A core column plate rapid design system and method based on finite element parameter regression

Abstract

The application discloses a kind of core column plate fast design system and method based on finite element parameter regression.Firstly, ABAQUS is combined with concrete damage plastic model, and a multidimensional parameterized finite element-experience formula database is established, and the function relationship of limit load, stiffness degradation and unit volume bearing capacity and key parameters is obtained by regression.On this basis, database and regression model are called, and multi-objective optimization that satisfies bearing capacity, stiffness and self-weight / hollow ratio constraint simultaneously is carried out, and the optimal combination parameters such as UHPC strength grade, upper and lower plate thickness, tensile reinforcement ratio, core column diameter and spacing and rib width are quickly deduced back, and reinforcement drawing and checking report are automatically generated.The application preposes tedious single finite element analysis as reusable parameter library, realizes the engineering fast design of core column plate, and is conducive to the popularization and application of the new plate system.

Description

Technical Field

[0001] This invention relates to the field of civil engineering structural design and computer-aided design technology, specifically to a rapid design system and method for ultra-high performance concrete (UHPC) core column slabs based on finite element parameter regression, which can be used for scheme design and parameter optimization of UHPC hollow core column slab structures in building and bridge engineering. Background Technology

[0002] Ultra-high performance concrete (UHVPC), with its high strength, high toughness, and high durability, has been widely researched and applied in bridge pavement, composite beam bridges, and reinforcement and widening projects. To further reduce self-weight, increase span, and improve overall economic efficiency, the engineering community has proposed various hollow slab, ribbed slab, and core column slab systems. These systems achieve lightweighting and efficient material utilization by incorporating cavities or core columns within the slab. The stress performance of such components is complex, and traditional designs often rely on simplified mechanical models and empirical coefficients, making it difficult to systematically reflect the coupled effects of changes in material and structural parameters on load-bearing capacity and deformation performance.

[0003] With the development of finite element analysis (FEM) technology, researchers have utilized commercial FEM software combined with concrete damage-plasticity models to conduct extensive numerical simulations and parametric analyses of UHPC slabs, composite slabs, and hollow slabs. This research aims to reveal the stress mechanisms and failure modes under different reinforcement, thicknesses, span-to-depth ratios, and structural forms. Simultaneously, some scholars have established bearing capacity prediction formulas for specific components (such as shear connectors and composite components) using regression methods based on FEM parametric analysis results, thus providing simplified calculation methods for engineering design. Furthermore, in the design of conventional components such as reinforced concrete ribbed slabs or hollow slabs, existing literature has attempted to use optimization algorithms to optimize the cost or weight of reinforcement and cross-sectional dimensions.

[0004] However, existing technologies still have the following shortcomings:

[0005] (1) For the new system of core plate, most of the published literature focuses on single structural form or experimental and finite element analysis within a limited parameter range. There is a lack of a large-scale system database covering multiple parameters such as material, plate thickness, core column size and spacing, rib width, span-to-height ratio, etc., and a parametric finite element-empirical formula library that can be reused in engineering has not yet been formed 41318.

[0006] (2) Existing regression formulas based on finite element results are usually geared towards a single performance index, such as the prediction of the ultimate bearing capacity of a certain type of shear connector 12. They are difficult to simultaneously take into account multiple performance indicators such as bearing capacity, stiffness degradation and bearing capacity per unit volume, and have also failed to construct a multi-objective design framework for specific plate systems (such as core column plates).

[0007] (3) The optimization design research on hollow slabs or ribbed slabs is mostly focused on the cost or reinforcement optimization of conventional reinforced concrete components.17 There is little comprehensive consideration of UHPC material properties, core column relative density and hollowness ratio and span-to-depth ratio. Furthermore, there is a lack of a rapid design tool that can solidify the pre-completed finite element parameter analysis results into a database and directly back-derive the component parameters through multi-objective optimization.

[0008] (4) Existing UHPC related designs mostly adopt the process of “modeling component by component - single finite element analysis - manual trial calculation and comparison”. Each scheme needs to be remodeled and calculated. Designers find it difficult to systematically compare and select a large number of alternative core column plate parameter combinations within a limited time, which limits the promotion and application of this new type of plate system in engineering practice.

[0009] Therefore, it is necessary to provide a new design method and system for core column plates. By pre-establishing a multi-parameter finite element-regression database, a large number of numerical analysis results can be structurally stored. In the engineering application stage, key parameters of the components can be quickly back-calculated through multi-objective optimization, while meeting multiple requirements such as bearing capacity, deflection, and self-weight / void ratio. This significantly improves design efficiency and scheme quality, and overcomes the shortcomings of existing technologies such as single finite element analysis, manual trial calculation, and lack of integrated design tools. Summary of the Invention

[0010] This invention addresses the following problems in existing core column plate designs: Designers typically need to establish and analyze separate finite element models for each core column arrangement and plate thickness combination, resulting in a large workload and long cycle, making it difficult to fully compare and select multiple solutions in the early stages of engineering. Existing empirical formulas based on finite element results are mostly oriented towards single indicators and have not yet established a parametric finite element-regression database for core column plate systems that simultaneously considers multi-dimensional performance such as ultimate bearing capacity, stiffness degradation, and unit volume bearing capacity. Furthermore, there is a lack of design tools for core column plates that can directly use plate span, design load, allowable deflection, crack width limit, and target void ratio / self-weight as inputs to automatically derive key parameters such as UHPC strength grade, upper and lower plate thicknesses, reinforcement ratio, core column dimensions and spacing, and rib width.

[0011] The purpose of this invention is to provide a rapid design method and system for core column plates based on finite element parameter regression. This method stores and models a large number of pre-completed finite element parameter analysis results in a structured manner. In the engineering application stage, multi-objective optimization is used to directly deduce the component parameter combination that meets the requirements of bearing capacity, stiffness, and self-weight / void ratio. This significantly shortens the design cycle, improves the quality of the scheme, and facilitates the promotion and application of this new type of core column plate system in engineering practice.

[0012] To achieve the above objectives, the present invention provides the following technical solution.

[0013] 1. Core Plate Design Method

[0014] A core plate design method includes:

[0015] Finite element parametric analysis and data acquisition steps: Using finite element software and the concrete damage plasticity (CDP) model, the tensile strength of UHPC at different values ​​was analyzed. Tensile reinforcement ratio Thickness of upper and lower plates The system parametric analysis was carried out on the combination of parameters such as core column diameter, core column spacing, rib width and span-to-height ratio to obtain the ultimate bearing capacity, load-deflection curve, stiffness degradation index and crack control index under each combination, and recorded as the original parametric finite metadata.

[0016] Steps for constructing a multi-parameter finite element-regression database: The original finite element data is structured and stored according to material parameters, geometric parameters, and mechanical performance indicators to establish a parametric finite element result database. Based on this, multiple regression, nonlinear regression, or piecewise regression methods are used to fit and obtain the ultimate load and... , , Functional relationships between them; functional relationships between stiffness degradation coefficient and span-to-depth ratio and core column spacing; bearing capacity per unit volume relative density with core column The functional relationship between them is determined; and the obtained empirical formulas and their applicable ranges are stored in the database to form a multi-parameter finite element-empirical formula library.

[0017] Engineering design input and constraint conversion steps: Obtain the design input parameters of the target project, including: slab span, slab width, design dead load and live load combination value, allowable deflection limit, allowable crack width limit, and target void ratio and / or upper limit of self-weight; convert the above input parameters into constraints on the core column slab in terms of bending capacity, shear capacity, stiffness (deflection control) and durability (crack width control), and introduce constraints on self-weight or void ratio.

[0018] The steps for establishing a multi-objective optimization model are as follows: Design variables include UHPC strength grade, upper and lower slab thickness, tensile reinforcement ratio, core column diameter, core column spacing, and rib width; objective functions include minimizing component self-weight, minimizing material usage, and / or minimizing overall cost; constraints include bearing capacity not being less than the design effect calculated from the design load, deflection not exceeding a certain proportion of the span height, crack width not exceeding the code limit, and self-weight or void ratio meeting design requirements; and a multi-objective optimization design model is established by calling a regression model from the parametric finite element-empirical formula library.

[0019] Multi-objective optimization solution steps: Use genetic algorithm, particle swarm optimization algorithm or other multi-objective heuristic algorithm to solve the above optimization model; during the solution process, use empirical formulas to replace the reconstruction of finite element model and calculation to obtain the optimal or suboptimal solution set of core column plate cross-sectional parameters that satisfy various constraints.

[0020] Results output and verification report generation steps: Based on the optimization results, the recommended UHPC strength grade, upper and lower plate thickness, tensile reinforcement ratio, core column diameter and spacing, and rib width are automatically generated; graphical output including structural diagrams and reinforcement diagrams is automatically generated; at the same time, based on the regression model and detailed finite element results of corresponding parameter points or adjacent points in the database, load-bearing capacity verification, deformation verification, and crack control verification reports are generated to achieve traceable verification of the recommended scheme.

[0021] 2. Core Plate Rapid Design System

[0022] A rapid design system for core plates based on finite element parameter regression, which can be deployed on a server or local terminal, includes:

[0023] Parametric Finite Element Result Database (20): Used to store finite element analysis results and empirical formulas derived from the regression of different combinations of UHPC material parameters, geometric parameters and reinforcement parameters; the database may include a sub-database of original finite element data and a sub-database of empirical formulas, and supports multi-dimensional retrieval by material, geometry and performance indicators.

[0024] Regression Analysis Module (30): Used to import, clean and extract features of newly added finite element cases; according to the preset model type (such as multiple linear regression, nonlinear regression, piecewise function, etc.), fit the relationship between the ultimate bearing capacity, stiffness degradation and unit volume bearing capacity and key design parameters, and write the fitting results and their error indicators into the database.

[0025] Constraint Solving and Optimization Module (40): It is used to automatically construct a multi-objective optimization model based on the engineering parameters input by the user through the user interface; call the empirical formulas in the parameterized finite element result database to quickly calculate the bearing capacity, deflection, crack width and self-weight under different combinations of design variables; and use genetic algorithm, particle swarm algorithm or other multi-objective heuristic algorithm to perform iterative solution and output one or more sets of optimized solutions that meet the constraint conditions.

[0026] Graphical component generation module (50): It is used to automatically generate a schematic diagram of the core column plate structure, a schematic diagram of the core column layout and a schematic diagram of the reinforcement according to the combination of cross-sectional parameters output by the optimization module; it can further output standardized BIM family files or CAD component block files for integration with existing structural design software or BIM platform.

[0027] User interface (60): Provides a graphical interface for users to input the slab span, slab width, design load, allowable deflection limit, allowable crack width limit, and target void ratio and / or self-weight limit of the target project; displays the convergence status during the optimization calculation process, the key performance indicators of candidate schemes, and the parameter list, graphical components, and verification report summary of the final recommended scheme.

[0028] Processor (13) and storage medium (70): The processor is used to execute the computer program stored in the storage medium to realize the functions of the above modules; the storage medium stores instructions to implement each step of the core plate design method. When the instructions are executed by the processor, the system completes the entire process from parametric finite element-regression database call to multi-objective optimization solution and graphical output.

[0029] Through the above methods and systems, this invention transforms the traditional process of "component-by-component fine finite element modeling - single calculation - manual comparison" into a new design mode of "pre-establishing parametric finite elements - regression database - rapid optimization and back-deriving of parameters in the engineering stage", realizing rapid scheme comparison and engineering application of core column plates.

[0030] 3. Beneficial effects of the present invention

[0031] Compared with the prior art, the present invention has at least the following beneficial effects:

[0032] Significantly improves design efficiency: A large amount of finite element parameter analysis work is carried out in advance and solidified into a reusable database. During the engineering application stage, the performance of components can be quickly evaluated through regression models, avoiding repeated modeling and single finite element recalculation, and greatly shortening the core column plate scheme comparison time.

[0033] Achieving multi-objective comprehensive optimization: Within the same optimization framework, multiple indicators such as ultimate bearing capacity, stiffness degradation, crack control, and self-weight / void ratio are considered simultaneously. The multi-objective optimization algorithm automatically seeks the best solution that balances performance and economy.

[0034] Enhance the traceability and integrability of design results: all recommended solutions can be supported by corresponding or adjacent finite element examples in the database, facilitating the traceability and verification of results; graphical component outputs can be directly integrated with existing design processes as BIM families or CAD component blocks, lowering the threshold for promotion.

[0035] Facilitating the promotion and application of the new system in engineering: Transforming a large number of parameter analysis results from the thesis stage into a "rapid design tool" that can be directly called in engineering, reducing the repeated understanding and modeling costs of the core column plate stress mechanism for designers, and facilitating the application and promotion of this new core column plate system in building and bridge engineering. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the embodiments of the present invention will be briefly described below with reference to the accompanying drawings. Obviously, the accompanying drawings described below are only for illustrating exemplary embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0037] Figure 1 This is a schematic diagram of the overall structure of a rapid design system for core plates based on finite element parameter regression according to the present invention.

[0038] Figure 2 This is a flowchart illustrating a core plate design method according to the present invention.

[0039] Figure 3 This is a schematic diagram of the structure of the parametric finite element result database in this invention.

[0040] Figure 4 This is a schematic diagram of the user interface in this invention.

[0041] To facilitate understanding of the structure and steps in the accompanying drawings, the main reference numerals in the drawings are explained below.

[0042] exist Figure 1 In the process, the core column plate rapid design system (10) can be deployed on a server (12) for multiple user terminals (11) to access via a communication network (80); or it can be deployed on a single workstation, in which case the server and the user terminal can be the same physical device. The processor (13) executes the program in the storage medium (70) to control the parametric finite element result database (20), regression analysis module (30), constraint solving and optimization module (40), graphical component generation module (50), and user interface (60).

[0043] exist Figure 2 In this process, the steps form a series of steps: the output data of the finite element parametric analysis and data acquisition step (S10) is input into the database construction step (S20); the empirical formula library after database construction is called in the engineering design input and constraint conversion step (S30) and the multi-objective optimization model establishment step (S40); then the multi-objective optimization solution step (S50) completes the scheme optimization; finally, the result output and verification report generation step (S60) outputs the recommended scheme and verification results.

[0044] exist Figure 3In the original finite element data sub-library (21), the structural performance data directly output by the finite element calculation is stored and structured according to the material parameter field set (211), geometric parameter field set (212), reinforcement parameter field set (213), and mechanical performance result field set (214). The empirical formula sub-library (22) stores the ultimate bearing capacity regression model set (221), stiffness degradation regression model set (222), and unit volume bearing capacity regression model set (223) obtained by the regression analysis module (30), as well as the corresponding applicable scope and error index (224).

[0045] exist Figure 4 In the process, users complete the design input through the basic engineering information input area (601), geometric parameter input area (602), load and control index input area (603), and target void ratio / self-weight control input area (604). The constraint solution and optimization module (40) is started through the calculation and optimization control area (605). After optimization, the recommended scheme and its performance index can be viewed in the result parameter output area (606) and the performance index and verification result display area (607). The corresponding component shape and reinforcement diagram can be viewed in the graphical component display area (608). Detailed Implementation

[0046] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the invention. Without departing from the concept of the invention, those skilled in the art can make various modifications or equivalent substitutions to the following embodiments, and all such modifications or substitutions fall within the protection scope of the present invention.

[0047] I. System Overall Structure and Deployment Method (corresponding to) Figure 1 )

[0048] like Figure 1 As shown, this embodiment provides a rapid design system 10 for core plates based on finite element parameter regression. The system can adopt a server-client architecture or be deployed on a standalone workstation.

[0049] In a preferred embodiment: the user terminal 11 is a personal computer or workstation with structural design software and the client program of the present invention installed; the server 12 is a computing server with high computing power and large storage capacity; the user terminal 11 and the server 12 are connected via a communication network 80 (such as a local area network or the Internet); the processor 13 is located inside the server 12, or can be located in a standalone system, and is used to execute the computer program stored on the storage medium 70; the storage medium 70 can be a hard disk, solid-state drive, array storage, flash memory, etc., and stores an instruction set for implementing the method steps of the present invention.

[0050] System 10 mainly includes the following functional components:

[0051] 1. Parametric Finite Element Result Database 20

[0052] Original finite element metadata sub-library 21: stores a large amount of original result data obtained from the finite element parametric analysis of core plate; Empirical formula sub-library 22: stores various empirical formulas and related metadata obtained by fitting the regression analysis module 30.

[0053] 2. Regression Analysis Module 30

[0054] Deployed on server 12 or local terminal, it is responsible for: importing, cleaning and standardizing the results of newly added finite element calculation cases; automatically identifying material, geometry, reinforcement and load parameter fields; performing regression analysis according to preset model type, and writing the obtained regression coefficients, residual indices, applicable scope, etc. into the empirical formula sub-library 22.

[0055] 3. Constraint Solving and Optimization Module 40

[0056] The program executed by processor 13 is used to: automate the user-input plate span, plate width, design load, deflection and crack control index into several constraints; call the regression model in the empirical formula sub-library 22 to quickly calculate the ultimate bearing capacity, deflection, crack width and self-weight and other performance indicators under a given combination of design variables; and use a multi-objective optimization algorithm to solve the problem and output the optimal or suboptimal parameter combination that satisfies the constraints.

[0057] 4. Graphical component generation module 50

[0058] Deployed on server 12 or user terminal 11, it is used to: convert the component parameters output by constraint solving and optimization module 40 into planar and three-dimensional structural diagrams; generate reinforcement diagrams including information such as plate thickness, core column arrangement, rib width, reinforcement location and reinforcement ratio; and output BIM family files or CAD component block files as needed, and integrate with mainstream design software (such as Revit, AutoCAD, etc.).

[0059] 5. User interface 60

[0060] It is generally implemented by a client program running on user terminal 11, or it can be deployed on server 12 in the form of a web page and accessed by a browser to achieve: inputting basic project information and design requirements; starting or stopping optimization calculations; and viewing and exporting result parameters, performance indicators and graphical components.

[0061] Through the above structure, system 10 can achieve rapid design and scheme optimization of core plate.

[0062] II. Core Column Plate Design Method and Flow (corresponding) Figure 2 )

[0063] like Figure 2 As shown, the core plate design method of this invention includes the following steps:

[0064] Step S10: Finite element parametric analysis and data acquisition

[0065] (1) Establishment of finite element model

[0066] A three-dimensional solid model of the core column plate was built using finite element software (such as ABAQUS), and the nonlinear behavior of the UHPC material was described using the concrete damage plasticity (CDP) constitutive model. The model includes: upper and lower UHPC panels (upper and lower plates); several UHPC core columns arranged in a regular or irregular array; ribs connecting the upper and lower plates (if the core column and rib are combined, they can also be regarded as thickened core column areas); the reinforcement uses embedded or solid steel reinforcement elements, considering the joint action of the steel reinforcement and concrete.

[0067] (2) Setting parametric design variables

[0068] Set multiple discrete values ​​for the following parameter and combine them: UHPC tensile strength. For example, grades such as 6 MPa, 8 MPa, 10 MPa, and 12 MPa are used; UHPC compressive strength: corresponding to different strength grades, such as 120 MPa and 150 MPa, are used as input for the CDP model; tensile reinforcement ratio. For example, 0.5%, 0.8%, 1.0%, 1.2%, etc.; thickness of upper and lower plates. For example, 30 mm, 40 mm, 50 mm, etc.; core diameter For example, 80 mm, 100 mm, 120 mm, etc.; core spacing For example, 300 mm, 400 mm, 500 mm, etc.; rib width For example, 80 mm, 100 mm, 120 mm, etc.; span-to-depth ratio Controlled by a combination of span and total component thickness, such as 20, 25, 30, etc.

[0069] (3) Loads and boundary conditions

[0070] Apply uniformly distributed loads and / or concentrated loads as determined by the specifications for each parameter combination, set different boundary conditions such as simply supported, continuous or fixed support, and record: load-deflection curves; crack width or equivalent tensile strain distribution; failure mode and ultimate load; stiffness changes at different loading stages.

[0071] (4) Result extraction and formatting

[0072] For each calculation case, extract the ultimate load from the finite element results. Or the corresponding uniformly distributed load Key deflection points (e.g.) , The corresponding load and deflection; stiffness degradation coefficient (such as the stiffness ratio before and after yielding or before and after cracking); maximum crack width or crack width of the control section (obtained through post-processing or equivalent crack model); component self-weight and bearing capacity per unit volume, etc.

[0073] The above results, along with the material, geometry, and reinforcement parameters, are formatted and written into the original finite metadata sub-database 21.

[0074] Step S20: Construction of Multi-parameter Finite Element-Regression Database

[0075] like Figure 3 As shown, the data obtained in step S10 is further structured:

[0076] (1) Structured storage of raw data

[0077] In the original finite metadata sub-database 21, it is divided according to field sets: Material parameter field set 211: including UHPC compressive strength, tensile strength, elastic modulus, Poisson's ratio, etc.; Geometric parameter field set 212: including upper plate thickness, lower plate thickness, core column diameter, core column spacing, rib width, span, total thickness, span-to-depth ratio, etc.; Reinforcement parameter field set 213: including tensile reinforcement ratio, rebar diameter, reinforcement spacing, rebar strength grade, etc.; Mechanical performance result field set 214: including ultimate load, key points of load-deflection curve, stiffness degradation coefficient, maximum crack width, and unit volume bearing capacity. wait.

[0078] (2) Construction of regression model

[0079] The regression analysis module 30 reads data from the original finite metadata sub-database 21 and performs multivariate regression analysis on the target performance indicators: for the ultimate load or In the preferred embodiment, a multiple linear or piecewise linear regression form is used: For the stiffness degradation coefficient Using exponential or power function forms, the span-to-height ratio and core column spacing are taken as independent variables: For the bearing capacity per unit volume relative density with core column The relationship is expressed using a single-peak function or a piecewise function to reflect the existence of an optimal load-bearing efficiency within a certain void ratio range: .

[0080] (3) Model performance evaluation and screening

[0081] Cross-validation and residual analysis are performed on the regression model. If the error of a certain model in the target parameter domain exceeds a preset threshold (e.g., relative error greater than 5%), the model type is automatically changed (e.g., from linear to piecewise linear or nonlinear) and refitted.

[0082] The final selected regression model is written into the empirical formula sub-library 22, including: ultimate bearing capacity regression model set 221; stiffness degradation regression model set 222; unit volume bearing capacity regression model set 223; and model applicability range and error index field set 224 (recording the effective parameter range, goodness of fit, maximum error, etc. of each model).

[0083] Step S30: Engineering Design Input and Constraint Transformation

[0084] like Figure 4 As shown, the user inputs the following through the user interface 60: Basic project information (601): Project name, component number, usage environment, etc.; Geometric parameters (602): Design slab span. , board width Support conditions (simply supported, continuous, etc.); Loads and control parameters (603): Dead load, live load, combined value, allowable deflection limit (e.g., , ), allowable crack width limit (e.g., 0.2 mm, 0.3 mm, etc.); target void ratio / weight control (604): target void ratio range (e.g., 30% to 60%) or upper limit of weight.

[0085] The constraint solving and optimization module 40 automatically converts the above input into the following constraints:

[0086] (1) Strength constraints: Calculate the design bending moment Design shear force The flexural bearing capacity is required to be estimated by the regression model. and shear bearing capacity satisfy ;

[0087] (2) Stiffness and serviceability limit state constraints: The maximum deflection under the design load combination is estimated using a stiffness degradation regression model. ,Require ,in Allow for deflection control parameters (such as 250, 400, etc.).

[0088] (3) Crack control constraints: estimate crack width using empirical formulas or by interpolation from a database. ,Require .

[0089] (4) Self-weight / void ratio constraint: Calculate the self-weight of the component based on the geometric parameters. The relative density is calculated from the core geometry. or holm rate ,Require .

[0090] Step S40: Establishing a multi-objective optimization model

[0091] In this embodiment, the following variables are used as design variables: UHPC strength level (through different , (Combined representation); upper plate thickness Bottom plate thickness Tensile reinforcement ratio Core diameter Spacing with core post ; Rib width .

[0092] Optional objective functions include, but are not limited to: minimizing the component's self-weight. Minimize material costs (considering UHPC unit price, steel bar unit price, etc.): Maximizing the overall performance score (combining indicators such as bearing capacity reserve coefficient, stiffness margin, and self-weight into a unified score): ,in To design the variable vector, in the case of multiple objectives, the weighted sum method or the Pareto front method can be used to achieve a compromise optimization of multiple objectives.

[0093] Step S50: Multi-objective optimization solution

[0094] The constraint solving and optimization module 40 calls the regression model in the empirical formula sub-library 22. In each iteration, for a given combination of design variables... Calculate: Ultimate bearing capacity , Deflection Crack width Self-respect , empty rate or And check whether the above quantities meet the constraints.

[0095] In a preferred embodiment, a genetic algorithm is used to achieve multi-objective optimization: an initial population is randomly generated based on the given range of variable values ​​and step size; for each individual, a regression model is called to calculate the objective function and constraint function values; constraints are handled using a penalty function or a feasibility ranking strategy; selection, crossover, and mutation operations are performed according to fitness; the process iterates for several generations until the convergence condition is met or a preset number of generations is reached; and the Pareto optimal solution set or a single comprehensive optimal solution that satisfies the constraints is output.

[0096] Since the required performance indicators can be quickly calculated using empirical formulas, it avoids performing full finite element analysis for every design scheme, greatly reducing the computational load for optimization solutions.

[0097] Step S60: Output Results and Generate Verification Report

[0098] Once the optimization solution is complete: the optimization module 40 passes the recommended scheme's design variable combination and corresponding performance indicators to the graphical component generation module 50; the graphical component generation module 50 automatically draws, based on parameters such as the upper plate thickness, lower plate thickness, core column diameter and spacing, rib width, and reinforcement ratio: a schematic diagram of the core column plate layout; detailed drawings of typical sections (including the arrangement of core columns and ribs, and the positions of upper and lower tie rods); and optional three-dimensional views.

[0099] Meanwhile, based on empirical formulas and their corresponding original finite element examples, System 10 generates detailed reports on bearing capacity verification, deflection verification, and crack control verification, including: explanations of the sources of key formulas and parameters; conclusive prompts on whether the verification results meet the requirements; and, if necessary, can provide finite element example numbers similar to the recommended scheme, as well as reference links to their detailed calculation results, to achieve traceability of the results.

[0100] Finally, users can view and export the complete design results through the result parameter output area 606, the performance index and verification result display area 607, and the graphical component display area 608 in the user interaction interface 60.

[0101] III. Database Structure and Regression Model Implementation (corresponding) Figure 3 )

[0102] like Figure 3 As shown in the figure, this embodiment further explains the parametric finite element result database 20.

[0103] 1. Original finite metadata sub-repository 21

[0104] The original finite element metadata sub-database 21 can be implemented using a relational database or a document-oriented database. Each record represents a finite element calculation case or a parameter combination, and has the following fields: Material parameter field set 211: UHPC compressive strength UHPC tensile strength Elastic modulus Poisson's ratio CDP model parameters (such as compression softening parameters, tensile softening parameters, etc.).

[0105] Geometric parameter field set 212: Span , board width ;Top plate thickness Bottom plate thickness Core diameter Core spacing ; Rib width Total component height Support conditions, span-to-depth ratio wait.

[0106] Reinforcement parameter field set 213: Tensile reinforcement ratio ; diameter and spacing of reinforcing bars; strength grade of reinforcing bars, etc.

[0107] Mechanical performance result field set 214: Ultimate load Or uniformly distributed ultimate load Load and deflection corresponding to several key points (such as cracking point, yield point, and ultimate point) in the load-deflection curve; stiffness degradation coefficient. Maximum deflection under design load Maximum crack width Or equivalent value; bearing capacity per unit volume (V is the volume of the component) etc.

[0108] 2. Empirical Formula Sub-Library 22

[0109] In the empirical formula sub-library 22, each type of regression model is maintained as a "model group":

[0110] Ultimate bearing capacity regression model set 221: may contain multiple sub-models for different support conditions and different span-to-depth ratio ranges; each sub-model records its applicable parameter range (e.g., , (etc.), and the corresponding regression coefficients and goodness of fit. Maximum error, etc.

[0111] Stiffness degradation regression model set 222: Divided into different sub-models according to the span-to-height ratio and core column spacing, for example, modeling is performed separately for dense core column arrangement and sparse core column arrangement; each model records the functional form of stiffness degradation coefficient and geometric parameters and error index.

[0112] Unit volume bearing capacity regression model set 223: describes the relative density of different core columns The variation pattern of unit volume load-bearing capacity helps to balance lightweighting and load-bearing performance.

[0113] Model Applicability and Error Index Field Set 224: Used to uniformly store the applicable scope information and error range information of all models, so as to facilitate the quick selection of the matching model based on user input during the design phase.

[0114] When the constraint solving and optimization module 40 calls the database, it will automatically match a suitable regression model based on the current design variable values. If it is in the overlapping area of ​​multiple models, a weighted average or the model with smaller error can be selected.

[0115] IV. User Interface and Operation Flow (corresponding) Figure 4 )

[0116] like Figure 4 As shown in the figure, this embodiment provides a typical user interface layout:

[0117] 1. Basic Project Information Input Area 601: Users input project name, project number, component number, design stage (scheme, preliminary design, construction drawings), etc. It does not directly participate in calculations, but is used for identification of reports and deliverables.

[0118] 2. Geometric parameter input area 602: User input: plate span , board width The system can provide recommended values ​​based on common slab types, such as support conditions (e.g., two-way or one-way slab, simply supported or continuous), and whether edge beam constraints are considered. For example, if the slab width is not entered, it will be calculated based on a unit width of 1.0 m.

[0119] 3. Load and Control Index Input Area 603: User input: dead load, live load and their combination coefficients, allowable deflection limit, allowable crack width. The system can provide commonly used code-recommended values ​​for users to select, or allow users to customize them.

[0120] 4. Target Void Ratio / Weight Control Input Area 604: Users can select either "Control Weight" or "Control Void Ratio" mode. In "Control Weight" mode, input the upper limit of the weight; in "Control Void Ratio" mode, input the target void ratio range. The system automatically establishes the corresponding constraints in the optimization model based on the selection.

[0121] 5. Calculation and Optimization Control Area 605: Provides buttons such as "Start Calculation", "Stop Calculation", and "Optimization Strategy Selection". Users can select the optimization algorithm type (such as fast genetic algorithm, particle swarm optimization, heuristic search, etc.) and key parameters (population size, maximum number of iterations, convergence criterion, etc.).

[0122] 6. Result Parameter Output Area 606: Displays the main geometric and material parameters of the recommended scheme, including: UHPC strength grade; upper and lower plate thickness; tensile reinforcement ratio and recommended steel bar specifications and spacing; core column diameter, spacing and arrangement (square arrangement, oblique arrangement, etc.); rib width and arrangement.

[0123] 7. Performance Indicators and Verification Results Display Area 607: Displays the recommended scheme under the design load combination: ultimate bearing capacity and safety factor; maximum deflection and comparison with the limit; maximum crack width and comparison with the limit; component self-weight and void ratio; verification conclusion (pass / fail).

[0124] 8. Graphical component display area 608: Displays the core column layout plan, representative cross-sectional view, and optional 3D view. Users can rotate and zoom to view details of each part and export it as an image or CAD / BIM file.

[0125] V. Engineering Application Examples (Optional Implementation Examples)

[0126] The following simplified engineering example will further illustrate the application process of this invention.

[0127] Assume an office building uses core-column slabs as its floor structure, with one-way slab spans... m, designed based on a unit width of 1.0m, board width The design load includes a dead load of 6.0 kN / m. Live load 3.0 kN / m The combined design uniformly distributed load is approximately 11.0 kN / m. The allowable deflection limit is... The allowable crack width is 0.2 mm, and the target hollowness is 35% to 55%.

[0128] Designers can perform the following operations through the user interface 60: In 601, enter the project name, component number, etc.; in 602, enter the slab span of 8.0 m, slab width of 1.0 m, and support condition as simply supported at both ends; in 603, enter the dead and live load parameters and select... As the deflection control value, the crack width is limited to 0.2 mm; in step 604, select the "Control Void Rate" mode and enter the void rate range of 35% to 55%; in step 605, select the genetic algorithm as the optimization method, set the population size to 80, the maximum number of iterations to 60, and start "Start Calculation".

[0129] The system background calls the empirical formulas in the parameterized finite element result database 20 to automatically establish a multi-objective optimization model. With self-weight and material cost as the main objective functions, it iteratively searches through a genetic algorithm while satisfying constraints such as bearing capacity, deflection and crack control.

[0130] After approximately 30 to 40 iterations, the system obtains a set of optimized solutions that satisfy the constraints. For example, the key parameters of a recommended solution might be: UHPC strength grade: C150, tensile strength... MPa; upper slab thickness 40 mm, lower slab thickness 50 mm; tensile reinforcement ratio approximately 0.9%, using The core pillars are 100 mm in diameter and spaced 400 mm apart in a square arrangement; the ribs are 100 mm wide; and the calculated self-weight is approximately 3.8 kN / m. This corresponds to a hollow rate of approximately 45%.

[0131] The system also provides: the calculated ultimate bearing capacity is 1.6 times the design bending moment requirement; the maximum deflection is... ,satisfy The limit requirement is met; the maximum crack width is estimated to be 0.18 mm, which is less than the 0.2 mm limit; the message "Check passed" is displayed.

[0132] The values ​​above are merely examples to illustrate the application process of this invention. In actual engineering, users can further adjust and optimize the target weights as needed to obtain more alternative solutions that are biased towards lightweighting or stiffness reserves.

[0133] VI. Optional and Modified Implementation Methods

[0134] 1. Algorithm diversity: In addition to genetic algorithms, the constraint solving and optimization module 40 can also use particle swarm optimization, multi-island genetic algorithms, simulated annealing algorithms or combinations of multiple algorithms to achieve higher global search capabilities or faster convergence speeds.

[0135] 2. Database expansion mechanism: The regression analysis module 30 supports the continuous import of newly added finite element cases and model retraining. When new UHPC formulas or new core column structures appear in the engineering field, the empirical formula sub-library 22 can be quickly updated through the addition of new cases to ensure the applicability and accuracy of the system.

[0136] 3. Integration with standards: The system can pre-set structural design standard clauses for different regions or different versions, and automatically convert the bearing capacity, deflection, crack limit and other conditions in the standard into constraints. Users can complete the setting of control indicators by selecting the standard version.

[0137] 4. Some applications of the method of the present invention: The method of the present invention is not limited to the complete core column plate system, but can also be simplified and applied to: rapid comparison of different core column arrangement schemes (fixed material and plate thickness, optimized core column diameter and spacing); under a given UHPC grade and reinforcement ratio, balancing self-weight and stiffness by only changing the void ratio; for the reinforcement or modification of existing engineering components, using a database to evaluate the performance change trend under small-range parameter adjustments.

[0138] The above-described optional and modified embodiments do not change the basic idea and technical solution of the present invention, and should all be considered to fall within the protection scope of the present invention.

[0139] In summary, as can be seen from the above specific implementation methods, this invention achieves rapid design and scheme optimization of the core column plate by pre-establishing a multi-parameter finite element-regression database for the core column plate and using a multi-objective optimization method to solve the key parameters of the component in reverse during the engineering application stage. It has significant practical value and promotional significance.

Claims

1. A core post plate design method, characterized in that, The steps include: (1) Based on finite element software and concrete damage plasticity model, the tensile strength of UHPC is compared with that of concrete. Tensile reinforcement ratio , plate thickness (1) Parametric analysis of the core column diameter, core column spacing, rib width and span-to-height ratio combination to obtain bearing capacity, load-deflection curve and crack control index; (2) Structure the analysis results of step (1) to establish a parametric finite element-empirical formula database, and obtain the ultimate load and load-deflection curve through regression. , , The relationship between stiffness degradation and span-to-depth ratio, core column spacing, and unit volume bearing capacity. relative density with core column The relationship; (3) Obtain the design input parameters of the target project, including slab span, slab width, design load, allowable deflection limit, allowable crack width limit and target void ratio and / or self-weight limit; (4) Based on the database and regression model in step (2), the design input is transformed into bearing capacity, stiffness and self-weight / hollow ratio constraints. A multi-objective optimization model is established with component self-weight, material usage and / or cost as objective functions. The design variables include at least UHPC strength grade, upper and lower plate thickness, tensile reinforcement ratio, core column diameter and spacing and rib width; (5) Solve the multi-objective optimization model in step (4) to obtain the optimal or suboptimal solution of the core column plate section parameters that satisfy the bearing capacity, deflection and self-weight / hollow ratio constraints; (6) Based on the solution of step (5), automatically generate the recommended section parameters, reinforcement diagram and bearing capacity and serviceability limit state verification report of the core column plate.

2. The method according to claim 1, characterized in that, The ultimate load regression model in step (2) adopts a multiple linear or piecewise linear regression form, and the relationship between stiffness degradation and span-to-depth ratio and core column spacing adopts an exponential or power function regression form. and The relationship is obtained by fitting a single-peak function or a piecewise function to ensure that the error is controlled within a preset threshold in the target parameter domain.

3. The method according to claim 1 or 2, characterized in that, The multi-objective optimization in step (4) simultaneously considers the following constraints: (1) The flexural bearing capacity of the section is not less than the design bending moment, and the shear bearing capacity is not less than the design shear force; (2) The deflection in the serviceability limit state does not exceed a certain proportion of the span, and the crack width does not exceed the limit specified in the code; (3) The self-weight of the core column plate does not exceed the upper limit of the design self-weight and / or the void ratio is not lower than the target void ratio.

4. The method according to any one of claims 1 to 3, characterized in that, The multi-objective optimization algorithm in step (4) is a combination of one or more of the following: genetic algorithm, particle swarm optimization algorithm, or multi-objective heuristic algorithm. The convergence efficiency is improved by training and validating existing examples in the database.

5. A rapid design system for core plates based on finite element parameter regression, characterized in that, include: (1) A parameterized finite element results database is used to store the load-bearing capacity, stiffness and crack performance indicators under different combinations of UHPC materials and structural parameters, as well as the empirical formulas obtained by regression from them. (2) Regression analysis module, used to clean the data, extract features and fit regressions of the newly added finite element calculation results, and update the empirical formula; (3) Constraint solution and optimization module, used to call the database and empirical formula according to the engineering design input, establish and solve the multi-objective optimization model, and obtain the best combination of cross-sectional parameters that meet the constraints of bearing capacity, deflection and self-weight / void ratio; (4) Graphical component generation module, used to automatically generate the cross-sectional schematic diagram, reinforcement diagram and verification report of the core column plate based on the optimization results; (5) User interaction interface, used to input the plate span, plate width, design load, allowable deflection and crack width limit and target void ratio or self-weight upper limit, and display the optimization results and graphical output; wherein, the system is deployed on a server or local terminal, and the corresponding computer program is executed by the processor to realize the module function.

6. The system according to claim 5, characterized in that, Each record in the parametric finite element results database includes at least: UHPC compressive strength, tensile strength, tensile reinforcement ratio, upper and lower plate thickness, core column diameter, core column spacing, rib width, span-to-height ratio, and corresponding ultimate load, key points of the load-deflection curve, stiffness degradation coefficient, and unit volume bearing capacity.

7. The system according to claim 5 or 6, characterized in that, The graphical component generation module is also configured to automatically output standardized BIM family or CAD component block files based on the optimization results, so as to facilitate integration with structural design software.

8. A computer-readable storage medium having a computer program stored thereon, the computer program, when executed by a processor, implementing the steps of the core plate design method as described in any one of claims 1 to 4.

Images