A safety risk assessment method and system for prefabricated buildings

Abstract

The present invention discloses a safety risk assessment method and system for prefabricated buildings. The method includes the following steps: collecting data of prefabricated building components; establishing a three-dimensional geometric model based on the collected data; dividing the boundary joints of the three-dimensional geometric model into multiple finite elements and defining the shape functions of the finite elements; calculating the mass matrix, stiffness matrix, and load vector according to the shape functions and forming a finite element equation; solving the finite element equation to obtain a displacement vector, calculating strain based on the displacement vector, and calculating stress based on the strain; performing element stress integration according to the stress of a single finite element to calculate the total stress at the boundary joints of the prefabricated building components; calculating the bending degree according to the total stress value and displacement at the boundary joints of the prefabricated building components, and evaluating the safety of the prefabricated building based on the bending degree. The present invention calculates the bending degree according to the total stress value and displacement at the boundary joints of the components to evaluate the safety of the prefabricated building.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and particularly relates to a safety risk assessment method and system for prefabricated buildings. Background Art

[0002] With the acceleration of the industrialization process, the traditional on-site construction method is difficult to meet the needs of large-scale and rapid construction. Prefabricated buildings, through the factory production mode, prefabricate some or all components of the building in the factory and then transport them to the construction site for assembly, which improves construction efficiency and shortens the construction period.

[0003] Currently, prefabricated buildings have been widely used globally, especially in the fields of residential, commercial, industrial, and infrastructure. However, due to the characteristics of prefabricated buildings that require assembly, their safety needs to be evaluated. For this reason, the present invention proposes a safety risk assessment method and system for prefabricated buildings. Summary of the Invention

[0004] The present invention provides a safety risk assessment method for prefabricated buildings, including:

[0005] S10. Collect data of prefabricated building components;

[0006] S20. Establish a three-dimensional geometric model based on the collected data of prefabricated building components;

[0007] S30. Divide the boundary joints of the three-dimensional geometric model into multiple finite elements and define the shape functions of the finite elements;

[0008] S40. Calculate the mass matrix, stiffness matrix, and load vector according to the shape functions, and form a finite element equation from the mass matrix, stiffness matrix, and load vector;

[0009] S50. Solve the finite element equation to obtain the displacement vector, calculate the strain according to the displacement vector, and calculate the stress according to the strain;

[0010] S60. Integrate the unit stresses of individual finite elements to calculate the total stress at the boundary joints of prefabricated building components;

[0011] S70. Calculate the bending degree according to the total stress value and displacement at the boundary joints of prefabricated building components, and evaluate the safety of prefabricated buildings according to the bending degree.

[0012] A safety risk assessment method for prefabricated buildings as described above, wherein the establishment of the three-dimensional geometric model should simulate the real environment of the prefabricated building and the actual usage of the building, use the data of the prefabricated building components collected to establish a three-dimensional geometric model of the connections between the components, assign real physical and mechanical properties to each material in the model, and set reasonable support conditions and apply various loads.

[0013] A safety risk assessment method for prefabricated buildings as described above, wherein the composition of the finite element equation includes a mass matrix, a stiffness matrix, and a load vector. The elements of the mass matrix are obtained by integrating the product of the density and the shape function within the volume of the prefabricated building component; the elements of the stiffness matrix are obtained by integrating the product of the strain energy density and the derivative of the shape function within the prefabricated building component; the load vector needs to calculate the contribution of each finite element, and then use the shape function to project these forces onto the nodes to form the load vector of the entire structure.

[0014] A safety risk assessment method for prefabricated buildings as described above, wherein solving the finite element equation requires establishing a frequency domain equation, converting the time domain function into a frequency domain function, and then performing an inverse Fourier transform to solve the unknown displacement vector in the frequency domain.

[0015] A safety risk assessment method for prefabricated buildings as described above, wherein for the unit stress integration based on the stress of a single finite element, it is necessary to collect the Gaussian point stress values, calculate the average stress of the finite element, and perform a summation calculation on the average stress values of the finite elements to obtain the total stress value at the boundary of the prefabricated building.

[0016] The present invention also provides a safety risk assessment system for prefabricated buildings, including: a collection module, a modeling module, a calculation module, and an evaluation module.

[0017] The collection module: used to collect the data of the prefabricated building components;

[0018] The modeling module: used to establish a three-dimensional geometric model according to the data of the prefabricated building components collected;

[0019] The calculation module: used to divide the boundary joints of the three-dimensional geometric model into multiple finite elements, define the shape function of the finite element, calculate the mass matrix, stiffness matrix, and load vector according to the shape function, form a finite element equation from the mass matrix, stiffness matrix, and load vector, solve the finite element equation to obtain the displacement vector, calculate the strain according to the displacement vector, calculate the stress according to the strain, perform unit stress integration based on the stress of a single finite element, and calculate the total stress at the boundary joints of the prefabricated building components;

[0020] The evaluation module: evaluate the safety of the prefabricated building according to the bending degree calculated based on the total stress value and displacement at the boundary joints of the prefabricated building components.

[0021] A safety risk assessment system for prefabricated buildings as described above, wherein the establishment of the three-dimensional geometric model should simulate the real environment of the prefabricated building and the actual usage of the building, use the data of the prefabricated building components collected to establish a three-dimensional geometric model of the connection between the components, assign real physical and mechanical properties to each material in the model, and set reasonable support conditions and apply various loads.

[0022] A safety risk assessment system for prefabricated buildings as described above, wherein the composition of the finite element equation includes a mass matrix, a stiffness matrix, and a load vector. The elements of the mass matrix are obtained by integrating the product of the density and the shape function within the volume of the prefabricated building component; the elements of the stiffness matrix are obtained by integrating the product of the strain energy density and the derivative of the shape function within the prefabricated building component; the load vector needs to calculate the contribution of each finite element, and then use the shape function to project these forces onto the nodes to form the load vector of the entire structure.

[0023] A safety risk assessment system for prefabricated buildings as described above, wherein solving the finite element equation requires establishing a frequency domain equation, converting the time domain function into a frequency domain function, and then performing an inverse Fourier transform to solve the unknown displacement vector in the frequency domain.

[0024] A safety risk assessment system for prefabricated buildings as described above, wherein for the unit stress integration according to the stress of a single finite element, it is necessary to collect the Gaussian point stress values, calculate the average stress of the finite element, and perform a summation calculation on the average stress values of the finite elements to obtain the total stress value of the boundary of the prefabricated building.

[0025] The beneficial effects achieved by the present invention are as follows: calculating the degree of bending according to the total stress value and displacement at the joint of the component boundary is beneficial to improving the safety of prefabricated buildings. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings.

[0027] Figure 1 It is a flowchart of a safety risk assessment method for prefabricated buildings provided in Embodiment 1 of the present application.

[0028] Figure 2 It is a schematic diagram of a safety risk assessment system for prefabricated buildings provided in Embodiment 2 of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0029] Combined with the accompanying drawings in the embodiments of the present invention, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative efforts fall within the protection scope of the present invention.

[0030] Embodiment 1

[0031] As Figure 1 shown, Embodiment 1 of the present application provides a safety risk assessment method for prefabricated buildings, including:

[0032] S10. Collect data of prefabricated building components.

[0033] To establish an accurate three-dimensional model, precast components, connectors, and filling materials need to be accurately represented. Therefore, data of precast components, connectors, and filling materials of prefabricated buildings are collected. The data of precast components include component numbers, quantities, lengths, widths, heights, weights, concrete strength grades, bearing capacities, and durability indexes. Connectors include fasteners, welded connectors, embedded parts, dry connectors, chemical anchor bolts and mechanical anchor bolts, composite beam and slab connectors, thermal insulation connectors, and prestressed connectors. Filling materials include grouting materials, epoxy resin mortar, polymer mortar, thermal insulation materials, sealants, sound insulation materials, and high-performance concrete.

[0034] Collect design data, including structural design drawings, connection detail drawings, material specifications, and design loads.

[0035] S20. Establish a three-dimensional geometric model according to the collected data of prefabricated building components.

[0036] Use the collected data of prefabricated building components and design data to establish a three-dimensional geometric model of the connections between components, and assign real physical and mechanical properties to each material in the model, including elastic modulus, Poisson's ratio, yield strength, and ultimate strength, etc. And set reasonable support conditions and apply various loads, including self-weight, floor live load, wind load, seismic load, and stress caused by temperature change, to simulate the real environment of the prefabricated building and the actual use situation of the building.

[0037] S30. Divide the boundary joints of the three-dimensional geometric model into multiple finite elements and define the shape functions of the finite elements.

[0038] Divide the boundary joints of the three-dimensional geometric model into multiple simple, tight, non-overlapping but connected finite elements. The boundary points of the finite elements are called nodes, and there is stress at each node. The sum of the stress values at each node is the total stress at the boundary joints between prefabricated building components.

[0039] To simulate the stress conditions of real components, material properties are specified for each finite element, and the friction coefficient, pre-tightening force, displacement constraints, pressure loads, and force distributions of the contact interface are correctly set, especially when simulating bolt connections and welded connections.

[0040] To solve for the stress at the boundary connection using finite elements, an equation consisting of a mass matrix, a stiffness matrix, and a load vector needs to be established and solved. This process calculates the displacements and stresses of each node.

[0041] The formation of the mass matrix and the stiffness matrix requires shape functions. Therefore, for each finite element, shape functions are defined, which are non-zero inside the element and zero outside the element. Given the stresses at each node, the stress distribution within the prefabricated building component can be accurately reconstructed through a linear combination of these shape functions.

[0042] The finite element is set as a two-dimensional quadrilateral element with four nodes. The shape functions at each node are linear inside the element, take the value of 1 at the node, and 0 at other nodes. The four nodes are labeled A, B, C, D, and the position of any internal point P is given by local coordinates (ξ, η), where ξ and η represent two independent variables, and the ranges of ξ and η are both from -1 to 1. The formula for the shape function is: (1 + ηβ I ), where I = A, B, C, D, and for each node, α I , β I take the following values: for node A: α A = β A = -1, for node B: α B = 1, β B = -1, for node C: α C = β C = 1, for node D: α D = -1, β D = 1. The shape function for each node is: In the mass matrix, N i (ξ, η), N j (ξ, η) represents the shape function of two degrees of freedom at a node.

[0043] S40. Calculate the mass matrix, stiffness matrix, and load vector according to the shape function, and form a finite element equation from the mass matrix, stiffness matrix, and load vector.

[0044] The mass matrix reflects the internal mass distribution of prefabricated building components and their response to external forces, and can be obtained by integrating the product of the density ρ within the volume of the prefabricated building component and the shape function. The mass matrix of a two-dimensional quadrilateral finite element has four nodes, each with two degrees of freedom in the x and y directions. Thus, the mass matrix of a finite element is an 8×8 matrix. The formula for the mass matrix of a single node is: ρ(ξ, η) is the density within the volume of the prefabricated building component at this node, and N i (ξ, η), N j (ξ, η) are the shape functions in the x and y directions at this node. ξ and η are two independent variables with a value range of [-1, 1]. d ξ is the integral with respect to the variable ξ, and d η is the integral with respect to the variable η.

[0045] The stiffness matrix describes the relationship between the external forces and displacements of prefabricated building components, reflecting the ability of prefabricated building components to resist deformation. The stiffness matrix can be obtained by integrating the product of the strain energy density within the prefabricated building component and the derivative of the shape function. The strain energy density is the product of stress and strain. Strain refers to the degree of shape change of the prefabricated building component caused by displacement, and stress refers to the internal force distribution within the prefabricated building component. The specific formula is: where B is the strain-displacement matrix, which contains the derivatives of the shape function with respect to the coordinate axes and reflects the relationship between displacement and strain. B T represents the transpose of B. C is the elastic matrix of the material, which contains the elastic constants of the material, the elastic modulus and Poisson's ratio. |J| represents the area scaling from the natural coordinate system to the physical coordinate system. ξ and η are two independent variables with a value range of [-1, 1]. d ξ is the integral with respect to the variable ξ, and d η is the integral with respect to the variable η.

[0046] The load vector describes the external forces and boundary conditions acting on the prefabricated building component. For surface forces, by calculating the contribution of each finite element and then using the shape function to project these forces onto the nodes, the load vector of the entire structure is formed. The formula for the load vector is where n e is the total number of finite elements, Ω is the region where the finite elements are located, and Ω e represents the partial region occupied by the e-th finite element. N T is the transpose of the shape function matrix, b is the surface force distribution, and dΩ is the area element.

[0047] A linear algebraic equation Mü + Ku = F(t) is formed based on the mass matrix, stiffness matrix, and load vector, where M is the mass matrix, ü represents the second derivative of displacement, K is the stiffness matrix, u is the unknown displacement vector, and the load vector F(t) represents the external force varying with time.

[0048] S50. Solve the finite element equation to obtain the displacement vector, calculate the strain based on the displacement vector, and calculate the stress based on the strain.

[0049] Solving the finite element equation Mü + Ku = F(t) requires converting the time-domain problem into a frequency-domain problem, which is specifically divided into the following sub-steps:

[0050] S51. Establish a frequency-domain equation and convert the time-domain function into a frequency-domain function.

[0051] Perform Fourier transforms on the displacement vector u, external force F(t), and derivative ü of the displacement vector in the equation Mü + Ku = F(t) to convert the time-domain function into a frequency-domain function. Let be the Fourier transform operator, then we have: And represents the Fourier transform of u, represents the Fourier transform of F(t), represents the Fourier transform of ü, and ω represents the angular frequency in the frequency domain. Converting the time-domain equation into the frequency domain, we get:

[0052] S52. Perform an inverse Fourier transform to solve for the unknown displacement vector in the frequency domain.

[0053] Rewrite the above equation as: Perform an inverse Fourier transform on the frequency-domain displacement to obtain the displacement vector u in the time domain: is the Fourier transform operator, ω represents the angular frequency in the frequency domain, ω = 2πf, M is the mass matrix, K is the stiffness matrix, represents the Fourier transform of F(t), and F(t) represents the external force varying with time.

[0054] Thus, the displacement vector u of the precast building component caused by the force at the boundary connection of the component is obtained.

[0055] The strain of the finite element can be expressed as the product of the shape function and the displacement vector, i.e., ε = Bu, where B is the strain-displacement matrix, and its elements are the first and second partial derivatives of the shape function with respect to the coordinates.

[0056] The stress formula is σ = Eε, where E is the elastic modulus of the material, and ε represents the strain of the finite element. Thus, the stress σ of a single finite element is obtained.

[0057] S60. Integrate the element stresses according to the stresses of individual finite elements to calculate the total stress at the boundary connection of prefabricated building components.

[0058] After obtaining the stresses of individual finite elements, sum up the stresses of the finite elements to obtain the stress distribution of the entire boundary. The calculation of the stresses of the finite elements is specifically divided into the following sub-steps:

[0059] S61. Collect the stress values at Gauss points.

[0060] For multiple finite elements divided at the boundary of prefabricated building components, select some specific finite elements as Gauss points so that the approximate value of the calculated total stress value is equal to the exact value. For Gauss point i, its stress value σ i The formula for transferring to node j is ω i is the weight from Gauss point i to node j, and is the temporary stress accumulation value of node j.

[0061] S62. Calculate the average stress of the finite element.

[0062] Calculate the average stress value of the finite element, that is, average all the relevant stress values at Gauss points. The specific formula is σ j represents the average stress value at Gauss point j, that is, the average stress value of the jth finite element, is the temporary stress accumulation value of Gauss point j, and n GaussPoints(j) is the number of Gauss points related to Gauss point j.

[0063] S63. Sum up the average stress values of the finite elements.

[0064] Calculate the total stress value at the boundary of the prefabricated building by calculating the average stress value σ j of the finite element. The specific formula is where S represents the total stress value at a certain boundary where the finite element j is located in the prefabricated building, Q is the number of Gauss points, and J q represents the degree of deformation from natural coordinates to physical coordinates.

[0065] S70. Calculate the bending degree according to the total stress value and displacement at the boundary connection of prefabricated building components, and evaluate the safety of prefabricated buildings according to the bending degree.

[0066] Obtain the total stress value S at a boundary of the prefabricated building component rThe displacement u of the prefabricated building component caused by stress at the boundary of the prefabricated building component. If the bending degree W of the prefabricated building component under the action of stress and displacement does not exceed the maximum bending limit of the prefabricated building component, it indicates that there is no safety risk. If the bending degree W exceeds the maximum bending limit of the prefabricated building component, it indicates that there is a safety risk and it needs to be dealt with as soon as possible. The specific formula is:

[0067]

[0068] R is the total number of boundaries between components in the prefabricated building, ω1 and ω2 are the weights of stress and displacement respectively, S r is the total stress value at one boundary, δ is the influence factor of the structural composition on the load, is the influence factor of the material property on the stress, γ m represents the m-th kind of load force, m ∈ e, and e is the number of types of load forces. b is the cross-sectional width of the prefabricated building component, and h is the cross-sectional height of the prefabricated building component. E is the elastic modulus of the material of the prefabricated building component, I is the moment of inertia of the cross-section, x u , y u , z u represent the displacement components of the displacement u in the x, y, and z directions. w(x u ) is the deflection of the prefabricated building component in the x direction, w(y u ) is the deflection of the prefabricated building component in the y direction, w(z u ) is the deflection of the prefabricated building component in the z direction, d 2 w(x u ), d 2 w(y u ), d 2 w(z u ) are the second derivatives of the deflection functions w(x u ), w(y u ), w(z u ). d represents the differential operation, L is the length of the prefabricated building component, and n is the safety factor.

[0069] Example 2

[0070] As Figure 2 shown, Example 2 of the present application provides a safety risk assessment system for a prefabricated building, including:

[0071] Collection module: used to collect data of prefabricated building components.

[0072] To establish an accurate three-dimensional model, it is necessary to precisely represent precast components, connectors, and filling materials. Therefore, data on precast components, connectors, and filling materials of prefabricated buildings are collected. The data of precast components include component numbers, quantities, lengths, widths, heights, weights, concrete strength grades, load-bearing capacities, and durability indicators. Connectors include fasteners, welded connectors, embedded parts, dry connectors, chemical anchor bolts and mechanical anchor bolts, composite beam and slab connectors, thermal insulation connectors, and prestressed connectors. Filling materials include grouting materials, epoxy resin mortar, polymer mortar, thermal insulation materials, sealants, sound insulation materials, and high-performance concrete.

[0073] Collect design data, including structural design drawings, connection joint details, material specifications, and design loads.

[0074] Modeling module: Used to establish a three-dimensional geometric model based on the data of prefabricated building components collected.

[0075] Use the data of prefabricated building components collected and design data to establish a three-dimensional geometric model of the connections between components, and assign real physical and mechanical properties to each material in the model, including elastic modulus, Poisson's ratio, yield strength, and ultimate strength, etc. And set reasonable support conditions and apply various loads, including self-weight, floor live load, wind load, seismic load, and stress caused by temperature changes, to simulate the real environment of the prefabricated building and the actual usage of the building.

[0076] Calculation module: Used to divide the boundary joints of the three-dimensional geometric model into multiple finite elements, define the shape functions of the finite elements, calculate the mass matrix, stiffness matrix, and load vector according to the shape functions, form a finite element equation from the mass matrix, stiffness matrix, and load vector, solve the finite element equation to obtain the displacement vector, calculate the strain according to the displacement vector, calculate the stress according to the strain, and perform element stress integration based on the stress of a single finite element to calculate the total stress at the boundary joints of prefabricated building components. Specifically, it is divided into the following sub-steps:

[0077] 1. Divide the boundary joints of the three-dimensional geometric model into multiple finite elements and define the shape functions of the finite elements.

[0078] Divide the boundary joints of the three-dimensional geometric model into multiple simple, tight, non-overlapping but interconnected finite elements. The boundary points of the finite elements are called nodes, and there is stress at each node. The sum of the stress values at each node is the total stress at the boundary joints between prefabricated building components.

[0079] To simulate the real stress situation of components, assign material properties to each finite element and correctly set the friction coefficient, pre-tightening force, displacement constraint, pressure load, and force distribution of the contact interface, especially when simulating bolt connections and welded connections.

[0080] To solve for the stress at the boundary connection using the finite element method, an equation consisting of a mass matrix, a stiffness matrix, and a load vector needs to be established and solved. This process calculates the displacement and stress of each node.

[0081] The formation of the mass matrix and the stiffness matrix requires shape functions. Therefore, for each finite element, shape functions are defined, which are non-zero inside the element and zero outside the element. Given the stress at each node, the stress distribution within the prefabricated building component can be accurately reconstructed through a linear combination of these shape functions.

[0082] The finite element is set as a two-dimensional quadrilateral element with four nodes. The shape functions at each node are linear inside the element, take the value of 1 at the node, and 0 at other nodes. The four nodes are labeled A, B, C, and D, and the position of any internal point P is given by the local coordinates (ξ, η), where ξ and η represent two independent variables, and the ranges of ξ and η are both from -1 to 1. The formula for the shape function is: where I = A, B, C, D, and for each node, α I , β I take the following values: For node A: α A = β A = -1, for node B: α B = 1, β B = -1, for node C: α C = β C = 1, for node D: α D = -1, β D = 1. The shape function for each node is: In the mass matrix, N i (ξ, η), N j (ξ, η) represents the shape functions of two degrees of freedom at a node.

[0083] 2. Calculate the mass matrix, stiffness matrix, and load vector according to the shape functions, and form a finite element equation from the mass matrix, stiffness matrix, and load vector.

[0084] The mass matrix reflects the internal mass distribution of the prefabricated building component and its response to external forces, and can be obtained by integrating the product of the density ρ within the volume of the prefabricated building component and the shape function. The mass matrix of a two-dimensional quadrilateral finite element has four nodes, each with two degrees of freedom in the x and y directions. Thus, the mass matrix of a finite element is an 8×8 matrix, and the formula for the mass matrix of a node is: ρ(ξ, η) is the density within the volume of the prefabricated building component at this node, N i (ξ, η), Nj (ξ, η) are the shape functions along the x and y directions at this node. ξ and η are two independent variables with a value range of [-1, 1], and d ξ is the integral with respect to the variable ξ, and d η is the integral with respect to the variable η.

[0085] The stiffness matrix describes the relationship between the external forces and displacements of prefabricated building components, reflecting the ability of prefabricated building components to resist deformation. The stiffness matrix can be obtained by integrating the product of the strain energy density and the derivative of the shape function within the prefabricated building component. The strain energy density is the product of stress and strain. Strain refers to the degree of shape change of the prefabricated building component caused by displacement, and stress refers to the internal force distribution within the prefabricated building component. The specific formula is: where B is the strain-displacement matrix, which contains the derivatives of the shape function with respect to the coordinate axes and reflects the relationship between displacement and strain. B T represents the transpose of B, C is the elastic matrix of the material, which contains the elastic constants, elastic modulus, and Poisson's ratio of the material, |J| represents the area scaling from the natural coordinates to the physical coordinate system, ξ and η are two independent variables with a value range of [-1, 1], and d ξ is the integral with respect to the variable ξ, and d η is the integral with respect to the variable η.

[0086] The load vector describes the external forces and boundary conditions acting on the prefabricated building component. For surface forces, by calculating the contributions of each finite element and then using the shape function to project these forces onto the nodes, the load vector of the entire structure is formed. The load vector formula is where n e is the total number of finite elements, Ω is the region where the finite elements are located, and Ω e represents the partial region occupied by the e-th finite element, N T is the transpose of the shape function matrix, b is the surface force distribution, and dΩ is the surface element.

[0087] According to the mass matrix, stiffness matrix, and load vector, a linear algebraic equation Mü + Ku = F(t) is formed, where M is the mass matrix, ü represents the second derivative of displacement, K is the stiffness matrix, u is the unknown displacement vector, and the load vector F(t) represents the external force varying with time.

[0088] 3. Solve the finite element equation to obtain the displacement vector, calculate the strain based on the displacement vector, and calculate the stress based on the strain.

[0089] To solve the finite element equation Mü + Ku = F(t), the time-domain problem needs to be converted into a frequency-domain problem, which is specifically divided into the following sub-steps:

[0090] (1) Establish a frequency-domain equation and convert the time-domain function into a frequency-domain function.

[0091] For the displacement vector u, the external force F(t), and the derivative ü of the displacement vector in the equation Mü + Ku = F(t), perform Fourier transforms to convert the time-domain functions into frequency-domain functions. Let be the Fourier transform operator, then we have: And represents the Fourier transform of u, represents the Fourier transform of F(t), represents the Fourier transform of ü, and ω represents the angular frequency in the frequency domain. Converting the time-domain equation to the frequency domain gives:

[0092] (2) Perform inverse Fourier transform to solve for the unknown displacement vector in the frequency domain.

[0093] Rewrite the above equation as: For the frequency-domain displacement perform inverse Fourier transform to obtain the displacement vector u in the time domain: is the Fourier transform operator, ω represents the angular frequency in the frequency domain, ω = 2πf, M is the mass matrix, K is the stiffness matrix, represents the Fourier transform of F(t), and F(t) represents the external force varying with time.

[0094] Thus, the displacement vector u of the precast building component caused by the force at the boundary connection of the component is obtained.

[0095] The strain of the finite element can be expressed as the product of the shape function and the displacement vector, i.e., ε = Bu, where B is the strain-displacement matrix, and its elements are the first and second partial derivatives of the shape function with respect to the coordinates.

[0096] The stress formula is σ = Eε, where E is the elastic modulus of the material, and ε represents the strain of the finite element. Thus, the stress σ of a single finite element is obtained.

[0097] 4. Integrate the element stresses according to the stresses of a single finite element to calculate the total stress at the boundary connection of the precast building component.

[0098] After obtaining the stresses of a single finite element, sum up the stresses of the finite elements to obtain the stress distribution of the entire boundary. The calculation of the stresses of the finite elements is specifically divided into the following sub-steps:

[0099] (1) Collect the stress values at the Gauss points.

[0100] For the multiple finite elements divided at the boundary of the precast building component, select some specific finite elements as Gauss points so that the approximate value of the calculated total stress value is equal to the exact value. For Gauss point i, its stress value σi The formula passed to node j is ω i is the weight from Gaussian point i to node j, and is the cumulative value of the temporary stress of node j.

[0101] (2) Calculate the finite element average stress.

[0102] Calculate the average stress value of the finite element, that is, average the stress values of all relevant Gaussian points. The specific formula is σ j represents the average stress value of Gaussian point j, that is, the average stress value of the jth finite element, is the cumulative value of the temporary stress of Gaussian point j, n GaussPoints(j) is the number of Gaussian points related to Gaussian point j.

[0103] (3) Calculate the sum of the average stress values of the finite elements.

[0104] Calculate the total stress value of the boundary of the prefabricated building from the average stress value σ j The specific formula is where S represents the total stress value of a certain boundary where the finite element j is located in the prefabricated building, Q is the number of Gaussian points, J q represents the degree of deformation from natural coordinates to physical coordinates.

[0105] Evaluation module: Calculate the bending degree according to the total stress value and displacement at the boundary connection of the prefabricated building components, and evaluate the safety of the prefabricated building according to the bending degree.

[0106] Obtain the total stress value S of a boundary of the prefabricated building component r and the displacement u generated by the component due to the force at the boundary of the prefabricated building component. If the bending degree W of the prefabricated building component under the action of stress and displacement does not exceed the maximum bending limit of the prefabricated building component, it means that there is no safety risk. If the bending degree W exceeds the maximum bending limit of the prefabricated building component, it means that there is a safety risk and it needs to be dealt with as soon as possible. The specific formula is:

[0107]

[0108] R is the total number of boundaries between components in the prefabricated building, ω1 and ω2 are the weights of stress and displacement respectively, S r is the total stress value at a boundary, δ is the influence factor of the structural composition on the load, is the influence factor of the material property on the stress, γ mDenote the m-th load force, where m ∈ e and e is the number of load force types. b is the cross-sectional width of the prefabricated building component, and h is the cross-sectional height of the prefabricated building component. E is the elastic modulus of the material of the prefabricated building component, I is the moment of inertia of the cross-section, and x u , y u , z u represent the displacement components of the displacement u in the three directions of x, y, and z. w(x u ) is the deflection of the prefabricated building component in the x direction, w(y u ) is the deflection of the prefabricated building component in the y direction, w(z u ) is the deflection of the prefabricated building component in the z direction, and d 2 w(x u ), d 2 w(y u ), d 2 w(z u ) are the second derivatives of the deflection functions w(x u ), w(y u ), w(z u ). d represents the differential operation, L is the length of the prefabricated building component, and n is the safety factor.

[0109] The specific embodiments described above further elaborate on the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made on the basis of the technical solutions of the present invention shall be included within the protection scope of the present invention.

Claims

1. A safety risk assessment method for prefabricated buildings, characterized in that, Including: S10. Collect data of prefabricated building components; S20. Establish a three-dimensional geometric model based on the collected data of prefabricated building components; S30. Divide the boundary joints of the three-dimensional geometric model into multiple finite elements and define the shape functions of the finite elements; Divide the boundary connections of the three-dimensional geometric model into multiple simple, tight, non-overlapping but interconnected finite elements. The boundary points of the finite elements are called nodes. Set the finite elements as two-dimensional quadrilateral elements, which have four nodes. The shape functions at each node are linear within the element and take the value of 1 at the node and 0 at other nodes. Among them, the four nodes are labeled A, B, C, and D, and the position of any internal point P is given by local coordinates given by , representing two independent variables and both ranging from -1 to 1; The formula for the shape function is: , where I = A, B, C, D, and for each node, , takes the following values: for node , for node , for node , for node ; S40. Calculate the mass matrix, stiffness matrix, and load vector according to the shape functions, and form a finite element equation from the mass matrix, stiffness matrix, and load vector; The elements of the mass matrix are obtained by integrating the product of the density and the shape function within the volume of the prefabricated building component, and are expressed as: , is the density within the volume of the prefabricated building component at this node, , are the shape functions in the x and y directions at this node, and are two independent variables, and the value range is [-1, 1], is the integral with respect to the variable , is the integral with respect to the variable ; The elements of the stiffness matrix are obtained by integrating the product of the strain energy density and the derivative of the shape function within the prefabricated building component, and are expressed as: , where B is the strain-displacement matrix, which contains the derivatives of the shape function with respect to the coordinate axes and reflects the relationship between displacement and strain, represents the transpose of B, and C is the elastic matrix of the material, which contains the elastic constants, elastic modulus, and Poisson's ratio of the material, represents the area scaling from natural coordinates to the physical coordinate system, and are two independent variables, and the value range is [-1, 1], is the integral with respect to the variable , is the integral with respect to the variable ; The load vector needs to calculate the contribution of each finite element and then project these forces onto the nodes using the shape function to form the load vector of the entire structure, and is expressed as: , where, is the total number of finite elements, is the region where the finite element is located, represents the partial region occupied by the e-th finite element, is the transpose of the shape function matrix, b is the area force distribution, is the area differential; Form a linear algebraic equation based on the mass matrix, stiffness matrix, and load vector , where M is the mass matrix, represents the second derivative of displacement, K is the stiffness matrix, u is the unknown displacement vector, and the load vector represents the external force varying with time; S50. Solve the finite element equation to obtain the displacement vector, calculate the strain according to the displacement vector, and calculate the stress according to the strain; S60. Integrate the element stresses according to the stresses of individual finite elements to calculate the total stress at the boundary joints of prefabricated building components; S70. Calculate the bending degree according to the total stress value and displacement at the boundary joints of prefabricated building components, and evaluate the safety of prefabricated buildings according to the bending degree; The calculation formula for the bending degree W is as follows: , is the total number of boundaries between components in the prefabricated building, , are the weights of stress and displacement respectively, is the total stress value at a boundary, is the influence factor of the structural composition on the load, is the influence factor of the material property on the stress, represents the m-th type of load force, , where e is the number of types of load forces; b is the cross-sectional width of the prefabricated building component, h is the cross-sectional height of the prefabricated building component; E is the elastic modulus of the material of the prefabricated building component, I is the moment of inertia of the cross-section, represents the displacement components of the displacement u in the x, y, and z directions, is the deflection of the prefabricated building component in the x direction, is the deflection of the prefabricated building component in the y direction, is the deflection of the prefabricated building component in the z direction, , , are the second derivatives of the deflection function , where d represents the differential operation, L is the length of the prefabricated building component, and n is the safety factor.

2. The safety risk assessment method for a prefabricated building according to claim 1, wherein When establishing the three-dimensional geometric model, the real environment of the prefabricated building and the actual use situation of the building should be simulated. Use the collected data of prefabricated building components to establish a three-dimensional geometric model of the connections between components, assign real physical and mechanical properties to each material in the model, and set reasonable support conditions and apply various loads. When establishing the three-dimensional geometric model, the real environment of the prefabricated building and the actual use situation of the building should be simulated. Use the collected data of prefabricated building components to establish a three-dimensional geometric model of the connections between components, assign real physical and mechanical properties to each material in the model, and set reasonable support conditions and apply various loads.

3. The safety risk assessment method for a prefabricated building according to claim 1, characterized in that, To solve the finite element equation, a frequency-domain equation needs to be established, convert the time-domain function to a frequency-domain function, and then perform an inverse Fourier transform to solve the unknown displacement vector in the frequency domain.

4. The safety risk assessment method for a prefabricated building according to claim 1, wherein To integrate the element stresses according to the stresses of individual finite elements, it is necessary to collect the stress values at Gauss points, calculate the average stress of the finite element, and sum up the average stress values of the finite elements to obtain the total stress value at the boundary of the prefabricated building.

5. A safety risk assessment system for prefabricated buildings, which is used to execute a safety risk assessment method for prefabricated buildings as described in any one of claims 1-4, characterized in that, Including: Collection module: Used to collect data of prefabricated building components; Modeling module: Used to establish a three-dimensional geometric model based on the collected data of prefabricated building components; Calculation module: Used to divide the boundary joints of the three-dimensional geometric model into multiple finite elements, define the shape functions of the finite elements, calculate the mass matrix, stiffness matrix, and load vector according to the shape functions, form a finite element equation from the mass matrix, stiffness matrix, and load vector, solve the finite element equation to obtain the displacement vector, calculate the strain according to the displacement vector, calculate the stress according to the strain, integrate the element stresses according to the stresses of individual finite elements, and calculate the total stress at the boundary joints of prefabricated building components; Evaluation module: Calculate the bending degree according to the total stress value and displacement at the boundary joints of prefabricated building components, and evaluate the safety of prefabricated buildings according to the bending degree.

6. The safety risk assessment system for a prefabricated building according to claim 5, characterized in that, When establishing the three-dimensional geometric model, the real environment of the prefabricated building and the actual use situation of the building should be simulated. Use the collected data of prefabricated building components to establish a three-dimensional geometric model of the connections between components, assign real physical and mechanical properties to each material in the model, and set reasonable support conditions and apply various loads.

7. The safety risk assessment system for a prefabricated building according to claim 5, characterized in that, The composition of the finite element equation includes a mass matrix, a stiffness matrix, and a load vector. The elements of the mass matrix are obtained by integrating the product of the density within the volume of the prefabricated building component and the shape function; the elements of the stiffness matrix are obtained by integrating the product of the strain energy density within the prefabricated building component and the derivative of the shape function. The load vector needs to calculate the contribution of each finite element, and then use the shape function to project these forces onto the nodes to form the load vector of the entire structure.

8. The safety risk assessment system for a prefabricated building according to claim 5, characterized in that, To solve the finite element equation, a frequency-domain equation needs to be established, convert the time-domain function to a frequency-domain function, and then perform an inverse Fourier transform to solve the unknown displacement vector in the frequency domain.

9. The safety risk assessment system for a prefabricated building according to claim 5, wherein, To perform element stress integration based on the stress of a single finite element, it is necessary to collect the Gaussian point stress values, calculate the average stress of the finite element, and sum up the average stress values of the finite elements to obtain the total stress value at the boundary of the prefabricated building.

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