Multi-objective optimization design method for precast concrete staircase molds

Abstract

The present invention discloses a multi-objective optimization design method for a precast concrete stair mold, comprising the following steps: S1: splitting the precast concrete stair mold into multiple mold components; S2: parametrically describing the number and size of each mold component; S3: determining the model plane control points and the plane positions of the mold components; S4: establishing a parametric model of the mold; S5: meshing using finite element software and performing finite element analysis under load conditions; S6: obtaining the maximum lateral deformation of all mold nodes; S7: establishing a multi-objective optimization model for the mold; S8: solving the optimal design scheme of the multi-objective optimization model using the NSGA-II algorithm; and S9: establishing a mold BRep model using OPENCASCADE technology based on the optimized design scheme, and then drawing a graphic in a drawing template file. The method provides a theoretical basis for the rationality of the mold design scheme, and at the same time, provides multiple alternative mold design schemes according to different design requirements, thereby reducing mold material and processing costs.

Description

Technical Field

[0001] The invention relates to a mold design technology, and in particular to a multi-objective optimization design method for a precast concrete staircase mold. Background Art

[0002] Precast concrete stair molds are the basic components used in factory production. They are assembled by welding steel plates. According to the different casting methods of precast stairs, the molds are divided into vertical molds and horizontal molds. Although horizontal molds use less steel, the solid area not covered by the mold is large, and the surface smoothing treatment requires a lot of manpower. Vertical molds, on the other hand, have a small solid area not covered by the mold, and the casting quality is reliable. They are widely used in precast factories.

[0003] Precast stairs are independent precast concrete components with a high prefabrication rate. To ensure the reliability of precast staircase molds, designers often rely on project experience to over-design, resulting in poor economic benefits. Although mold design units often reduce production costs through combined molds and common molds, the actual effect is not good.

[0004] Therefore, there is an urgent need to provide a new multi-objective optimization design method for precast concrete stair molds to solve the above technical problems. Summary of the Invention

[0005] In view of this, the present invention provides a multi-objective optimization design method for precast concrete stair molds. Finite element analysis is used to verify the mold design scheme, and the NSGA-II algorithm is used to perform non-dominated sorting and congestion calculation according to the fitness value. Multiple individuals with the highest ranking are selected, and one or more optimal design schemes are automatically provided for designers to choose from according to design requirements.

[0006] In order to achieve the above object, the specific technical solutions adopted by the present invention are as follows:

[0007] A multi-objective optimization design method for precast concrete staircase molds includes the following steps:

[0008] S1: splitting the precast concrete staircase mold into multiple assemblies according to the connection method, and splitting each assembly into multiple mold parts;

[0009] S2: parametric description of the number and size of each mold component;

[0010] S3: determining a model plane control point according to geometric parameters of the precast concrete staircase and mold design parameters, and determining a plane position of a mold component by the model plane control point;

[0011] S4: Establishing the mold parametric model;

[0012] S5: Using finite element software, mesh the established mold parametric model; set the geometric properties, material properties, and boundary conditions of the mold components, simulate the load condition of the mold being subjected to lateral water pressure during concrete pouring, and perform finite element analysis under the load condition;

[0013] S6: Obtain the maximum lateral deformation of all nodes of the mold based on the finite element analysis results;

[0014] S7: Establish a mold multi-objective optimization model, where the optimization variable is the mold design scheme, the optimization target is the economy and processing convenience evaluation index, and the constraint condition is the mold reliability evaluation index;

[0015] S8: Use NSGA-II algorithm to solve the optimal design scheme of the multi-objective optimization model;

[0016] S9: According to the optimized design scheme, the mold BRep model is established using OPENCASCADE technology, and then the plane data of each mold component is obtained using the hidden layer and sectioning algorithm. Finally, the graphics are drawn in the drawing template file to obtain the mold component production data.

[0017] Optionally, the mold components are composed of steel plates, connected by welds, and the individual components are bolted together. Taking a common staircase mold as an example, the mold shape includes a base mold, a bent front mold, a flat rear mold, a left end mold, a right end mold, and a restraining member. The bent front mold and the flat rear mold are arranged opposite each other and connected to the base mold by bolts and positioning pins. At the same time, the front mold and the rear mold are connected by restraining members (channel steel and tie rods).

[0018] Optionally, when performing finite element analysis in step S5, the finite element model adopts a shell element model.

[0019] Optionally, in step S6, the maximum lateral deformation values ​​of the front and rear molds are automatically extracted based on the finite element analysis results.

[0020] Optionally, the mold design scheme in step S7 is the geometric size, plate thickness, and quantity of each component. The mold reliability evaluation index refers to whether the maximum lateral deformation meets the specification requirements. According to the "Technical Standard for Prefabricated Concrete Buildings" GB / T51231-2016, the maximum lateral deformation of the mold does not exceed 1 / 1500 of the longest side. The mold processing convenience evaluation index refers to the number of ribs, the thickness of the panel, and the number of types of rib thickness restrictions. Usually, the requirements of the mold panel welding cannot penetrate and is easy to bend are considered, and the minimum and maximum plate thicknesses of the mold components are limited; at the same time, the requirements of welding and installation workload are considered, and the number of transverse and longitudinal ribs of the mold is limited; in addition, in order to improve the utilization rate of the original plate of the steel component, the types of different plate thicknesses of the mold are reduced.

[0021] Optionally, when using the NSGA-II algorithm to solve the optimal design solution for a multi-objective optimization model, selection, crossover, and mutation operations are used in each generation to calculate the fitness values ​​of all individuals. Non-dominated sorting and crowding calculations are also performed. A certain number of individuals with the highest ranking form the next generation population. Through iterative optimization, when the maximum number of iterations or convergence conditions are met, a certain number of individuals with the highest ranking are output as alternative optimization design solutions. The NSGA-II algorithm, short for the non-dominated sorting genetic algorithm, is essentially a genetic algorithm with the same selection, crossover, and mutation operators as the genetic algorithm. Compared to the genetic algorithm, this algorithm adds non-dominated sorting and crowding operations. When performing multi-objective mold optimization design, a rounding strategy is used to convert each dimension of the individual into an integer to facilitate finite element modeling and analysis.

[0022] Optionally, in step S9 , the graphics are drawn in the DXF template file at a 1:1 ratio.

[0023] Optionally, according to the optimized design solution, OPENCASCADE technology is used to automatically generate DXF production data, and the laser cutting equipment directly reads the DXF production data to complete the cutting process of the mold components.

[0024] Optionally, in step S5 , the finite element method meshes the mold component according to a fixed length and a fixed number of intervals to form quadrilateral shell elements.

[0025] Compared with the prior art, the multi-objective optimization design method for precast concrete staircase molds provided by the present invention has the following beneficial effects:

[0026] The method proposed in the present invention can provide a theoretical basis for the rationality of the mold design scheme, and at the same time provide a variety of alternative mold design schemes according to different design requirements. Through the multi-objective optimization design of the mold, the mold design task can be completed efficiently, and mold design schemes with diversified requirements can be provided, thereby reducing mold material and processing costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is a schematic diagram of the composition of the precast concrete staircase mold;

[0028] Figure 2 for Figure 1 Schematic diagram of the bottom mold composition of the prefabricated staircase mold shown;

[0029] Figure 3 for Figure 1 A schematic diagram of the bending front side mold composition of the mold shown;

[0030] Figure 4 for Figure 1 A schematic diagram of the flat rear mold composition of the mold shown;

[0031] Figure 5 for Figure 1 Schematic diagram of the left end mold and the right end mold of the mold shown;

[0032] Figure 6 Schematic diagram of the stairs and geometric control points of the mold;

[0033] Figure 7 The finite element design flow chart of the staircase mold;

[0034] Figure 8 This is the flow chart for the multi-objective optimization design of the stair mold. DETAILED DESCRIPTION

[0035] The present invention is described in detail below through specific examples. It is pointed out that the following examples are only used to further illustrate the present invention and are not to be construed as limiting the scope of protection of the present invention. Those skilled in the art can make some non-essential improvements and adjustments to the present invention based on the above invention content.

[0036] This embodiment provides a multi-objective optimization design method for a precast concrete staircase mold, comprising the following steps:

[0037] S1: splitting the precast concrete staircase mold into multiple assemblies according to the connection method, and splitting each assembly into multiple mold parts;

[0038] S2: parametric description of the number and size of each mold component;

[0039] S3: determining a model plane control point according to geometric parameters of the precast concrete staircase and mold design parameters, and determining a plane position of a mold component by the model plane control point;

[0040] S4: Establishing the mold parametric model;

[0041] S5: Using finite element software, mesh the established mold parametric model; set the geometric properties, material properties, and boundary conditions of the mold components, simulate the load condition of the mold being subjected to lateral water pressure during concrete pouring, and perform finite element analysis under the load condition;

[0042] S6: Obtain the maximum lateral deformation of all nodes of the mold based on the finite element analysis results;

[0043] S7: Establish a mold multi-objective optimization model, where the optimization variable is the mold design scheme, the optimization target is the economy and processing convenience evaluation index, and the constraint condition is the mold reliability evaluation index;

[0044] S8: Use NSGA-II algorithm to solve the optimal design scheme of the multi-objective optimization model;

[0045] S9: According to the optimized design scheme, the mold BRep model is established using OPENCASCADE technology, and then the plane data of each mold component is obtained using the hidden layer and sectioning algorithm. Finally, the graphics are drawn in the drawing template file to obtain the mold component production data.

[0046] by Figure 1 Taking the precast concrete staircase mold structure shown as an example, the mold includes a bottom mold, a bent front side mold, a flat rear side mold, a left end mold, and a right end mold;

[0047] pass Figure 2 It can be seen that the bottom mold is surrounded by panels and edge ribs to form a closed area, and middle ribs are set inside the closed area, and the number of middle ribs is determined according to the structure;

[0048] pass Figure 3 It can be seen that the bending front mold consists of a bending panel, edge transverse ribs, edge longitudinal ribs, middle transverse ribs, and middle longitudinal ribs. Each component is connected by welds, and the size, thickness, and quantity of each component are obtained by finite element analysis and intelligent algorithms.

[0049] pass Figure 4 It can be seen that the flat plate rear mold consists of a panel, edge transverse ribs, edge longitudinal ribs, middle transverse ribs, and middle longitudinal ribs. The ribs are connected by welds, and the size, thickness, and quantity of each component are optimized using finite element analysis and intelligent algorithms.

[0050] pass Figure 5 It can be seen that the left end mold and the right end mold are initially positioned at the two ends of the prefabricated staircase mold by positioning rivets, and then bolts are added to connect and fix them. The number of bolts is determined by the construction.

[0051] pass Figure 6 It can be seen that the geometric parameters of the prefabricated stairs and the shape parameters of the mold are used to establish the control points of the prefabricated stairs and the mold plane, so that the mold parametric model can be established; Figure 6In the figure, the geometric parameters of the precast staircase are a2, a3, d2, d3, e1, e2, b, c, m, and s. A2 is the upper length of the staircase bottom, a3 is the lower length of the staircase bottom, d2 is the upper length of the staircase top, d3 is the lower length of the staircase top, e1 is the thickness of the staircase bottom plate, e2 is the thickness of the staircase top plate, b is the stair tread height, c is the stair tread width, m is the number of staircase treads, and s is the total length of the staircase. Furthermore, the mold's external parameters are a1, a4, d1, d4, g, and f. A1 is the upper length of the mold bottom, a4 is the lower length of the mold bottom, d1 is the upper length of the mold top, d4 is the lower length of the mold top, g is the height of the mold ribs on the front side of the mold bend, and f is the height of the mold ribs on the rear side of the mold plate. The number of transverse ribs in the middle of the plate side is n-1, and their edge spacing is a5. The edge distance and outermost spacing of the restraining channel steel are a6 and ab, respectively.

[0052] pass Figure 7 It can be seen that in the specific implementation, the finite element method is used to establish the mold model, and the shell unit model is used for finite element analysis. The finite element method is used to verify the rationality of the mold design scheme. The finite element design process is as follows:

[0053] The first step is to obtain the parameters of stairs and molds;

[0054] The second step is to establish the mold geometry model through parameters;

[0055] The third step is to start meshing based on the mold design parameters;

[0056] The fourth step is to determine the geometric characteristics, material properties, and boundary conditions of the mold model;

[0057] The fifth step is to define the actual load conditions of the mold by simulating the concrete pouring process;

[0058] Step 6: Submit the calculation;

[0059] In the seventh step, after the mold calculation is completed, the maximum lateral deformation of all nodes of the mold panel is extracted, and the maximum deformation value of the mold is compared with the deformation limit allowed by the specification to obtain a conclusion on whether the mold design scheme is feasible.

[0060] The NASA-II algorithm is a multi-objective optimization algorithm, the full name of which is the non-dominated sorting algorithm. Its essence is a genetic algorithm that integrates non-dominated sorting and crowding distance.

[0061] In this embodiment, the NSGA-II algorithm is used to optimize the mold design scheme. In each generation, selection, crossover, and mutation operations are used to calculate the fitness values ​​of all individuals. Non-dominated sorting and crowding calculations are performed. A certain number of individuals with the highest ranking form the new generation population. Through iterative optimization, when the maximum number of iterations or convergence conditions are met, a certain number of individuals with the highest ranking are output as the optional mold design scheme.

[0062] refer to Figure 8 As shown in the figure, the optimization design process of the present invention is as follows: first, the stair parameters and mold parameters are obtained to form a mold parameterized model. Then, considering the reliability of the design, the amount of steel used, and the convenience of processing, the component height, component plate thickness, component spacing, etc. of the mold are optimized to form multiple mold assembly models. Then, the finite element software is used to extract the maximum lateral deformation of each assembly model, and each individual is evaluated. According to the individual fitness value f v and f c Perform non-dominated sorting and crowding calculations, and form a new generation of population with a certain number of individuals at the top of the sorting. Perform the same selection, crossover, and mutation operations in the next generation. Then calculate the fitness value of each individual and perform non-dominated sorting and crowding distance calculations. When the population evolves to the maximum number of iterations or convergence conditions, output a certain number of mold design schemes, and select the optimal mold design scheme according to design needs.

[0063] f v =g v +p r (1)

[0064] f c =g c +p r (2)

[0065]

[0066] Where, f v is the steel usage adaptability value, f c is the mold processing convenience adaptability value, g c For the convenience of steel processing, g v is the steel consumption, p r is the maximum deformation violation penalty value of the steel mold panel, t f is the thickness of the front side formwork panel, t b is the thickness of the rear mold panel, t r is the thickness of the rib panel, n fl is the number of longitudinal ribs in the middle of the front side mold, n bl is the number of longitudinal ribs in the middle of the rear mold, n bh is the number of transverse ribs in the middle of the rear mold, n limitis the optimal number of transverse ribs in the middle of the rear mold, l bm is the length of the middle area of ​​the rear mold of the mold, disp1 is the maximum lateral deformation of the front mold, disp2 is the maximum lateral deformation of the rear mold, and l is the longest side of the front and rear molds of the mold.

[0067] By using finite element analysis and multi-objective optimization methods to solve a variety of mold design schemes that take into account economy, processing convenience, and reliability, the optimal mold design scheme is selected according to design requirements, and an OCC model is established using OCCT. Then, OCCT's hidden layer removal algorithm and cutting algorithm are used to obtain the component plane data. Then, the shape of each component is drawn in a 1:1 ratio in the DXF template, and the component name, plate thickness, and quantity information are added. Finally, the component production data that can be read by laser cutting equipment is obtained.

[0068] In summary, it can be seen that the method proposed in the present invention can produce prefabricated staircase molds, and the turnover times of the molds can meet actual production needs.

[0069] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A multi-objective optimization design method for precast concrete staircase molds, characterized in that: The following steps are involved: S1: splitting the precast concrete staircase mold into multiple assemblies according to the connection method, and splitting each assembly into multiple mold parts; S2: parametric description of the number and size of each mold component; S3: determining a model plane control point according to geometric parameters of the precast concrete staircase and mold design parameters, and determining a plane position of a mold component by the model plane control point; S4: Establishing the mold parametric model; S5: Using finite element software, mesh the established mold parametric model; set the geometric properties, material properties, and boundary conditions of the mold components, simulate the load condition of the mold being subjected to lateral water pressure during concrete pouring, and perform finite element analysis under the load condition; S6: Obtain the maximum lateral deformation of all nodes of the mold based on the finite element analysis results; S7: Establish a mold multi-objective optimization model, where the optimization variable is the mold design scheme, the optimization target is the economy and processing convenience evaluation index, and the constraint condition is the mold reliability evaluation index; The mold design scheme includes the geometric dimensions, plate thickness, and quantity of each component; the mold reliability evaluation index refers to whether the maximum lateral deformation meets the specification requirements; the processing convenience evaluation index refers to the requirements for the number of ribs, the thickness of the panel, and the number of thickness types of ribs; S8: Use NSGA-II algorithm to solve the optimal design scheme of the multi-objective optimization model; S9: According to the optimized design scheme, the mold BRep model is established using OPENCASCADE technology, and then the plane data of each mold component is obtained using the hidden layer and sectioning algorithm. Finally, the graphics are drawn in the drawing template file to obtain the mold component production data.

2. The multi-objective optimization design method for precast concrete staircase molds according to claim 1 is characterized by: The mold parts are composed of steel plates, the mold parts are connected by welds, and the various assemblies are connected by bolts.

3. The multi-objective optimization design method for precast concrete staircase molds according to claim 1 is characterized by: When performing finite element analysis in step S5, the finite element model adopts a shell element model.

4. The multi-objective optimization design method for precast concrete staircase molds according to any one of claims 1 to 3, characterized in that: In step S6, the maximum lateral deformation values ​​of the front and rear molds are automatically extracted based on the finite element analysis results.

5. The multi-objective optimization design method for precast concrete staircase mold according to claim 1 is characterized in that: When using the NSGA-II algorithm to solve the optimal design scheme of the multi-objective optimization model, selection, crossover, and mutation operations are used in each generation to calculate the fitness values ​​of all individuals, and non-dominated sorting and crowding calculations are performed. A certain number of individuals with the highest rankings form a new generation population. Through iterative optimization, when the maximum number of iterations or convergence conditions are met, a certain number of individuals with the highest rankings are output as alternative optimization design schemes.

6. The multi-objective optimization design method for precast concrete staircase molds according to claim 5 is characterized in that: In step S9, the graphics are drawn in the DXF template file at a 1:1 ratio.

7. The multi-objective optimization design method for precast concrete staircase mold according to claim 5 or 6, characterized in that: According to the optimized design scheme, OPENCASCADE technology is used to automatically generate DXF production data, and the laser cutting equipment directly reads the DXF production data to complete the cutting process of the mold parts.

8. The multi-objective optimization design method for precast concrete staircase mold according to claim 1 or 3, characterized in that: In step S5, the finite element method meshes the mold component according to a fixed length and a fixed number of intervals to form quadrilateral shell elements.

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