Printed Structure Design and Parameter Optimization Method Based on Process Defect Tolerance Coefficient

Abstract

This invention relates to the field of cement-based 3D printed structures, specifically a method for designing and optimizing printed structures based on a process defect tolerance coefficient. The method includes: S1, obtaining initial parameters of the printed structure and determining printing parameters during the printing process based on these initial parameters. These printing parameters include printing material parameters, printing path parameters, model parameters, equipment parameters, printing environment parameters, and curing parameters; S2, calculating the process defect tolerance coefficient based on the printing parameters; and S3, evaluating the structure type of the printed structure based on the process defect tolerance coefficient to determine its suitability. If suitable, a printing scheme for the printed structure is obtained; if unsuitable, the initial parameters of the printed structure are adjusted, and S1-S3 are repeated to design a suitable printing scheme. This invention achieves quantitative evaluation of additive manufacturing printed structures and constructs a design and parameter optimization method for 3D printed concrete structures, effectively reducing the difficulty of verifying the reliability of printed structures and lowering economic costs.

Description

Technical Field

[0001] This invention relates to the field of cement-based 3D printing structure technology, and in particular to a method for designing and optimizing printed structures based on process defect tolerance coefficients. Background Technology

[0002] 3D printing technology, as a novel construction method integrating mechatronics and additive manufacturing, achieves automated structural forming by layer-by-layer deposition of cement-based materials. It boasts significant advantages such as high design freedom, short construction cycles, and high material utilization, showing broad application prospects in areas such as irregular structure construction and emergency engineering repair. However, inherent process defects such as the rheological properties of cement-based materials, cumulative errors in the printing path, and differences in interlayer bonding performance have led to a long-term lag between the design theory of 3D printed structures and the needs of engineering practice. Currently, the industry generally lacks specific design specifications for printed concrete structures, and there are technological gaps in key aspects such as printing parameter optimization (e.g., the matching of extrusion rate and path planning) and quality assessment standards (e.g., interlayer strength testing methods). This results in poor consistency of the mechanical properties of printed components and difficulty in quantifying structural safety reserves, severely restricting the standardized conversion process from material properties to structural load-bearing capacity.

[0003] To address these issues, the design of embossed structures employs two approaches: first, blindly increasing the safety factor (typically by 20%-30%) based on traditional cast-in-place concrete structure specifications, leading to material waste and soaring construction costs; second, verifying structural reliability through scaled-down model tests, but the scale effect of the embossing process makes it difficult to directly extrapolate test results, and full-scale testing incurs extremely high economic and time costs. Furthermore, the lack of a dynamic parameter adjustment mechanism during construction prevents real-time adjustments to embossing parameters based on environmental temperature and humidity, equipment operating status, and other factors, further exacerbating the uncertainty of structural quality. Summary of the Invention

[0004] The purpose of this invention is to address the lack of quantitative design methods for cement-based 3D printed structures, which makes it impossible to achieve precise matching between printing parameters and structural performance; and to provide a method for designing printed structures and optimizing parameters based on process defect tolerance coefficients.

[0005] In a first aspect, the present invention provides a method for designing and optimizing printed structures and parameters based on process defect tolerance coefficients, comprising the following steps:

[0006] S1. Obtain the initial parameters of the printed structure, and determine the printing parameters during the printing process based on the initial parameters of the printed structure. The printing parameters include printing material parameters, printing path parameters, model parameters, equipment parameters, printing environment parameters, and curing parameters.

[0007] S2. Calculate the process defect tolerance coefficient based on the printing parameters. The formula for calculating the process defect tolerance coefficient is as follows:

[0008]

[0009] In the formula The process defect tolerance coefficient is K, the expansion coefficient is Ω, and the structural safety correction parameter is composed of printing material parameters, printing path parameters, model parameters, equipment parameters, printing environment parameters, and curing parameters.

[0010] S3. Evaluate the structure type of the printed structure according to the process defect tolerance coefficient, and determine whether it is qualified. If it is qualified, the printing scheme of the printed structure is obtained. If it is not qualified, adjust the initial parameters of the printed structure and repeat steps S1 to S3 to design a qualified printing scheme.

[0011] Preferably, the initial parameters of the printed structure include the structure type and the structure dimensions. The structure type is determined based on the terrain and construction control factors, and the structure dimensions include cross-sectional dimensions, etc.

[0012] Preferably, the printing material parameters include the anisotropic strength and durability properties of the material under the casting and printing processes;

[0013] The printing path parameters include the spatial layout of the printing strip, the position of the neutral axis of the structural cross section, and the size of the printing strip.

[0014] The model parameters include cantilever angle, maximum cross-section, model size, and volume.

[0015] The equipment parameters include travel speed, extrusion speed, travel time and interval for maximum printing cross-section, extrusion nozzle shape, material mixing time / number of batches, and pumping / extrusion pressure.

[0016] The printing environment parameters include temperature, humidity, and wind speed;

[0017] The maintenance parameters include maintenance methods and parameters.

[0018] Preferably, the scaling factor is related to parameters such as printing environment, structural implementation, and technological maturity, and the scaling factor ranges from 0.8 to 1.8.

[0019] Preferably, the formula for calculating the structural safety correction parameter is:

[0020]

[0021] In the formula , , p、 , These are printing material parameter factors, printing path parameter factors, equipment parameter factors, curing parameter factors, printing environment parameter factors, and model accuracy factors. The weightings are for printing material parameters, printing path parameters, equipment parameters, maintenance parameters, printing environment parameters, and model accuracy, respectively.

[0022] Preferably, the calculation formula for the printing material parameter factor is:

[0023]

[0024] In the formula To print the strength grade of the specimen, The required strength grade for the cast-in-place components for the project. To determine the durability rating of the printed specimens, The durability performance level of the cast-in-place components required by the project;

[0025] And / or the calculation formula for the device parameter factors is as follows:

[0026]

[0027] In the formula This represents the minimum actual interlayer bonding surface area. This represents the theoretical interlayer bonding surface area. This represents the minimum actual bonding surface area between strips. Theoretical bonding surface area between strips;

[0028] And / or the calculation formula for the maintenance parameter factors is as follows:

[0029]

[0030] In the formula This represents the average springback strength of the printed structural entity after curing. The springback strength error value of the printed structural entity after curing;

[0031] And / or at an ambient temperature of 15-25℃, the printing environment parameter factor is 1; at an ambient temperature between 5-15℃ and 25-35℃, the printing environment parameter factor is the same as the printing material parameter factor; if the temperature is below 5℃ or above 35℃, the printing environment parameter factor is 0.

[0032] And / or if in-situ printing and / or mature rectangular printhead printing technology is used, the model accuracy factor is 1; if secondary assembly / installation is subsequently used, the calculation formula for the model accuracy factor is:

[0033]

[0034] In the formula The number of key parameters; The weight of the i-th key parameter, To print the value of the i-th key parameter of the model, This represents the key parameter value of the i-th model of the printed structure.

[0035] Preferably, when subjected to unidirectional pressure, the calculation formula for the printing path parameter factor is as follows:

[0036]

[0037] In the formula, A is the theoretical cross-sectional area of ​​the printed model, and A' is the theoretical cross-sectional area of ​​the printed strip.

[0038] During bending / shearing, the calculation formula for the printing path parameter factor is as follows:

[0039]

[0040] In the formula This is the ratio of the theoretically printed cross-sectional area to the theoretically cast cross-sectional area. This represents the ratio of the moment of inertia of the printed cross-section, which is composed of several printed strips, to the cross-section of the theoretical cast model. Let be the moment of inertia of the printed cross section composed of several printing strips. The moment of inertia of the cross-section of the theoretically cast model. The number of print strips for the printed cross section. Let be the distance from any infinitesimal element within the cross-section of the i-th printing strip to the neutral axis of the printing cross-section. Let be the distance from any infinitesimal element within the cross-section of the casting model to the neutral axis. Let d be the area of ​​the cross-section of the i-th printed strip. Let be the area of ​​a micro-element within the cross-section of the i-th printed strip;

[0041] When twisting, the formula for calculating the print path parameter factor is:

[0042]

[0043] To print the polar moment of inertia of the cross section about the center, The polar moment of inertia of the cross section of the casting model about the center. The number of print strips for the printed cross section. Let be the distance from any infinitesimal element within the cross-section of the i-th printing strip to the center of the printing cross-section. Let be the distance from any infinitesimal element within the cross-section of the casting model to the center. Let be the area of ​​the cross-section of the i-th printed strip.

[0044] Preferably, The value range is 0.2-0.8. The value range is 0.1-0.5. The value range is 0.1-0.5. The value range is 0-0.2. The value range is 0-0.2. The value range is 0.8-1.2.

[0045] Preferably, the detailed method for evaluating the structural type of the printed structure based on the process defect tolerance coefficient is as follows:

[0046] The process defect tolerance coefficient is incorporated into the structural type industry assessment method to establish a structural type assessment model;

[0047] Based on the initial parameters of the printed structure and the process defect tolerance coefficient, it is determined whether the structure type evaluation model is met. If the structure type evaluation model is met, the printed structure is evaluated as qualified; otherwise, it is unqualified.

[0048] Preferably, the structure type evaluation model is as follows:

[0049]

[0050] In the formula, R() is the bearing capacity function of the component; α d Design values ​​for geometric parameters; S is the structural importance coefficient; S is the design value of the combined effect. f d This refers to the design value for the material strength grade. f c打印构件回弹值 This represents the measured springback value of the printed component.

[0051] Preferably, the method further includes S4: performing an economic estimate on the printed structure that has passed the structural type evaluation, and determining whether it is qualified. If qualified, a printing scheme for the printed structure is obtained; if unqualified, the printing parameters are adjusted, and steps S2 to S4 are repeated to design a qualified printing scheme.

[0052] In a second aspect, the present invention provides a system for designing and optimizing printed structures and parameters based on process defect tolerance coefficients, for executing the above-described method for designing and optimizing printed structures and parameters, the system comprising:

[0053] The parameter acquisition module is used to acquire the initial parameters of the printed structure and determine the printing parameters during the printing process based on the initial parameters of the printed structure. The printing parameters include printing material parameters, printing path parameters, model parameters, equipment parameters, printing environment parameters, and curing parameters.

[0054] The calculation module is used to calculate the process defect tolerance coefficient based on the printing parameters. The formula for calculating the process defect tolerance coefficient is as follows:

[0055]

[0056] In the formula The process defect tolerance coefficient is K, the expansion coefficient is Ω, and the structural safety correction parameter is composed of printing material parameters, printing path parameters, model parameters, equipment parameters, printing environment parameters, and curing parameters.

[0057] The judgment module is used to evaluate the structure type of the printed structure according to the process defect tolerance coefficient, and determine whether it is qualified. If it is qualified, the printing scheme of the printed structure is obtained. If it is unqualified, the initial parameters of the printed structure are adjusted and steps S1 to S3 are repeated to design a qualified printing scheme.

[0058] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0059] 1. This invention provides a method for designing and optimizing parameters of printed structures based on a process defect tolerance coefficient. By introducing a process defect tolerance coefficient, it achieves quantitative evaluation of additive manufacturing components / structures in civil engineering, constructs a design and parameter optimization system for 3D printed concrete structures, and forms a quality assessment framework. This innovation overcomes the technical bottleneck of traditional printing quality consistency, solves the problem of standardized conversion from printing materials to structural components, and effectively eliminates potential safety hazards and technical uncertainties in engineering applications.

[0060] 2. This invention provides a solution that, under the core premise of ensuring structural safety and reliability, significantly improves the standardization level of engineering applications of 3D printed concrete structures through standardized design methods and parameter optimization systems. At the same time, through quantitative control of the quality assessment system, it greatly reduces construction costs and construction difficulty, and effectively reduces the difficulty and economic cost of verifying the reliability of printed structures. This forms a closed-loop technical advantage of "safety and controllability - cost optimization - quality reliability", providing a systematic solution for the large-scale engineering application of additive manufacturing technology in civil engineering. Attached Figure Description

[0061] Figure 1 This is a flowchart of the method for designing and optimizing printed structures based on process defect tolerance coefficients according to the present invention;

[0062] Figure 2 This is a schematic diagram of the base coordinate system and the XYZ sub-coordinate system in the printed model;

[0063] Figure 3 This is a flowchart of the printed structure design and parameter optimization method based on the process defect tolerance coefficient in Example 2;

[0064] Figure 4 This is a schematic diagram of the walking path of a single arch block in Example 2. Detailed Implementation

[0065] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0066] Example 1

[0067] like Figure 1 As shown, this embodiment 1 provides a method for designing and optimizing printed structures and parameters based on process defect tolerance coefficients, including the following steps:

[0068] S1. Obtain the initial parameters of the printed structure, and determine the printing parameters during the printing process based on the initial parameters of the printed structure. The printing parameters include printing material parameters, printing path parameters, model parameters, equipment parameters, printing environment parameters, and curing parameters.

[0069] S2. Calculate the process defect tolerance coefficient based on the printing parameters. The formula for calculating the process defect tolerance coefficient is:

[0070]

[0071] In the formula The process defect tolerance coefficient is K, the expansion coefficient is Ω, and the structural safety correction parameter is composed of printing material parameters, printing path parameters, model parameters, equipment parameters, printing environment parameters, and curing parameters.

[0072] S3. Evaluate the structure type of the printed structure based on the process defect tolerance coefficient to determine whether it is qualified. If qualified, the printing scheme of the printed structure is obtained. If unqualified, adjust the initial parameters of the printed structure and repeat steps S1 to S3 to design a qualified printing scheme.

[0073] In step S1, the initial parameters of the printed structure include the structure type and structure dimensions. The structure type is determined based on terrain analysis and construction control elements, and the structure dimensions include cross-sectional dimensions, etc.

[0074] In determining the structure type, terrain analysis involves preliminary surveys using scaled topographic maps, combined with on-site reconnaissance to assess terrain slope, geological stability, and the distribution of surrounding obstacles. For complex terrain, cantilevered or arched structures are preferred, while standardized printing structures are used for flat terrain, ensuring the printed structure matches the terrain conditions. Construction control follows the principle of "control first, then details." Triangulation or trilateration networks are used in areas with significant terrain undulations, traverse networks are laid out in flat areas with poor visibility, and building grids are used in regular sites. Control points must meet requirements for visibility, stability, and ease of measurement, and are established using concrete piles or rock markers. A horizontal and vertical control network is established using total stations and GPS equipment, with accuracy meeting standard requirements. The structural form is selected based on topographic survey data, and structural parameters are determined in conjunction with the accuracy level of the construction control network. Lightweight prefabricated structures are preferred for mountainous projects, while modular designs are used in densely populated urban areas. The operating radius of construction equipment and the distribution of control points are also considered to ensure the feasibility of structural construction.

[0075] Based on the existing working conditions, the printing parameters used in this project are defined. These parameters include printing material parameters, printing path parameters, model parameters, equipment parameters, printing environment parameters, and curing parameters. Printing material parameters include the anisotropic strength and durability properties of the material under both casting and printing processes; specifically, the printability of the material, the hardening performance of the cast specimen, and the hardening performance of the printed specimen, as well as the material number, mixing water volume, raw material state / batch, and equipment number used. Printing path parameters include the simplified spatial layout of the printing strips, the position of the neutral axis of the structural section, and the dimensions of the printing strips (length, width, and height boundaries). The printing strip dimensions are the length, width, and height boundaries of the printing strips; more specifically, the path spacing, slice layer height, filling method, and whether the inter-layer movement is continuous. Model parameters include the cantilever angle, maximum cross-section, model dimensions, and volume. Model dimensions include the necessary dimensions such as length, width, and height, as well as the maximum cantilever angle. Equipment parameters include travel speed, extrusion rate, maximum printing cross-section travel time and interval, extrusion nozzle shape, material mixing time / number of batches, pumping / extrusion pressure, and other related parameters. They also include unit size boundaries, overhang boundaries, operating parameters (e.g., turning, travel acceleration / deceleration rate changes), and composite process boundaries, thus clarifying the actual bonding area between printed strips along the printing path in this project, including side bonding surfaces and interlayer bonding surfaces. Printing environment parameters include temperature, humidity, and wind speed. Curing parameters include curing methods and parameters, such as steam curing, temperature rise / constant / cooling, and static shutdown parameters.

[0076] For the process defect tolerance coefficient γ PDTC The Process Defect Tolerance Coefficient (PDTC) is used to determine the selection and size of the printed structure by increasing the load.

[0077]

[0078] If the calculated process defect tolerance coefficient is less than 0.8, it indicates that the material and / or structure selection is too conservative, and it is recommended to reduce the strength and / or durability grade of the printing material. If the calculated process defect tolerance coefficient is between 0.8 and 1, it indicates that the material and / or structure selection is relatively appropriate, and the conclusions of conventional structural estimation methods can be directly applied. The process defect tolerance coefficient is assumed to be 1 by default.

[0079] The scaling factor is related to parameters such as printing environment, structural implementation, and technology maturity, and ranges from 0.8 to 1.8. Under normal conditions such as general printing environment and implementation of a non-first-time structural form, the scaling factor is 1.2. Under unconventional conditions such as implementation of a first-time structural form, extreme printing environment, and low technology maturity, the scaling factor is 1.5. The determination of general and extreme printing environments is based on the experience of those skilled in the art, as is the determination of low technology maturity.

[0080] The formula for calculating the structural safety correction parameter is:

[0081]

[0082] In the formula , , p、 , These are printing material parameter factors, printing path parameter factors, equipment parameter factors, curing parameter factors, printing environment parameter factors, and model accuracy factors. The weightings are for printing material parameters, printing path parameters, equipment parameters, maintenance parameters, printing environment parameters, and model accuracy, respectively.

[0083] The following provides a detailed explanation of the printing material parameter factors, printing path parameter factors, equipment parameter factors, maintenance parameter factors, printing environment parameter factors, and model accuracy factors.

[0084] For the printing material parameter factor, in actual printing environments, the printing material parameter factor is the product of the ratios between the strength grade and durability grade of anisotropic printed specimens and cast parts. In conventional environments, durability only needs to consider the material's resistance to steel corrosion; in unconventional environments, it needs to be refined according to weights and considered separately. The calculation formula for the printing material parameter factor is:

[0085]

[0086] In the formula To print the strength grade of the specimen, The required strength grade for the cast-in-place components for the project. To determine the durability rating of the printed specimens, The durability performance level of the cast-in-place components required by the project;

[0087] Regarding the determination of the strength grade of printed specimens, this paper, based on the unique mechanical properties of printed specimens, uses a method for characterizing the anisotropy of cement-based 3D printed components, as described in the invention patent with publication number CN114414343B. If the mechanical anisotropy coefficient I ≤ 15%, mechanical performance tests are conducted sequentially in each direction, with at least three surface load test results and at least six line load test results for each direction. The strength grade classification of printed specimens refers to the "Standard for Testing and Evaluation of Concrete Strength" (GB / T 50107-2010). For the mechanical properties of printed specimens under the same material and engineering parameters, if I > 15%, the strength grade is determined according to the direction of the minimum ultimate load. The specific method for evaluating the mechanical performance grade of 3D printed concrete materials and specimens is as follows:

[0088] Referring to the "Standard for Testing and Evaluation of Concrete Strength" (GB / T 50107-2010), the compressive strength grade of 3D printed concrete materials and specimens was determined. Among them, the compressive strength of concrete cubes... f cu,o The formula is expressed as follows:

[0089]

[0090] In the formula: f cu,o The cube compressive strength is expressed in MPa. f cu,k This represents the standard compressive strength of a cube, expressed in MPa.

[0091] Referring to the "Standard for Testing and Evaluation of Concrete Strength" (GB / T 50107-2010), the axial tensile strength grades of 3D printed concrete materials and specimens were determined. The specific strength grades are shown in Table 1. The standard value of axial tensile strength is... f tk The formula is expressed as follows:

[0092]

[0093] In the formula The axial tensile strength conversion factor is used to convert the splitting tensile strength to the axial tensile strength factor when the specimen is a standard 150mm×150mm×150mm specimen. The value is 0.9; if a non-standard specimen of 100mm×100mm×100mm is used, then... The value is 0.85; R tF represents the splitting tensile strength in MPa; F represents the ultimate load in N; and A represents the splitting surface area of ​​the specimen in mm². 2 The strength grade of the cast-in-place component is also determined according to the strength grade determination of the printed specimen as described above.

[0094] Table 1. Standard values ​​of axial tensile strength corresponding to concrete strength grades

[0095]

[0096] Regarding the determination of the durability performance grade of printed specimens, this paper, based on the unique mechanical properties of printed specimens, uses a method for characterizing the anisotropy of cement-based 3D printed components, as described in the invention patent with publication number CN114414343B. If the anisotropy coefficient I of the durability performance is ≤15%, durability performance tests are conducted sequentially in each direction. At least three surface action test results and at least six line action test results are required for each direction. The durability performance grade evaluation method refers to the "Standard for Testing and Evaluation of Concrete Durability JGJ / T 193-2009". For the durability performance of printed specimens under the same material and engineering parameters, if I > 15%, the durability grade is determined according to the most unfavorable direction. The durability performance grade of cast parts is also determined according to the above determination of the durability performance grade of printed specimens.

[0097] The print path parameter factor is the degree of influence of the print strip spatial layout under print path planning on the overall performance of the printed structure.

[0098] Given that the printed structure consists of printed strips arranged at fixed positions and composed of weak connections, it can be divided into a process defect area and the printed entity. The process defect area is further divided into side defects, top defects, and internal defects between printed strips caused by the printing process.

[0099] After establishing the printing model for the printed structure, a reference coordinate system is established. The horizontal printing platform is defined as the LW plane, and the H direction is perpendicular to the horizontal printing platform. That is, the L direction is the length direction of the printed model, the W direction is the width direction of the printed model, and the H direction is the height direction of the printed model. Based on the reference coordinate system, an XYZ sub-coordinate system is established. The center point of this coordinate system is located at the point where the printing nozzle extrudes the material. X is the direction perpendicular to the cross-section of the printed strip in the horizontal plane, Y is the direction perpendicular to the side of the printed strip in the horizontal plane, and Z is the direction perpendicular to the XY plane. That is, the three directions are orthogonal to each other. Figure 2 As shown.

[0100] The calculations are categorized according to the type of structural stress, as follows:

[0101] When subjected to unidirectional pressure, the formula for calculating the printing path parameter factor is:

[0102]

[0103] In the formula, A is the theoretical cross-sectional area of ​​the printed model, and A' is the theoretical cross-sectional area of ​​the printed strip.

[0104] Among them, when the walking direction is the same as the compression direction (i.e., the L direction is consistent with the X direction) or the compressive strength of the printed structure is isotropic (I≤15%), based on the plane section assumption, the theoretical cross-sectional area of ​​the printed model can be simplified to A=A'+B+C+D, where B, C, and D are the side defects, top defects, and internal printing strip defects caused by the printing process, respectively. Figure 2 Based on experience and prior research, it is deduced that the interlayer bonding width and height of the extruded strip under a rectangular nozzle are consistent with the theoretical width w (interlayer printing path travel interval) and theoretical height h (path slice layer height) of the printing strip. Therefore, A' = A under a rectangular nozzle. For a circular nozzle, the average width of the interlayer core bonding is assumed to be... The average height of the inter-strip core bonding is 2 / 3w. The value is 1 / 2h, and the number of columns and layers printed are c and l respectively. n=c l n is the number of printed strips within the printed cross-section. Let be the theoretical height of the cross-section of the i-th printed strip. Let be the theoretical width of the cross-section of the i-th printed strip.

[0105] Therefore, A' under the circular nozzle can be simplified to:

[0106]

[0107]

[0108]

[0109]

[0110]

[0111] The formula for calculating the print path parameter factor during bending / shearing is as follows:

[0112]

[0113] In the formula This is the ratio of the theoretically printed cross-sectional area to the theoretically cast cross-sectional area. This represents the ratio of the moment of inertia of the printed cross-section, which is composed of several printed strips, to the cross-section of the theoretical cast model. Let be the moment of inertia of the printed cross section composed of several printing strips. The moment of inertia of the cross-section of the theoretically cast model. The number of print strips for the printed cross section. Let be the distance from any infinitesimal element within the cross-section of the i-th printing strip to the neutral axis of the printing cross-section. Let be the distance from any infinitesimal element within the cross-section of the casting model to the neutral axis. Let d be the area of ​​the cross-section of the i-th printed strip. Let be the area of ​​a micro-element within the cross-section of the i-th printed strip;

[0114] When the travel direction is perpendicular to the bending moment direction or the tensile stress of the printed part is fully borne by the steel bars and other reinforcement measures, the calculation formula for the printing path parameter factor is:

[0115]

[0116] In the formula i Let be the width of the cross-section of the i-th printing strip, which is parallel to the neutral axis of the printing cross-section.

[0117] When twisting, the formula for calculating the print path parameter factor is:

[0118]

[0119] To print the polar moment of inertia of the cross section about the center, The polar moment of inertia of the cross section of the casting model about the center. The number of print strips for the printed cross section. Let be the distance from any infinitesimal element within the cross-section of the i-th printing strip to the center of the printing cross-section. Let be the distance from any infinitesimal element within the cross-section of the casting model to the center of the cross-section. Let be the area of ​​the cross-section of the i-th printed strip.

[0120] Special Case: When the travel direction is parallel to the torsional direction or the tensile stress of the printed part is fully borne by the steel reinforcement and other strengthening measures, the formula for calculating the printing path parameter factor is:

[0121]

[0122] Under fixed equipment parameters, the equipment parameter factor is the ratio between the actual bonding surface between the printing strips and the set theoretical bonding surface. This includes both lateral bonding and interlayer bonding between the strips; (the actual bonding surface is obtained using the device and testing method described in the invention patent CN114563345A, "A Test Device and Test Method for Interlayer Bond Strength of Cement-Based 3D Printed Specimens"). The calculation formula for the equipment parameter factor is as follows:

[0123]

[0124] In the formula It is the minimum value; This represents the minimum actual interlayer bonding surface area. This represents the theoretical interlayer bonding surface area, which is also the in-layer printing path travel interval w × travel length. This represents the minimum actual bonding surface area between strips. The theoretical bonding surface area between strips is also known as the path slice layer height h × walking length;

[0125] The curing parameter factor is the ratio of the difference between the average rebound strength of the printed structure after curing and the error value, divided by the average value. The formula for calculating the curing parameter factor is as follows:

[0126]

[0127] In the formula This represents the average springback strength of the printed structural entity after curing. To determine the springback strength error value of the printed structure after curing, a springback strength test is conducted. If a circular printhead is used for printing or the flatness of the test surface is substandard, the surface should be smoothed before measurement. If a rectangular printhead is used for printing or the flatness of the test surface meets the standard, no further action is required. The springback strength and test error are not limited to testing methods such as the springback method or a combination of ultrasonic and springback methods.

[0128] For the printing environment parameter factor, in a normal environment between 15-25℃, the default value of the printing environment parameter factor is 1. In an environment with temperatures between 5-15℃ and 25-35℃, the printing environment parameter factor takes the same value as the printing material parameter factor. If the temperature is below 5℃ or above 35℃, the default value of the printing environment parameter factor is 0.

[0129] The model accuracy factor is the ratio of key parameters (angles, cross-sectional dimensions, length, etc.) between the spatial dimensions of the printed structural entity and the printed model. If in-situ printing and / or mature rectangular printhead printing technology are used, the default value of the model accuracy factor is 1. If secondary assembly / installation is subsequently used, the ratio is calculated using a weighted average based on the impact of the key parameters on the overall structural performance. The formula for calculating the model accuracy factor is:

[0130]

[0131] In the formula This refers to the number of key parameters, which are specifically categorized as angles, cross-sectional dimensions, lengths, etc. The weight of the i-th key parameter, To print the value of the i-th key parameter of the model, This represents the key parameter value of the i-th model of the printed structure.

[0132] In step S3, the objective of structural type evaluation is to ensure that the printed structure can safely withstand various loads (such as self-weight, live load, wind load, seismic action, etc.) during construction and throughout its service life, and meet the requirements of the normal serviceability limit state (such as deformation, cracking). The detailed method for evaluating the structural type of the printed structure based on the process defect tolerance coefficient is as follows:

[0133] A structural type assessment model is established by incorporating a process defect tolerance coefficient into the industry assessment method for structural types; a finite element stress analysis is established based on the structural design geometry and boundary conditions.

[0134] The initial parameters of the printed structure and the tolerance coefficient for process defects are used to determine whether the structure type assessment model is met. If the model is met, the printed structure is deemed qualified; otherwise, it is deemed unqualified. Specifically, the theoretical bearing capacity design value and the combined effect value of ultimate limit state actions, along with the corresponding theoretical safety factor C1, are obtained from the stress analysis calculation results. This is then reduced by the aforementioned tolerance coefficient for process defects to obtain the safety factor C, where C = C1 / ... Based on the requirements of the printing project, determine whether the safety factor is up to standard.

[0135] Specifically, based on the existing industry evaluation standards for structural types, a process defect tolerance coefficient is added, resulting in the structural type evaluation model as follows:

[0136]

[0137] In the formula, R() is the bearing capacity function of the component; α d Design values ​​for geometric parameters; S is the structural importance coefficient; S is the design value of the combined effect. f d This refers to the design value for the material strength grade. f c打印构件回弹值 This represents the measured springback value of the printed component.

[0138] For refurbished structures such as highway bridges and culverts, the endurance design should be based on the requirements of the ultimate limit state of bearing capacity, performing load-bearing capacity and stability calculations on the components. If necessary, preliminary calculations for overturning and sliding should be performed. When expressed in the form of internal forces, the ultimate limit state calculation of bridge and culvert components should use the following expression:

[0139]

[0140] The structural importance coefficient is taken as 1.1, 1.0, and 0.9 according to the structural design safety level, which is Level I, Level II, and Level III, respectively. The structural design safety level should comply with the provisions of the "General Specifications for Design of Highway Bridges and Culverts" (JTG D60-2015). The design value of the effect of the action combination should be calculated according to the provisions of the "General Specifications for Design of Highway Bridges and Culverts" (JTG D60-2015), and the basic action combination should be used for the persistent design condition. The design value of the geometric parameter can adopt the standard value of the geometric parameter a. k That is, the value specified in the design documents.

[0141] By using the above design and parameter optimization methods, the initial parameters of the printed structure are adjusted based on the process defect tolerance coefficient to determine the appropriate printing parameter range, thereby completing the parameter boundary control of materials, path, model, environment, equipment, and maintenance, and thus realizing the integration of design and construction.

[0142] Example 2

[0143] This embodiment provides a method for designing and optimizing the parameters of a printed structure based on a process defect tolerance coefficient. In step S1, based on the existing working conditions, the initial parameters of the printed structure are obtained, which involves clarifying the structure selection, dimensions, and determining printing parameters such as materials, path, model, equipment, curing, and printing environment. In step S2, the process defect tolerance coefficient for extreme concrete printing is determined, and then the structural stress and economic feasibility are estimated to determine whether it is acceptable. If acceptable, a scheme comparison is performed to obtain the printing parameter range; if unacceptable, the initial parameters of the printed structure are adjusted. Figure 3 As shown, similar to Example 1, the difference is that the method also includes S4: performing an economic estimate on the printed structure that has passed the structural type evaluation, and determining whether it is qualified. If qualified, a printing scheme for the printed structure is obtained; if not qualified, the printing parameters are adjusted to design a qualified printing scheme.

[0144] The goal of economic feasibility studies is to assess the total lifecycle cost of a 3D printing project. After analyzing the composition of costs (construction costs, time costs, energy costs, safety costs, etc.) and conducting benefit and value analyses, economic indicators are obtained. Based on these economic indicators, cost and return on investment comparison analyses are performed. According to the requirements of the printing project, it is determined whether the economic feasibility is satisfactory. If it is satisfactory, a printing scheme for the printed structure is obtained. If it is unsatisfactory, the printing parameters are adjusted, and steps S2 to S4 are repeated to design a satisfactory printing scheme.

[0145] After structural stress and economic calculations, the recommended scheme is determined. During the construction drawing design phase, the recommended scheme is refined. The main facilities such as bridges, culverts, tunnels, and road ancillary facilities adhere to standardized structural forms but personalized cross-sectional forms; cultural landscape facilities adhere to personalized structural forms but standardized cross-sectional forms.

[0146] Example 3

[0147] This embodiment provides a method for designing and optimizing printed structures based on process defect tolerance coefficients. Using the method from Embodiment 2, specifically, for projects under normal conditions / with high technological maturity / low degree of irregularity in the main load-bearing structure / non-main load-bearing irregular ancillary facilities, the structural safety correction parameters are as follows:

[0148]

[0149] Given that additive manufacturing in civil engineering is significantly affected by factors such as the printing and usage environment, technological maturity, and the degree of model irregularity, the weights of each factor are not fixed. In other cases, weight optimization is required based on these factors to satisfy the following inequalities.

[0150]

[0151]

[0152]

[0153] The plan is to print a 3D-printed concrete landscape arch bridge. The preliminary cross-sectional design has been completed. Calculations show that the main arch ring will be constructed using a cast-in-place process, with a material design strength grade of C30 and a material durability performance meeting D100, fully satisfying the project requirements. The theoretical safety factor C1 > 1.5. Therefore, it is necessary to clarify... To ensure reliability using 3D printing technology, the main arch is designed with a 3.6m radius arc, a thickness of 35cm (with a 20cm cavity inside), a calculated span of 6m, a calculated rise of 1.6m, and a rise-to-span ratio of 1 / 3.75. A printing structure design and parameter optimization method based on process defect tolerance coefficient is adopted.

[0154] Based on the project's current status, including its normal environment, the construction unit's high level of technological maturity, and the relatively small degree of model irregularity, a general formula is used for calculation, with K taken as 1.2.

[0155] Material parameter factor: The printing material used has a mixing ratio of C50. 普 As shown in Table 2.

[0156] Table 2 Optimal mix proportion C50 普 (wt.%)

[0157] Components cement fly ash silica ash S95 mineral powder sand water Water reducing agent PVA fiber Thickener <![CDATA[C50 普 ]]> 50 18 14 18 115 32 0.23 0.21 0.016

[0158] According to the experimental method, the compressive strength, splitting tensile strength, and flexural strength of the cast and 3D printed specimens were tested after 28 days. The test results are shown in Tables 3, 4, and 5. Simultaneously, the splitting tensile strength data were converted into axial tensile strength, as shown in Table 6.

[0159] Table 3 F x28 F y28 F z28 Table of cube compressive strength data

[0160]

[0161] Table 4 Applying F xy F xz F yx F yz F zx F zy Test data table of splitting strength under six line loads

[0162]

[0163] Table 5 Applying F xy F xz F yx F yz F zx F zy Test data on flexural strength under six line loads

[0164]

[0165] Table 6 Applying F xy F xz F yx F yz F zx F zy Table of Calculation Results of Axial Tensile Strength under Six Line Loads

[0166]

[0167] As shown in the table above, the average strength of the cast parts with mix proportion C50 is 71.3 MPa >> 57.5 MPa, while the strength loss of the printed specimens is 80.33%. Based on the formula for the mechanical anisotropy coefficient, Ic28d is calculated to be 8.15%, which can be judged by the average mechanical properties of the printed specimens. Meanwhile, mix proportion C50... 普 The average printing strength is 57.27MPa≈57.5MPa, which basically meets the compressive strength requirements of strength grade C50.

[0168] Meanwhile, based on the formula for the anisotropy coefficient in mechanics, it is easy to see that Ip28d is much greater than 15%, so the XZ direction can be used as the basis for evaluating the strength grade. As shown in Table 6, under this direction... Since 2.699 MPa > 2.64 MPa, the concrete is classified as C50 based on the standard value of axial tensile strength. This also proves that the mix proportion C50... 普Meet the strength requirement of strength grade C50.

[0169] To sum up, the mix proportion C50 optimized by compound admixture 普 The printed strength grade basically meets the strength requirement of C50.

[0170] Meanwhile, for Material C40 普 The carbonation resistance, chloride ion erosion resistance, and frost resistance grade are in T-IV (Recommended opinion on durability performance level: good), RCM-V (Recommended opinion on durability performance level: very good), and "D100" (F200) respectively. It shows that this material meets the material requirements for application scenarios such as reinforced concrete buildings in fresh water environments (frost-affected areas, slightly frozen areas), and plain concrete structures (severely frozen areas). Therefore, the printing material parameter factor = 50 / 30×100 / 100 = 1.67.

[0171] Printing path parameter factor: Given that the compressive strength of the printed parts of this material is isotropic, the stress mode is uniaxial compression, and the arch ring. The divided single model is relatively simple. The model filling mode is determined as the "return" type filling, that is, the equidistant spiral polyline slicing method. Using the space path fitting technology, three-dimensional oblique space plane slicing printing is carried out. The shape of the extrusion tool end is rectangular (38mm×12mm), the slicing height is 12mm, the plane path interval is 38mm, and the plane path fitting slicing control technology is used to change the posture of the print head. A single arch block uses Figure 4 The walking path to complete the printing, that is, two printing strips are arranged side by side. Therefore, Take the value of 1.

[0172] The device parameter factor uses the device and test method of the invention patent "A device and test method for testing the interlayer bonding strength of cement-based 3D printing specimens" to obtain the real bonding surface. According to the printing parameters used in the project alone, that is, the shape of the extrusion tool end is rectangular (38mm×12mm), the slicing height is 12mm, the plane path interval is 38mm, the pumping speed is 8r / min, and the walking speed is 12cm / s. Complete the printing of two columns of printing strips. The number of printing layers is 2 layers, the printing length is 2m, and 3 printing specimens A, B, and C are printed. Use a ruler to complete the measurement of the real bonding width and length, and use an electronic vernier caliper to measure the real bonding height. The test results are shown in Table 7.

[0173] Table 7 Test results of three printing specimens

[0174] test piece A B C average value Percentage of actual bonded area between layers (%) 97.7% 98.0% 98.7% 98.1% Percentage of actual bonded area between strips (%) 98.2% 97.4% 99.0% 98.2%

[0175] Therefore, the device parameter factor p = 98.1%×98.2% = 0.963.

[0176] Maintenance parameter factors: The average rebound strength and error value of the printed structure are 45.3 MPa and 5.2 MPa, respectively. = (45.3 - 5.2) / 45.3 = 0.865.

[0177] Given that the project is conducted in a normal environment (20℃±5℃) and utilizes a mature rectangular printhead printing process, the printing environment parameter factors and model accuracy factors are... All are 1.

[0178] In conclusion, =1.2× =0.96≈1≥30 / 45.3=0.66

[0179] Therefore, the safety factor C = C1 / With a value greater than 1.5, the safety factor remains unchanged without modifying the original cross-sectional dimensions. The printing materials and printing process parameters used in this project are conservatively selected, and the calculation results fully meet the engineering requirements.

[0180] Example 4

[0181] A system for designing and optimizing printed structures based on process defect tolerance coefficients, used to execute the method for designing and optimizing printed structures in Example 1, the system comprising:

[0182] The parameter acquisition module is used to acquire the initial parameters of the printed structure and determine the printing parameters during the printing process based on the initial parameters of the printed structure. The printing parameters include printing material parameters, printing path parameters, model parameters, equipment parameters, printing environment parameters, and curing parameters.

[0183] The calculation module is used to calculate the process defect tolerance coefficient based on the printing parameters. The formula for calculating the process defect tolerance coefficient is as follows:

[0184]

[0185] In the formula The process defect tolerance coefficient is K, the expansion coefficient is Ω, and the structural safety correction parameter is composed of printing material parameters, printing path parameters, model parameters, equipment parameters, printing environment parameters, and curing parameters.

[0186] The judgment module is used to evaluate the structure type of the printed structure according to the process defect tolerance coefficient, and determine whether it is qualified. If it is qualified, the printing scheme of the printed structure is obtained. If it is unqualified, the initial parameters of the printed structure are adjusted and steps S1 to S3 are repeated to design a qualified printing scheme.

[0187] This embodiment also provides an electronic device, including at least one processor, a memory communicatively connected to the at least one processor, and at least one input / output interface communicatively connected to the at least one processor. The memory stores instructions executable by the at least one processor, which, when executed, enable the at least one processor to perform the printed structure design and parameter optimization method based on process defect tolerance coefficient of Embodiment 1 described above. The input / output interface may include a display, keyboard, mouse, and USB interface for inputting and outputting data. The electronic device may be a client-side electronic device, such as a mobile phone, laptop, tablet computer, or desktop computer, to execute the printed structure design and parameter optimization method based on process defect tolerance coefficient of Embodiment 1.

[0188] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for designing and optimizing printed structures based on process defect tolerance coefficients, characterized in that, Includes the following steps: S1. Obtain the initial parameters of the printed structure, and determine the printing parameters during the printing process based on the initial parameters of the printed structure. The printing parameters include printing material parameters, printing path parameters, model parameters, equipment parameters, printing environment parameters, and curing parameters. S2. Calculate the process defect tolerance coefficient based on the printing parameters. The formula for calculating the process defect tolerance coefficient is as follows: In the formula Here, K is the process defect tolerance coefficient, K is the amplification coefficient ranging from 0.8 to 1.8, and Ω is the structural safety correction parameter, composed of printing material parameters, printing path parameters, model parameters, equipment parameters, printing environment parameters, and curing parameters. The calculation formula for the structural safety correction parameter is as follows: In the formula , , p、 , These are printing material parameter factors, printing path parameter factors, equipment parameter factors, curing parameter factors, printing environment parameter factors, and model accuracy factors. The weightings are for printing material parameters, printing path parameters, equipment parameters, maintenance parameters, printing environment parameters, and model accuracy, respectively. S3. Evaluate the structure type of the printed structure according to the process defect tolerance coefficient, and determine whether it is qualified. If it is qualified, the printing scheme of the printed structure is obtained. If it is not qualified, adjust the initial parameters of the printed structure and repeat steps S1 to S3 to design a qualified printing scheme.

2. The method for designing and optimizing printed structures based on process defect tolerance coefficients according to claim 1, characterized in that, The initial parameters of the printed structure include the structure type and the structure dimensions. The structure type is determined based on the terrain and construction control factors, and the structure dimensions include the cross-sectional dimensions. And / or the printing material parameters include the material's strength and durability properties under the casting and printing processes; The printing path parameters include the spatial layout of the printing strip, the position of the neutral axis of the structural cross section, and the size of the printing strip. The model parameters include cantilever angle, maximum cross-section, model size, and volume. The equipment parameters include travel speed, extrusion speed, travel time and interval for maximum printing cross-section, extrusion nozzle shape, material mixing time / number of batches, and pumping / extrusion pressure. The printing environment parameters include temperature, humidity, and wind speed; The maintenance parameters include maintenance methods and parameters; And / or the scaling factor is related to the printing environment, structural implementation, and technology maturity parameters.

3. The method for designing and optimizing printed structures based on process defect tolerance coefficients according to claim 1, characterized in that, The calculation formula for the printing material parameter factor is as follows: In the formula To print the strength grade of the specimen, For the strength grade of the cast-in-place component, To print the durability rating of the test specimens, For the durability performance grade of the cast-in-place component; And / or the calculation formula for the device parameter factors is as follows: In the formula This represents the minimum actual interlayer bonding surface area. This represents the theoretical interlayer bonding surface area. This represents the minimum actual bonding surface area between strips. Theoretical bonding surface area between strips; And / or the calculation formula for the maintenance parameter factors is as follows: In the formula This represents the average springback strength of the printed structural entity after curing. The springback strength error value of the printed structural entity after curing; And / or at an ambient temperature of 15-25℃, the printing environment parameter factor is 1; at an ambient temperature between 5-15℃ and 25-35℃, the printing environment parameter factor is the same as the printing material parameter factor; if the temperature is below 5℃ or above 35℃, the printing environment parameter factor is 0. And / or if in-situ printing or rectangular printhead printing technology is used, the model accuracy factor is 1; if secondary assembly or installation is subsequently used, the calculation formula for the model accuracy factor is: In the formula The number of key parameters; The weight of the i-th key parameter, To print the value of the i-th key parameter of the model, This represents the key parameter value of the i-th model of the printed structure.

4. The method for designing and optimizing printed structures based on process defect tolerance coefficients according to claim 1, characterized in that, When subjected to unidirectional pressure, the formula for calculating the printing path parameter factor is: In the formula, A is the theoretical cross-sectional area of ​​the printed model, and A' is the theoretical cross-sectional area of ​​the printed cross-section; During bending / shearing, the calculation formula for the printing path parameter factor is as follows: In the formula This is the ratio of the theoretically printed cross-sectional area to the theoretically cast cross-sectional area. This represents the ratio of the moment of inertia of the printed cross-section, which is composed of several printed strips, to the cross-section of the theoretical cast model. Let be the moment of inertia of the printed cross section composed of several printing strips. The moment of inertia of the cross-section of the theoretically cast model. The number of print strips for the printed cross section. Let be the distance from any infinitesimal element within the cross-section of the i-th printing strip to the neutral axis of the printing cross-section. Let be the distance from any infinitesimal element within the cross-section of the casting model to the neutral axis. Let d be the area of ​​the cross-section of the i-th printed strip. Let be the area of ​​a micro-element within the cross-section of the i-th printed strip; When twisting, the formula for calculating the print path parameter factor is: To print the polar moment of inertia of the cross section about the center, The polar moment of inertia of the cross section of the casting model about the center. The number of print strips for the printed cross section. Let be the distance from any infinitesimal element within the cross-section of the i-th printing strip to the center of the printing cross-section. Let be the distance from any infinitesimal element within the cross-section of the casting model to the center. Let be the area of ​​the cross-section of the i-th printed strip.

5. The method for designing and optimizing printed structures based on process defect tolerance coefficients according to claim 1, characterized in that, The value range is 0.2-0.

8. The value range is 0.1-0.

5. The value range is 0.1-0.

5. The value range is 0-0.

2. The value range is 0-0.

5. The value range is 0.8-1.

2.

6. The method for designing and optimizing printed structures based on process defect tolerance coefficients according to claim 1, characterized in that, The detailed method for evaluating the structural type of the printed structure based on the aforementioned process defect tolerance coefficient is as follows: The process defect tolerance coefficient is incorporated into the structural type industry assessment method to establish a structural type assessment model; Based on the initial parameters of the printed structure and the process defect tolerance coefficient, it is determined whether the structure type evaluation model is met. If the structure type evaluation model is met, the printed structure is evaluated as qualified; otherwise, it is unqualified.

7. The method for designing and optimizing printed structures based on process defect tolerance coefficients according to claim 6, characterized in that, The structure type evaluation model is as follows: In the formula, R() is the bearing capacity function of the component; α d Design values ​​for geometric parameters; S is the structural importance coefficient; S is the design value of the combined effect. f d This refers to the design value for the material strength grade. f c打印构件回弹值 This represents the measured springback value of the printed component.

8. The method for designing and optimizing printed structures based on process defect tolerance coefficients according to any one of claims 1-7, characterized in that, The method further includes S4, which involves performing an economic estimate on the printed structure that has passed the structural type evaluation, and determining whether it is qualified. If it is qualified, a printing scheme for the printed structure is obtained. If it is not qualified, the printing parameters are adjusted, and steps S2 to S4 are repeated to design a qualified printing scheme.

9. A system for designing and optimizing printed structures and parameters based on process defect tolerance coefficients, characterized in that, The system is used to execute the printed structure design and parameter optimization method based on process defect tolerance coefficient as described in any one of claims 1-8, the system comprising: The parameter acquisition module is used to acquire the initial parameters of the printed structure and determine the printing parameters during the printing process based on the initial parameters of the printed structure. The printing parameters include printing material parameters, printing path parameters, model parameters, equipment parameters, printing environment parameters, and curing parameters. The calculation module is used to calculate the process defect tolerance coefficient based on the printing parameters. The formula for calculating the process defect tolerance coefficient is as follows: In the formula Here, K is the process defect tolerance coefficient, K is the amplification coefficient ranging from 0.8 to 1.8, and Ω is the structural safety correction parameter, composed of printing material parameters, printing path parameters, model parameters, equipment parameters, printing environment parameters, and curing parameters. The calculation formula for the structural safety correction parameter is as follows: In the formula , , p、 , These are printing material parameter factors, printing path parameter factors, equipment parameter factors, curing parameter factors, printing environment parameter factors, and model accuracy factors. The weightings are for printing material parameters, printing path parameters, equipment parameters, maintenance parameters, printing environment parameters, and model accuracy, respectively. The judgment module is used to evaluate the structure type of the printed structure according to the process defect tolerance coefficient, and determine whether it is qualified. If it is qualified, the printing scheme of the printed structure is obtained. If it is unqualified, the initial parameters of the printed structure are adjusted and steps S1 to S3 are repeated to design a qualified printing scheme.

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