Panel furniture structure optimization method based on nonlinear optimization method

Abstract

The invention relates to a panel furniture structure optimization method based on a nonlinear optimization method, which comprises the following steps of: measuring basic mechanical property parameters of a panel A in a compression and bending state; measuring the mechanical strength parameter of the panel A node; establishing a mathematical relationship between the structural volume of the panel furniture and the size of each part, and constructing a target function; constructing a constraint condition function according to the strength requirements of the plate A and the nodes; and compiling a target function and a constraint condition function program through MATLAB, and solving to obtain the limit size of the panel furniture plate A. According to the method, the structural size can be optimized, the design period of the panel furniture structure can be shortened and the cost can be reduced under the condition that the panel furniture structure meets the mechanical strength of the actual use function through a nonlinear optimization method.

Description

Technical Field

[0001] The invention belongs to the technical field of furniture structure optimization, and specifically relates to a panel furniture structure optimization method based on a nonlinear optimization method. Background Art

[0002] In the context of the "big home" and "smart manufacturing" era, panel furniture has the characteristics of simple structure, easy disassembly and assembly, easy transportation, and easy mechanization, automation, and collaboration in production, and has occupied a large market share.

[0003] However, the density of artificial boards used in panel furniture is usually greater than that of medium and high-grade wood, and due to the box-type structure of panel furniture, its overall volume is also much higher than that of frame furniture. For safety reasons, the thickness (strength) of the board is usually selected to be larger. At the same time, the current structural design of panel furniture has always adopted the methods of empirical design and analogy design, lacking in-depth analysis and precise calculation. As a result, on the one hand, the strength and rigidity of furniture products cannot meet the design requirements, resulting in deformation or even damage, and the service life cannot reach the designed life; on the other hand, the safety factor is too large, and raw materials are not saved to the maximum extent, resulting in waste of resources. The overall weight of the designed furniture is too large, which is not conducive to transportation and installation, and increases the material cost of the enterprise. Therefore, on the premise of meeting the strength requirements of panel furniture, it is imperative to study the structural optimization of panel furniture. Summary of the invention

[0004] The structural optimization design method of panel furniture is based on the stress conditions of panel furniture in real usage scenarios, and finally combined with the size requirements of the actual usage scenarios, by establishing the volume objective function and constraint condition function and using software for programming and solving, to achieve the optimal board size under the premise of meeting the usage function. This method has the advantages of low cost, parameterization and high efficiency, which can reasonably reduce material consumption and scrap rate, and provide a theoretical basis for the design of panel furniture, thereby reducing costs and improving the economic benefits of production enterprises on the basis of ensuring that the furniture meets the strength and stiffness requirements.

[0005] The present invention provides a method for optimizing the structure of panel furniture and selecting materials based on finite element analysis, comprising the following steps: S1. Measure the basic mechanical properties of sheet A and design a simple cabinet structure; S2, construct the objective function; S3, construct the constraint condition function based on the mathematical relationship between the structural volume of the panel furniture and the dimensions of each component and the strength requirements of the nodes; S4. Use MATLAB to write the objective function and constraint function program to solve and obtain the limit size of panel furniture board A.

[0006] Further, step S1 comprises: S1.1, Steps for selecting the board; Select the type of board and set the size range requirements of the board; The type of board can be one of particle board, multi-layer board, ecological board and medium-density fiberboard; The size range of the board should be selected according to the type of furniture, which can be a bookcase, wardrobe, or cabinet. Preferably, the length and width range of the shelf, top plate or bottom plate is determined according to common sizes; Preferably, the thickness selection range of the shelf, top plate or bottom plate is determined according to the model of the existing plate material; Further, step S1 comprises: S1.2, Steps for measuring mechanical properties of plates; Mechanical properties include: density , bending elastic modulus E, yield strength ; Further, step S1 comprises: S1.3. Design the furniture cabinet structure and determine the connection method between the shelf, top or bottom board and the side board; Furthermore, the connection mode selects T-type node connection and L-type node connection; Preferably, a two-in-one eccentric connector (including a pre-buried nut, a connecting rod and an eccentric body) and a positioning round bar tenon are used to connect the two ends of the shelf and the side plate; Preferably, in step S2, the inverse calculation formula of the volume of the shelf is used as the objective function of this optimization; Further, the strength requirements of the nodes in step S3 include maximum deflection, maximum bending stress and bending moment at the connection; Preferably, when calculating the maximum deflection, a creep correction coefficient K1 is set, and the creep correction coefficient K1 is used to correct the deviation between the maximum deformation and the instantaneous deformation; Preferably, the creep correction coefficient K1 is obtained through experiments; Preferably, when calculating the bending moment at the connection, a correction coefficient K2 is set, and the correction coefficient K2 is used to correct the bearing capacity of nodes of different widths in actual engineering; Preferably, the correction coefficient K2 is obtained through experiments; Furthermore, in step S3, the constraint conditions should satisfy that the maximum deflection change of the panel furniture shelf, top plate and bottom plate is less than 0.5%, the maximum bending stress of the component is less than the bending yield strength of plate A, the internal stress of the component is less than the compressive yield strength of plate A, and the node bending moment is less than the ultimate bending moment of the plate A node. Beneficial Effects

[0007] The present invention establishes a volume objective function and a constraint condition function and uses MATLAB software to perform programming and solving, thereby achieving the optimal board size under the premise of satisfying the use function; not only does it reduce the time of manual material screening, but it also saves materials and reduces costs to the maximum extent under the premise of ensuring the structural performance of the furniture; The present invention adopts a multi-parameter combination of maximum deflection, maximum bending stress and bending moment at the connection as constraints, and takes into account the influence of factors such as the node connection method and node width, thereby optimizing the quality of furniture design; In the present invention, when calculating the maximum deflection, the creep correction coefficient K1 and the correction coefficient K2 are introduced to accurately evaluate the performance of the plate under long-term stress conditions; when calculating the ultimate bending moment, the correction coefficient K2 is introduced to correct the bearing capacity of nodes of different widths in actual engineering; the optimized algorithm can improve the quality of furniture design; Since the correction coefficient is introduced in the present invention, the programming software needs to have a higher sensitivity to capture and respond to small changes in the design variables. The present invention adopts MATLAB software for programming, which improves the efficiency and quality of furniture design. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 : Schematic diagram of the process of the present invention.

[0009] Figure 2 : Shelf dimension diagram in an embodiment of the present invention.

[0010] Figure 3 : In the embodiment of the present invention, the load condition applied to the cabinet shelf.

[0011] Figure 4 : Force diagram of the cabinet shelf in the embodiment of the present invention.

[0012] Figure 5 : In the embodiment of the present invention, the program code based on the fmincon function. DETAILED DESCRIPTION

[0013] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0014] The present invention is a panel furniture structure optimization method based on a nonlinear optimization method. Figure 1 The purpose of this embodiment is to obtain the limit span of the particle board bookcase shelf based on this method.

[0015] In order to achieve the above object, the technical solution adopted by the present invention is: S1. Measure the basic mechanical properties of sheet A and design a simple bookcase structure; S1.1, select the board; According to the national standard GB / T 3327-2016 "Main Dimensions of Furniture Cabinets", the requirements for bookcase dimensions are as follows: the common length range of the shelf of a plate-type bookcase is 600-900mm, and the width range is 300-400mm. The particleboard with the length, width and thickness of the shelf are a, b, and c respectively. The shelf dimension diagram is as follows: Figure 2 The shelf size is limited by the actual usage scenario and the plate processing standard. The sizes of a, b, and c should meet the following requirements:

[0016] S1.2. Measure the air-dry density of the board according to the test method in GB / T 17657-2022 "Test methods for physical and chemical properties of wood-based panels and veneer wood-based panels", and perform a three-point bending test on the particleboard to obtain the particleboard density. , bending elastic modulus E, yield strength ; S1.3, design a simple bookcase structure; The bookcase is made of particleboard with a thickness of c. The two ends of the shelf and the side board are connected by a two-in-one eccentric connector (including embedded nuts, connecting rods and eccentric bodies) and a positioning round bar tenon, and the design is based on this. Figure 3 The simplified structure of the bookcase shown; S2, construct the objective function; Since the purpose of this example is to find the ultimate span of the shelf, the inverse calculation formula of the shelf volume is used as the objective function of this optimization, and the formula is as follows:

[0017] S3, construct the constraint condition function based on the mathematical relationship between the structural volume of the panel furniture and the dimensions of each component and the strength requirements of the nodes; The constraint conditions are set by calculating the maximum deflection change, maximum bending stress and node bending moment of the plate through the formula, and the constraint condition function is established. Common heavy books are large 16-page, with a specific size of 297mm×210mm (length×width). During the test, the uniformly distributed load applied is 2kg / dm 2 , the width of the force-bearing area is 2.1dm, and the uniformly distributed load q=0.04116N / mm; according to the provisions of GB / T 10357.5-2023 "Furniture Mechanical Properties Test-Part 5: Cabinet Strength and Durability" on the shelf bending test, the application location and direction are as follows Figure 4 As shown; S3.1. Calculate the maximum deflection of the plate; Figure 4 It is the force diagram of the left end of the shelf cross section when it is in the bending deformation position, where the maximum deflection occurs in the middle position. However, in practical applications, structures such as bookshelves will experience creep when subjected to a constant load for a long time, and the maximum deformation should be greater than the maximum deformation obtained by the shelf deflection formula with fixed constraints at both ends. However, considering that the deflection calculation formula is applicable to short-term stress conditions, in order to accurately evaluate the performance of the particleboard material used in this embodiment under long-term stress conditions, the present invention selects particleboard as the research object, and applies a uniformly distributed load q=2kg / dm to the shelf with geometric dimensions (a=700mm; b=300mm; c=18mm) to simulate actual use conditions. 2 , which lasts for seven days. During this period, the deformation is measured regularly at the same position in the center of the shelf to record the initial deformation at the moment of load application and the maximum deformation reached after seven days. The specimens are repeated for 5 times. By comparing the maximum deformation and instantaneous deformation obtained in the experimental data, the creep correction factor used to quantify the creep characteristics of the material can be calculated. The creep correction factor is calculated as follows: The specific experimental data are shown in Table 1, and it is concluded that K1=3; Table 1 Experimental data of creep correction factor

[0018] The calculation formula for shelf deflection is:

[0019] Where: Y max is the maximum deflection (mm), E is the bending elastic modulus (MPa), and q is the uniformly distributed load (N / mm); S3.2. Calculate the maximum bending stress of the plate; The maximum bending stress of the shelf when both ends are fixed is:

[0020] Where: is the maximum bending stress (MPa); S3.3, calculate the node bending moment; The bending moment at the connection when both ends are fixed is:

[0021] For node bending moment, in theory, if the installation and force of two groups of connectors are symmetrical, and the materials and connection methods are exactly the same, then the bending moment can be evenly distributed to each group of connectors. At this time, the maximum bending moment (limit bending moment) that the bookcase shelf node can withstand is twice the limit bending moment of a single T-node. However, in actual engineering, due to processing accuracy, installation error or material inhomogeneity, the bending moment may not be completely evenly distributed to the two groups of connectors. Therefore, in order to more accurately evaluate this relationship, the present invention introduces a correction factor K2. Specifically, wider nodes can share more bending moments due to the increase in the bearing area of ​​their connectors, while narrower nodes face a higher risk of reducing the limit bending moment due to the local stress concentration effect. Therefore, bending moment tests are performed on node samples of different widths under the same loading conditions. During the test, a standard reference node connected by a single connector is used as a benchmark, and a series of double connector node samples from narrow to wide are selected. The increasing bending moment is gradually applied until the node is destroyed, and the limit bending moment value of each width node sample is recorded. Subsequently, the ultimate bending moments measured in these experiments were compared with the ultimate bending moments of the standard reference nodes, and K2=0.4 was obtained through analysis, which was used to correct the bearing capacity of nodes with different widths in actual projects. The specific experimental data are shown in Table 2. The calculation formula is:

[0022] Table 2 Bending moment correction coefficient experiment

[0023] The calculation formula for the allowable bending moment at the connection is:

[0024] Where: M 许 is the allowable bending moment at the shelf connection (Nm), K2 is the bending moment correction factor, n is the number of connectors, b T is the width of the T-node (mm), M T is the ultimate bending moment of the T-node (Nm); S3.4, determine the constraints; In order to ensure that it meets the requirements of use strength, the constraints must be met: when the shelf is subjected to a uniformly distributed load, the maximum deflection change value should be less than 0.5% specified in the national standard, and the maximum bending stress should be less than the bending yield strength of the material itself =11.2MPa, the node bending moment should be less than the node allowable bending moment M 许 For safety reasons, a safety factor of 1.5 needs to be set, that is, the constraint condition of the objective function is:

[0025]

[0026]

[0027] In the existing structural optimization design of panel furniture, two to three constraints are usually used to ensure the rationality and performance of the design. These constraints usually include but are not limited to the following aspects: Maximum stress, maximum deflection and material consumption. However, this method is difficult to take into account all key performance indicators in a multi-objective optimization scenario, which may lead to insufficient accuracy and reliability of the optimization results. The present invention introduces multiple constraint function and its combination, corresponding to multiple constraint conditions such as shelf deflection, maximum bending stress, allowable node bending moment, maximum node bending moment, length, width and height of the plate, so that the optimization model can more comprehensively reflect the various limiting factors in the actual project, thereby significantly improving the accuracy and reliability of the optimization results; In addition, the present invention also introduces two different correction coefficients to adjust the importance of each constraint condition and the balance relationship between them. These two correction coefficients can be flexibly adjusted according to specific application scenarios, further improving the adaptability and flexibility of the optimization model. Specifically: Correction coefficient K1: used to adjust the weight relationship between the maximum deformation and the instantaneous deformation; Correction coefficient K2: used to adjust the weight relationship between the maximum node bending moment and the allowable bending moment; Through the comprehensive application of the above-mentioned multiple constraints and two correction coefficients, the present invention can not only control the design variables more accurately, but also achieve a better balance in multi-objective optimization, thereby significantly improving the accuracy and reliability of the optimization results and improving the safety performance of the product; S4. Use MATLAB to write the objective function and constraint function program to solve and obtain the limit size of panel furniture board A.

[0028] In the prior art, ANSYS is often used for optimization design, but due to the limitation of its module function diversity, when there are relatively many design variables, ANSYS will converge to the local optimal solution, and can only add constraints in numerical form. MATLAB is also one of the optimization design tools. MATLAB has a wealth of matrix operation commands and numerical calculation functions, and its complete graphics processing function can realize the visualization of programming. The use of algorithmic programming for structural optimization can realize the plasticity of the optimization program and is not limited to the existing MATLAB toolbox functions. In addition, MATLAB has a high sensitivity and can effectively capture and reflect the impact of small changes in design variables on the objective function, which is particularly important for finding the global optimal solution. The higher sensitivity enables MATLAB to more accurately identify the impact of parameter adjustment on the results during the optimization design process, thereby supporting more sophisticated model tuning. In addition, MATLAB is very flexible in regulating different coefficients, and users can use the graphical user interface to easily change various parameters in the model.

[0029] Among them, the objective function is:

[0030] Constraints: 600≤a≤900

[0031]

[0032]

[0033] ba≤0 ca≤0 After determining the objective function and constraints, the bookcase shelf volume optimization program was written using the fmincon function in MATLAB, and nonlinear optimization was performed, such as Figure 5 As shown, the solution is that when b=300 and c=18, that is, when the bookcase shelf made of 18mm thick particle board is 300mm deep, the maximum usable length of the shelf is 697mm, so the optimal size of the bookcase in the most commonly used size range is 600-697mm.

Claims

1. A panel furniture structure optimization method based on nonlinear optimization method, characterized in that: The following steps are involved: S1. Measure the basic mechanical properties of sheet A and design a simple cabinet structure; S2, construct the objective function; S3, construct the constraint condition function based on the mathematical relationship between the structural volume of the panel furniture and the dimensions of each component and the strength requirements of the nodes; S4. Use MATLAB to write the objective function and constraint function program to solve and obtain the limit size of panel furniture board A.

2. The panel furniture structure optimization method based on the nonlinear optimization method according to claim 1 is characterized in that: Basic mechanical properties include density, elastic modulus and yield strength.

3. The panel furniture structure optimization method based on the nonlinear optimization method according to claim 1, characterized in that: The constraint conditions should meet the requirements that the maximum deflection change of the shelf, top plate and bottom plate of the panel furniture is less than 0.5%, the maximum bending stress of the component is less than the bending yield strength of plate A, the internal stress of the component should be less than the compressive yield strength of plate A, and the node bending moment is less than the ultimate bending moment of the node of plate A.

4. The panel furniture structure optimization method based on the nonlinear optimization method according to claim 3 is characterized in that: When calculating the maximum deflection, the creep correction coefficient K1 is set. The creep correction coefficient K1 is used to correct the deviation between the maximum deformation and the instantaneous deformation.

5. The panel furniture structure optimization method based on the nonlinear optimization method according to claim 4 is characterized in that: The creep correction coefficient K1 is obtained through experiments, and the experimental method includes: S1. Select plates of the same size but different materials; S2, apply uniform load; S3. Record the deformation of the center of the partition for seven consecutive days; S4. Calculate the ratio of the instantaneous initial deformation to the maximum deformation after seven days; S5. Obtain the creep correction coefficient.

6. The panel furniture structure optimization method based on nonlinear optimization method according to claim 3, characterized in that: When calculating the bending moment at the connection, the correction factor K2 is set. The correction factor K2 is used to correct the bearing capacity of nodes of different widths in actual engineering.

7. The panel furniture structure optimization method based on the nonlinear optimization method according to claim 6 is characterized in that: The correction coefficient K2 is obtained through experiments, and the experimental method includes: S1. Select a series of double connector node samples from narrow to wide; S2, gradually apply increasing bending moment until the node is destroyed; S3. Record the ultimate bending moment value of each width node sample; S4, the ratio of the experimentally measured ultimate bending moment to the ultimate bending moment of the standard reference node and the actual node width to the reference node width; S5. Get the correction coefficient K2.

8. The panel furniture structure optimization method based on the nonlinear optimization method according to claim 1, characterized in that: Considering that the purpose of this method is to optimize the structural volume, a safety factor of 1.5 is selected.

9. The panel furniture structure optimization method based on nonlinear optimization method according to claim 1, characterized in that: Step S1 includes: S1.1 a step of selecting a plate material, selecting the type of plate material and establishing a size range requirement for the plate material.

10. The panel furniture structure optimization method based on the nonlinear optimization method according to claim 9, characterized in that: The range of board size requirements should be selected according to the type of furniture, and the length and width range of the shelf, top board or bottom board should be determined according to common sizes; the thickness selection range of the shelf, top board or bottom board should be determined according to the existing board model.

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