Design method and system of sandwich composite material sidewalk board and storage medium

Abstract

The invention relates to the technical field of sidewalk slab design, and discloses a design method and system of a sandwich composite sidewalk slab and a storage medium, and the design method comprises the following steps: constructing a calculation formula of flexural rigidity, shear rigidity and deflection of the sandwich composite sidewalk slab; constructing ultimate bearing capacity calculation formulas of the sidewalk slab in different failure modes according to the constructed calculation formulas of the flexural rigidity, the shear rigidity and the deflection; constructing a target function of the sidewalk slab by adopting the lowest total cost of the sandwich composite material sidewalk slab as a target; and performing optimization calculation on the established flexural rigidity, shear rigidity and deflection calculation formula, the ultimate bearing capacity calculation formula and the objective function by adopting a particle swarm algorithm to obtain optimal structural design parameters. According to the design method and system for the sandwich composite material sidewalk board and the storage medium, the design efficiency of the sandwich composite material bridge sidewalk board is improved while the design requirement is met.

Description

Technical Field

[0001] The present invention relates to the technical field of sidewalk slab design, and particularly relates to a design method and system for a sandwich composite sidewalk slab. Background Art

[0002] The composite sidewalk slab is a new type of building material based on polymer materials and manufactured through a composite process. Compared with traditional concrete or metal materials, it has significant performance advantages and is widely used in bridges, urban sidewalks, and temporary roads.

[0003] The structural design method of the composite sidewalk slab mainly includes determining the dimensions of the structure through experimental tests, simulation, or empirical formulas.

[0004] However, there are many structural design parameters for the composite sidewalk slab (such as panel thickness, core material thickness, core material density), and the sidewalk slab needs to meet the requirements of strength, stiffness, and economy. Whether through experimental tests, simulation, or empirical formulas, the structural design parameters need to be adjusted multiple times to meet the design requirements. Summary of the Invention

[0005] In view of the deficiencies in the prior art, the present invention provides a design method, system, and storage medium for a sandwich composite sidewalk slab to solve the above technical problems.

[0006] In a first aspect, a design method for a sandwich composite sidewalk slab is provided, including:

[0007] Constructing calculation formulas for the flexural stiffness, shear stiffness, and deflection of the sandwich composite sidewalk slab;

[0008] According to the constructed calculation formulas for the flexural stiffness, shear stiffness, and deflection, constructing calculation formulas for the ultimate bearing capacity of the sidewalk slab under different failure modes;

[0009] Taking the lowest total cost of the sandwich composite sidewalk slab as the objective, constructing an objective function for the sidewalk slab;

[0010] Using the particle swarm optimization algorithm to optimize and calculate the established calculation formulas for the flexural stiffness, shear stiffness, and deflection, the calculation formulas for the ultimate bearing capacity, and the objective function to obtain the optimal structural design parameters.

[0011] Further, the calculation formula for the flexural stiffness is:

[0012]

[0013] Where d = d t + h c , which is the distance between the neutral axes of the upper and lower panels of the sandwich beam, b is the width of the beam, hc is the height of the core material, d t is the thickness of the surface layer, E f is the compression modulus of the surface layer, I f is the moment of inertia of the surface layer, E c is the compression modulus of the core material, I c is the moment of inertia of the core material.

[0014] Furthermore, the calculation formula for the shear stiffness is:

[0015]

[0016] where G c is the shear modulus of the core material, and A is the cross-sectional area of the core material.

[0017] Furthermore, the calculation formula for the deflection is:

[0018]

[0019] where p is the concentrated force per unit width of the sandwich beam, Δ b is the deformation caused by bending, Δ s is the deformation caused by shear.

[0020] Furthermore, the failure modes include core material indentation failure, panel compressive yield failure, core material shear failure, and panel buckling failure.

[0021] Furthermore, the calculation formula for the objective function is:

[0022] g = 1000×l×h c ×ρ1×p1 + 1000×l×d t ×ρ2×2×p2;

[0023] where l is the calculation length of the sandwich beam, ρ1 is the density of the core material, ρ2 is the density of the panel, p1 is the price of the core material, p2 is the price of the panel, h c is the height of the core material, d t is the thickness of the surface layer.

[0024] Furthermore, the optimization process of the particle swarm algorithm includes:

[0025] Setting the initial position and velocity of the particles;

[0026] According to the current position of the particles, calculating the objective function and the penalty term of the constraint conditions, and constructing the fitness function, where the constraint conditions include the core material indentation destructive force, the panel yield destructive force, the core material shear destructive force, the panel buckling destructive force, the core material height limit, the surface layer thickness limit, and the deflection limit;

[0027] Compare the fitness function with the individual's historical best fitness, and update the individual's best position;

[0028] Select the global best position from all the individual best positions;

[0029] According to the individual best position and the global best position, iteratively update the particle velocity and position until the maximum number of iterations is reached or the global best solution converges.

[0030] In a second aspect, a design system for a sandwich composite sidewalk slab is provided, which is characterized in that, based on the design method of a sandwich composite sidewalk slab described in any one of the foregoing, it includes:

[0031] A first construction module configured to construct calculation formulas for the flexural stiffness, shear stiffness and deflection of a sandwich composite sidewalk slab;

[0032] A second construction module configured to construct calculation formulas for the ultimate bearing capacity of the sidewalk slab under different failure modes according to the constructed calculation formulas for the flexural stiffness, shear stiffness and deflection;

[0033] A third construction module configured to construct an objective function for the sidewalk slab with the goal of minimizing the total cost of the sandwich composite sidewalk slab;

[0034] An optimization calculation module configured to perform optimization calculations on the established calculation formulas for the flexural stiffness, shear stiffness and deflection, the calculation formula for the ultimate bearing capacity, and the objective function by using a particle swarm algorithm to obtain the optimal structural design parameters.

[0035] In a third aspect, a design system for a sandwich composite sidewalk slab is provided, including a processor and a memory storing program instructions, which is characterized in that the processor is configured to execute a design method of a sandwich composite sidewalk slab described in any one of the foregoing when running the program instructions.

[0036] In a fourth aspect, a computer-readable storage medium is provided, which is characterized in that the computer-readable storage medium stores a computer program, the computer program includes program instructions, and the program instructions cause the processor to execute a design method of a sandwich composite sidewalk slab described in any one of the foregoing when being executed by the processor.

[0037] The invention adopting the above technical solution has the following advantages:

[0038] The present invention provides an accurate theoretical basis for the design of sandwich composite sidewalk slabs by constructing calculation formulas for flexural stiffness, shear stiffness, and deflection based on the first-order shear deformation theory, as well as calculation formulas for ultimate bearing capacity under different failure modes. Then, the particle swarm optimization algorithm is used to optimize the calculation of the formulas and the objective function, which can quickly find the optimal structural design parameters that meet the design requirements, significantly reducing the number of experimental tests and simulation times in the design process, thereby greatly improving the design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the specific embodiments of the present invention, the drawings required for use in the specific embodiments will be briefly introduced below. In all the drawings, the components or parts are not necessarily drawn to actual scale.

[0040] Figure 1 It is a flowchart of a design method for a sandwich composite sidewalk slab of the present invention;

[0041] Figure 2 It is a flowchart of the particle swarm optimization algorithm in the design method for a sandwich composite sidewalk slab of the present invention;

[0042] Figure 3 It is a flowchart of a design system for a sandwich composite sidewalk slab of the present invention. SPECIFIC EMBODIMENTS

[0043] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present application.

[0044] The terms "first", "second", etc. in the specification and claims of the present application and the above-mentioned drawings are used to distinguish different objects, rather than to describe a specific order. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but optionally further includes steps or units not listed, or optionally further includes other steps or units inherent to these processes, methods, products, or devices.

[0045] References to "embodiments" in this application mean that the specific features, structures, or characteristics described in connection with the embodiments can be included in at least one embodiment of this application. The phrase appears in various places in the specification and does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.

[0046] As Figures 1 to 3 shown, a design method for a sandwich composite sidewalk slab of the present invention includes:

[0047] Step S01: Construct calculation formulas for the flexural stiffness, shear stiffness, and deflection of the sandwich composite sidewalk slab;

[0048] Step S02: According to the constructed calculation formulas for the flexural stiffness, shear stiffness, and deflection, construct calculation formulas for the ultimate bearing capacity of the sidewalk slab under different failure modes;

[0049] Step S03: With the goal of minimizing the total cost of the sandwich composite sidewalk slab, construct an objective function for the sidewalk slab;

[0050] Step S04: Use the particle swarm algorithm to optimize and calculate the established calculation formulas for the flexural stiffness, shear stiffness, and deflection, the calculation formula for the ultimate bearing capacity, and the objective function to obtain the optimal structural design parameters.

[0051] In this embodiment, the calculation formula for the flexural stiffness (sandwich panel stiffness) is:

[0052]

[0053] where d = d t + h c , which is the distance between the neutral axes of the upper and lower panels of the sandwich beam, b is the width of the beam, h c is the height of the core material, d t is the thickness of the surface layer, E f is the compressive modulus of the surface layer, I f is the moment of inertia of the surface layer, E c is the compressive modulus of the core material, I c is the moment of inertia of the core material.

[0054] In this embodiment, the calculation formula for the shear stiffness (equivalent shear stiffness of the sandwich beam) is:

[0055]

[0056] where G c is the shear modulus of the core material, and A is the cross-sectional area of the core material.

[0057] In this embodiment, the calculation formula for the deflection (the mid-span deflection of the sandwich beam) is as follows:

[0058]

[0059] where p is the concentrated force per unit width of the sandwich beam, Δ b is the deformation caused by bending, and Δ s is the deformation caused by shear.

[0060] In this embodiment, the failure modes include core material indentation failure, faceplate compressive yield failure, core material shear failure, and faceplate buckling failure.

[0061] Specifically, the core material indentation failure force

[0062] The faceplate compressive yield failure force The core material shear failure force P3 = 2τ c bd, and the faceplate buckling failure force

[0063] where σ c is the faceplate compressive strength, σ f is the faceplate compressive strength, and τ c is the core material shear strength.

[0064] In this embodiment, the calculation formula for the objective function is:

[0065] g = 1000×l×h c ×ρ1×p1 + 1000×l×d t ×ρ2×2×p2;

[0066] where l is the calculated length of the sandwich beam, ρ1 is the core material density, ρ2 is the faceplate density, p1 is the core material price, p2 is the faceplate price, h c is the core material height, and d t is the face layer thickness.

[0067] In this embodiment, the optimization process of the particle swarm algorithm includes:

[0068] Setting the initial position and velocity of the particles;

[0069] According to the current position of the particles, calculating the penalty terms of the objective function and the constraint conditions, and constructing the fitness function, where the constraint conditions include the core material indentation failure force, the faceplate yield failure force, the core material shear failure force, the faceplate buckling failure force, the core material height limit, the face layer thickness limit, and the deflection limit;

[0070] Comparing the fitness function with the individual historical best fitness, and updating the individual best position;

[0071] Select the global optimal position from all individual optimal positions;

[0072] According to the individual optimal position and the global optimal position, iteratively update the particle velocity and position until the maximum number of iterations is reached or the global optimal solution converges.

[0073] Specifically, initialize the particle swarm

[0074] Initialize the position of the particle according to the preliminary design parameters of the sandwich panel:

[0075]

[0076] where x min,d and x max,d are the upper and lower limits of the d-th design parameter of the sandwich panel, and rand is a random number between [0,1].

[0077] Velocity initialization:

[0078]

[0079] where v min,d and v max,d are the upper and lower limits of the particle velocity.

[0080] Initialize the parameters: set the inertia weight w, learning factors c1 and c2, and the maximum number of iterations T.

[0081] Calculate the fitness

[0082] Fitness function: Calculate the corresponding fitness function value according to the position of the particle

[0083] f(x i ) = min(g + λ1(P - P1) 2 + λ2(P - P2) 2 + λ3(P - P3) 2 + λ4(P - P4) 2 + λ5(h c - h clim) 2 + λ6(d t - d tlim ) 2 + λ7(Δ - Δ lim ) 2 )

[0084] where g is the objective function, x iis the position of the particle, P1 is the indentation failure force of the core material, P2 is the yield failure force of the panel under compression, P3 is the shear failure force of the core material, P4 is the buckling failure force of the panel, λ1 is the penalty factor for the maximum indentation failure force of the core material, λ2 is the penalty factor for the maximum yield failure force of the panel under compression, λ3 is the penalty factor for the maximum shear failure force of the core material, λ4 is the penalty factor for the maximum buckling failure force of the panel, λ5 is the penalty factor for the height of the core material, λ6 is the penalty factor for the thickness of the surface layer, λ7 is the penalty factor for the deflection of the sandwich panel, h clim is the limit value of the height of the core material, d tlim is the limit value of the thickness of the surface layer, Δ lim is the limit value of the deflection of the sandwich panel, Δ lim = l / 300.

[0085] Update the individual optimal position (pbest)

[0086] For the i-th particle, compare the current fitness of the particle in the t-th iteration process with the individual historical optimal fitness:

[0087]

[0088] Update the global optimal position (gbest)

[0089] Among the individual optimal positions of all particles, find the global optimal position:

[0090]

[0091] Update the velocity and position

[0092] Velocity update: Update the velocity of the particle according to the individual optimal position and the global optimal position:

[0093]

[0094] where rand1 and rand2 are random numbers between [0, 1].

[0095] Position update: Adjust the position of the particle according to the updated velocity:

[0096]

[0097] Check the termination condition

[0098] Termination condition: Judge whether the maximum number of iterations is reached or the change in the global optimal solution is less than a certain threshold.

[0099] If the termination condition is satisfied, end the algorithm; otherwise, return to update the individual optimal position and continue the iteration.

[0100] Output the optimal solution

[0101] Output the globally optimal position gbest as the final solution.

[0102] In some other embodiments, a design system for a sandwich composite sidewalk slab is provided, which is characterized in that, based on the design method of a sandwich composite sidewalk slab according to any one of the foregoing, it includes:

[0103] A first construction module configured to construct calculation formulas for the flexural stiffness, shear stiffness, and deflection of a sandwich composite sidewalk slab;

[0104] A second construction module configured to construct calculation formulas for the ultimate bearing capacity of the sidewalk slab under different failure modes according to the constructed calculation formulas for flexural stiffness, shear stiffness, and deflection;

[0105] A third construction module configured to construct an objective function for the sidewalk slab with the lowest total cost of the sandwich composite sidewalk slab as the goal;

[0106] An optimization calculation module configured to perform optimization calculations on the established calculation formulas for flexural stiffness, shear stiffness, and deflection, the calculation formula for ultimate bearing capacity, and the objective function by using the particle swarm algorithm to obtain the optimal structural design parameters.

[0107] In some other embodiments, a design system for a sandwich composite sidewalk slab is provided, including a processor and a memory storing program instructions, which is characterized in that the processor is configured to execute a design method of a sandwich composite sidewalk slab according to any one of the foregoing when running the program instructions.

[0108] In some other embodiments, a computer-readable storage medium is provided, which is characterized in that the computer-readable storage medium stores a computer program, and the computer program includes program instructions that cause the processor to execute a design method of a sandwich composite sidewalk slab according to any one of the foregoing when executed by the processor.

[0109] It should be noted that for the foregoing method embodiments, for the sake of simple description, they are all expressed as a series of action combinations. However, those skilled in the art should know that this application is not limited by the described action sequence, because according to this application, certain steps can be performed in other sequences or simultaneously. Secondly, those skilled in the art should also know that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0110] In the above embodiments, the descriptions of each embodiment have their own emphases. For the parts not detailed in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0111] In several embodiments provided by this application, it should be understood that the disclosed device can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units is only a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling, direct coupling, or communication connection to each other can be through some interfaces. The indirect coupling or communication connection of the device or unit can be in an electrical or other form.

[0112] The units described as separate components may or may not be physically separated. The components displayed as units may or may not be physical units, that is, they can be located in one place or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0113] In addition, in each embodiment of the application, each functional unit can be integrated in a processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit. The above-mentioned integrated units can be implemented in the form of hardware or in the form of software program modules.

[0114] If the above-mentioned integrated unit is implemented in the form of a software program module and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in each embodiment of this application. And the aforementioned memory includes: USB flash drives, read-only memories (ROM), random access memories (RAM), mobile hard disks, magnetic disks, or optical discs, etc., which can store program codes.

[0115] Those of ordinary skill in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing relevant hardware through a program. This program can be stored in a computer-readable memory. The memory can include: flash drives, read-only memories, random access memories, magnetic disks, or optical discs, etc.

[0116] The above has introduced the embodiments of the present application in detail. Specific examples are used herein to elaborate on the principle and implementation manner of the present application. The description of the above embodiments is only used to help understand the method of the present application and its core idea; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present application.

Claims

1. A design method for a sandwich composite sidewalk slab, characterized in that Including: Constructing calculation formulas for the flexural stiffness, shear stiffness, and deflection of the sandwich composite sidewalk slab; According to the constructed calculation formulas for the flexural stiffness, shear stiffness, and deflection, constructing calculation formulas for the ultimate bearing capacity of the sidewalk slab under different failure modes; Taking the lowest total cost of the sandwich composite sidewalk slab as the goal, constructing the objective function of the sidewalk slab; Using the particle swarm algorithm to optimize the established calculation formulas for the flexural stiffness, shear stiffness, and deflection, the calculation formulas for the ultimate bearing capacity, and the objective function, and obtaining the optimal structural design parameters.

2. The design method of a sandwich composite sidewalk slab according to claim 1, characterized in that, The calculation formula for the flexural stiffness is: where d = d t + h c , which is the distance between the neutral axes of the upper and lower panels of the sandwich beam, b is the width of the beam, h c is the height of the core material, d t is the thickness of the surface layer, E f is the compressive modulus of the surface layer, I f is the moment of inertia of the surface layer, E c is the compressive modulus of the core material, I c is the moment of inertia of the core material.

3. The design method of a sandwich composite sidewalk slab according to claim 2, characterized in that, The calculation formula for the shear stiffness is: Among them, G c is the shear modulus of the core material, and A is the cross-sectional area of the core material.

4. The design method of a sandwich composite sidewalk slab according to claim 3, characterized in that, The calculation formula for the deflection is: where p is the concentrated force per unit width of the sandwich beam, Δ b is the deformation caused by bending, and Δ s is the deformation caused by shear.

5. The design method of a sandwich composite sidewalk slab according to claim 1, characterized in that The failure modes include core material indentation failure, panel compressive yield failure, core material shear failure, and panel buckling failure.

6. The design method of a sandwich composite sidewalk slab according to claim 1, characterized in that, The calculation formula for the objective function is: g = 1000×l×h c ×ρ1×p1 + 1000×l×d t ×ρ2×2×p2; Among them, l is the calculated length of the sandwich beam, ρ1 is the density of the core material, ρ2 is the density of the panel, p1 is the price of the core material, p2 is the price of the panel, h c is the height of the core material, d t is the thickness of the surface layer.

7. A design method of a sandwich composite sidewalk slab according to claim 1, characterized in that, The optimization process of the particle swarm algorithm includes: Setting the initial position and velocity of the particles; According to the current position of the particles, calculating the penalty terms of the objective function and the constraint conditions, and constructing the fitness function, where the constraint conditions include core material indentation destructive force, panel yield destructive force, core material shear destructive force, panel buckling destructive force, core material height limit, surface layer thickness limit, and deflection limit; Comparing the fitness function with the individual historical optimal fitness and updating the individual optimal position; Selecting the global optimal position from all the individual optimal positions; According to the individual optimal position and the global optimal position, iteratively updating the particle velocity and position until the maximum iteration number is satisfied or the global optimal solution converges.

8. A design system for a sandwich composite sidewalk slab, characterized in that, A design method for a sandwich composite sidewalk slab according to any one of claims 1 to 7, including: A first construction module configured to construct calculation formulas for the flexural stiffness, shear stiffness, and deflection of the sandwich composite sidewalk slab; A second construction module configured to construct calculation formulas for the ultimate bearing capacity of the sidewalk slab under different failure modes according to the constructed calculation formulas for the flexural stiffness, shear stiffness, and deflection; A third construction module configured to take the lowest total cost of the sandwich composite sidewalk slab as the goal and construct the objective function of the sidewalk slab; An optimization calculation module configured to use the particle swarm algorithm to optimize the established calculation formulas for the flexural stiffness, shear stiffness, and deflection, the calculation formulas for the ultimate bearing capacity, and the objective function, and obtain the optimal structural design parameters.

9. A design system for a sandwich composite sidewalk slab, comprising a processor and a memory storing program instructions, characterized in that, The processor is configured to execute a design method for a sandwich composite sidewalk slab according to any one of claims 1 to 7 when running the program instructions.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, the computer program includes program instructions, and the program instructions cause the processor to execute a design method for a sandwich composite sidewalk slab according to any one of claims 1 to 7 when being executed by the processor.

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