the formula, Let be the fitness function value of the i-th intra-block connection node under the u-th pose vector. Let represent the sealant non-uniformity of the connecting node within the i-th plate under the u-th attitude vector. Let be the eccentric moment vector of the i-th intra-block connecting node under the u-th attitude vector. The maximum allowable eccentric moment for the bolt. To design standard adhesive joint width, The preset weighting coefficient is generally set between 0.3 and 0.6. In curtain wall structure design, the unevenness of the sealant... It has a significant impact on the performance and reliability of the curtain wall, but its importance is slightly lower than that of the eccentric moment vector when analyzing the overall stress and service life of the curtain wall. As an auxiliary optimization condition, its weighting coefficient is... Typically set arrive Between these, the width of the sealant should be appropriate but not excessively influential. To prevent division by zero constant, it is generally set to 0.00001, where u is the index of the attitude vector within the plate;

[0154] It should be noted that the impact of the eccentric moment vector on plate installation and service life has already been explained and will not be repeated here; (square term) The influence of changes in eccentric torque on the fitness function is emphasized; a larger eccentric torque will lead to a significant decrease in the fitness function, making it difficult to achieve the optimization objective.

[0155] The theoretical compression of the four adhesive joints of the plate under the attitude vector is determined by inputting the attitude vector and the initial preload into the finite element model, performing finite element analysis, obtaining the relative displacement at both ends of the adhesive joint, and thus obtaining the theoretical compression of the adhesive joint.

[0156] The maximum permissible eccentric moment for bolts Typically, industry standards specify the corresponding design standards based on different types of connection methods, or based on the mechanical properties of the bolt material. It is necessary to consult parameters such as the tensile strength and yield strength of the material, and use these parameters to calculate the allowable eccentric moment using conventional standard calculation formulas.

[0157] The recommended joint width for design standard adhesive joints can be obtained by referring to relevant national standards, such as the "Code for Design of Building Structures" GB50009 or the "Code for Seismic Design of Buildings" GB 50011.

[0158] The optimal attitude vector for any given segment is determined using a genetic algorithm. The specific logic is as follows: the attitude vector of the segment is taken as an individual, and the horizontal rotation angle, vertical rotation angle, and screw extension / retraction of all connected nodes within the attitude vector are taken as genes. Several attitude vectors of the segment are selected to form an initial population. Iterative operations of selection, crossover, and mutation are performed on the individuals in the initial population. The fitness function value corresponding to each individual is calculated in each iteration. When the preset maximum number of iterations is reached, which is generally set to 200-500, the iteration operation is stopped. The attitude vector with the maximum fitness function value in the iteration operation is selected as the optimal attitude vector for each connected node within the segment. Since the genetic algorithm is a conventional existing technology, its specific iteration process will not be described in detail here.

[0159] Please see Figure 3 The present invention also provides an installation and adjustment system for curtain wall connection nodes, used to perform the above-described installation and adjustment method for curtain wall connection nodes, comprising:

[0160] The feature acquisition module is used to acquire the spatial coordinates of the four corner points of each panel in the curtain wall model to be installed, and to calculate the warping geometric feature parameters of each panel based on them.

[0161] The eigenvalue decomposition module is used to construct the warping stiffness tensor of any given plate based on its warping geometric feature parameters and perform eigenvalue decomposition to obtain three eigenvalues ​​and corresponding eigenvectors.

[0162] The thermal drift detection module is used to calculate the angle between the eigenvector corresponding to the maximum eigenvalue under simulated temperature difference and the eigenvector corresponding to the maximum eigenvalue before the temperature difference is applied for any plate, and to use it as the thermal drift angle of the plate.

[0163] The panel classification module is used to calculate the warping anisotropy index of any panel based on its characteristic values, and classify all panels into quasi-planar compatible type or strong torsional warping type based on the warping anisotropy index and thermal drift angle. For panels belonging to the quasi-planar compatible type, the three-point leveling method is used for their installation.

[0164] The optimal attitude installation module is used to set an initial preload for any plate belonging to the strong torsional warping type. It constructs an attitude vector by using the horizontal and vertical rotation angles of each connection node and the screw extension / retraction amount as optimization objects. Based on the initial preload, it performs preload simulation on the connection nodes within the plate under each attitude vector to obtain the strain values ​​of each connection node under different attitude vectors. Based on this, it calculates the eccentric moment vector of each connection node under different attitude vectors. With minimizing the eccentric moment vector as the optimization objective, it determines the optimal attitude vector of each connection node within the plate through an optimization algorithm and performs installation based on it.

[0165] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0166] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0167] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0168] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. An installation and adjustment method for curtain wall connection nodes, characterized in that, include: Obtain the spatial coordinates of the four corner points of each panel in the curtain wall model to be installed, and calculate the warping geometric characteristic parameters of each panel based on them; For any given plate, based on its warping geometric characteristic parameters, the warping stiffness tensor of the plate is constructed and eigenvalue decomposition is performed to obtain three eigenvalues ​​and corresponding eigenvectors. For any given plate, calculate the angle between the direction of the eigenvector corresponding to the maximum eigenvalue under the simulated temperature difference and the eigenvector corresponding to the maximum eigenvalue before the temperature difference is applied, and use it as the thermal drift angle of the plate. For any given panel, its warping anisotropy index is calculated based on its characteristic value. Based on the warping anisotropy index and thermal drift angle, all panels are classified into quasi-planar compatible type or strong torsional warping type. For panels belonging to the quasi-planar compatible type, the three-point leveling method is used for their installation. For any plate belonging to the strong torsional warping type, an initial preload is set, and the horizontal rotation angle, vertical rotation angle, and screw extension / retraction of each connecting node are used as optimization objects to construct an attitude vector. Based on the initial preload, the preload simulation is performed on the connecting nodes in the plate under each attitude vector to obtain the strain value of each connecting node in the plate under different attitude vectors. Based on this, the eccentric moment vector of each connecting node in the plate under different attitude vectors is calculated. With minimizing the eccentric moment vector as the optimization objective, the optimal attitude vector of each connecting node in the plate is determined by the optimization algorithm, and installation is carried out based on it.

2. The installation and adjustment method for curtain wall connection nodes according to claim 1, characterized in that, Establish a spatial coordinate system for the curtain wall model to be installed, and map each panel in the curtain wall model to be installed into the spatial coordinate system to determine the spatial coordinates of the four corner points of each panel in the curtain wall model to be installed. The warping geometric feature parameters specifically include the shortest non-plane distance and the average Gaussian curvature.

3. The installation and adjustment method for curtain wall connection nodes according to claim 2, characterized in that, For any given plate, the construction logic for its warpage stiffness tensor is as follows: 1) The in-plane elastic modulus, moment of inertia, and Poisson's ratio of the plate material are used as the basic material constants; 2) Divide the shortest skew distance of the plate by its projected area in the positive direction, and then take the square root to obtain the warpage of the plate; 3) Using the identity matrix as the basis, the product between the average Gaussian curvature of the plate and its positive projected area is used as the curvature enhancement factor, and the constant 1 and 0.5 times the sum of the Poisson's ratio of the plate are used as the material enhancement factor. The curvature enhancement factor and the material enhancement factor are superimposed on the diagonal terms of the basis to form the stiffness basis matrix of the plate. 4) The product of the warpage, in-plane elastic modulus and cross-sectional moment of inertia of the plate is used as a common scaling factor to scale the stiffness basis matrix of the plate as a whole, and construct its warpage stiffness tensor.

4. The installation and adjustment method for curtain wall connection nodes according to claim 3, characterized in that, For any given plate, the calculation logic for its warpage anisotropy index is as follows: The plate warping stiffness tensor of the plate is decomposed into three eigenvalues. The difference between the maximum and minimum values ​​of the three eigenvalues ​​is used as the numerator, and the arithmetic mean of the three eigenvalues ​​is used as the denominator. The ratio of the numerator to the denominator is used as the warping anisotropy index of the plate.

5. The installation and adjustment method for curtain wall connection nodes according to claim 4, characterized in that, For any given plate, the calculation logic for its thermal drift angle is as follows: After adding a temperature correction coefficient that is negatively correlated with the simulated temperature difference value to the in-plane elastic modulus of the plate material, the construction and eigenvalue decomposition process of the warping stiffness tensor is re-executed to obtain the eigenvector corresponding to the maximum eigenvalue under the simulated temperature difference condition, and the angle between its direction and the eigenvector corresponding to the maximum eigenvalue before the temperature difference is applied is calculated as the thermal drift angle of the plate.

6. The installation and adjustment method for curtain wall connection nodes according to claim 4, characterized in that, For any given plate, if the plate simultaneously meets the following conditions, then the plate is classified as quasi-planar conforming type; otherwise, the plate is classified as strongly torsional warping type. Condition 1: The warpage anisotropy index of the plate is not greater than the preset stress concentration threshold; Condition 2: The thermal drift angle of the plate is not greater than the preset swing amplitude threshold.

7. The installation and adjustment method for curtain wall connection nodes according to claim 6, characterized in that, The calculation logic for the eccentric moment vector acting on any connection node is as follows: Subtract the initial zero-drift strain in the same direction from the strain values ​​of the connection node in the two orthogonal directions to obtain the actual strain increment of the connection node in the two orthogonal directions. First, sum the squares and then take the square root to obtain the resultant strain amplitude of the connection node. The initial zero-drift strain is the strain value calibrated by the connection node under completely unstressed conditions. Use the product of the elastic modulus of the bolt material at the connection node and the moment of inertia of the bolt shank section as the moment conversion factor. Divide the moment conversion factor by the bonding radius of the strain gauge at the connection node and multiply it by the resultant strain amplitude to obtain the eccentric moment vector of the bolt root at the connection node, which is the eccentric moment vector of the connection node.

8. The installation and adjustment method for curtain wall connection nodes according to claim 7, characterized in that, For any plate belonging to the strong torsional warping type, its attitude vector includes the horizontal rotation angle, vertical rotation angle, and screw extension / retraction of each connecting node within it. With minimizing the eccentric moment vector as the optimization objective, the fitness function value of the plate under any attitude vector is calculated. The specific logic is as follows: Using the maximum allowable eccentric moment of the bolts preset in the design specifications as the first normalized benchmark, the square of the ratio of the mean eccentric moment vector of all connection nodes in the plate under this attitude vector to the first normalized benchmark is calculated, and used as the mechanical off-center load evaluation item of the plate under this attitude vector. The theoretical compression of the four sealant seams of the plate under this attitude vector is determined. The difference between the maximum and minimum values ​​of the four theoretical compression values ​​is taken as the sealant non-uniformity. The design standard sealant seam width is taken as the second normalization benchmark. The square of the ratio of the sealant non-uniformity to the second normalization benchmark is calculated. The product of the square of the ratio and the preset weighting coefficient is taken as the sealant uniformity evaluation item of the plate under this attitude vector. The sum of the mechanical off-center load evaluation term and the sealant uniformity evaluation term of the plate under this attitude vector is calculated and its reciprocal is taken as the fitness function of the plate under this attitude vector.

9. The installation and adjustment method for curtain wall connection nodes according to claim 8, characterized in that, The optimal attitude vector for any given segment is determined using a genetic algorithm. The specific logic is as follows: the attitude vector of the segment is taken as an individual, and the horizontal rotation angle, vertical rotation angle, and screw extension / retraction of all connected nodes within the attitude vector are taken as genes. Several attitude vectors of the segment are selected to form an initial population. Iterative operations of selection, crossover, and mutation are performed on the individuals in the initial population. The fitness function value of each individual is calculated in each iteration. When the preset maximum number of iterations is reached, the iteration operation is stopped, and the attitude vector with the maximum fitness function value in the iteration operation is selected as the optimal attitude vector for each connected node within the segment.

10. An installation and adjustment system for curtain wall connection nodes, used to perform the installation and adjustment method for curtain wall connection nodes as described in any one of claims 1-9, characterized in that, include: The feature acquisition module is used to acquire the spatial coordinates of the four corner points of each panel in the curtain wall model to be installed, and to calculate the warping geometric feature parameters of each panel based on them. The eigenvalue decomposition module is used to construct the warping stiffness tensor of any given plate based on its warping geometric feature parameters and perform eigenvalue decomposition to obtain three eigenvalues ​​and corresponding eigenvectors. The thermal drift detection module is used to calculate the angle between the eigenvector corresponding to the maximum eigenvalue under simulated temperature difference and the eigenvector corresponding to the maximum eigenvalue before the temperature difference is applied for any plate, and to use it as the thermal drift angle of the plate. The panel classification module is used to calculate the warping anisotropy index of any panel based on its characteristic values, and classify all panels into quasi-planar compatible type or strong torsional warping type based on the warping anisotropy index and thermal drift angle. For panels belonging to the quasi-planar compatible type, the three-point leveling method is used for their installation. The optimal attitude installation module is used to set an initial preload for any plate belonging to the strong torsional warping type. It constructs an attitude vector by using the horizontal and vertical rotation angles of each connection node and the screw extension / retraction amount as optimization objects. Based on the initial preload, it performs preload simulation on the connection nodes within the plate under each attitude vector to obtain the strain values ​​of each connection node under different attitude vectors. Based on this, it calculates the eccentric moment vector of each connection node under different attitude vectors. With minimizing the eccentric moment vector as the optimization objective, it determines the optimal attitude vector of each connection node within the plate through an optimization algorithm and performs installation based on it.

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