Structural design and experimental verification of a thin-walled plastic chairs based on the finite element method | Scientific Reports

Scientific Reports volume 14, Article number: 22285 (2024) Cite this article

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This study focuses on the design and preparation of a thin-walled plastic chair, and its mechanical properties were investigated by high load, cyclic load and drop impact. The finite element method (FEM) was employed to accurately evaluate the chair’s safety under these forces. Additionally, the effects of important structural parameters on the loading process in different states were investigated. Furthermore, a solid plastic chair prototype was created for experimental analysis. The findings revealed that increasing the thickness of the key structural parameters enhanced the safety properties of the chair under various load conditions. Optimal results were obtained when both dimensions were set to 5 mm. The deformation errors in FEM, experimental strength analysis, fatigue analysis, and drop impact analysis were measured at 3.7%, 3.6%, and 11.7%, respectively. Similarly, the stress errors were determined to be 5.9%, 5.2%, and 6.5%. These results suggest that the structural design of the chair demonstrates excellent reliability. Studying the crucial structural parameters of a plastic chair can provide valuable insights for the scientific design and safety evaluation of thin-walled furniture.

The utilization of virtual tools offers significant advantages in terms of reducing experimental testing, development time, and costs while enhancing product quality1. However, when it comes to high-quality product development, traditional methods of product reliability assessment often fall short, particularly in situations where data may be limited2. This limitation is not exempt in furniture design, where the success of a furniture product relies not only on its appearance but also on its structural strength design3. This is especially crucial as furniture designs need to accommodate the size and weight requirements of current and future populations4. Thankfully, the finite element method (FEM) has emerged as an effective alternative to experimental methods in structural design and analysis. FEM has proven to be a reliable and cost-effective tool, widely employed in various industries5. Its application in furniture design has simplified the complexity of structural design, resulting in improved design efficiency and stability of furniture structures6,7.

The FEM is employed to analyze and understand the structural force characteristics of furniture. This involves discretizing the overall furniture structure and conducting a comprehensive analysis of individual nodes and units to obtain relevant data8. For instance, Podskarbi and Smardzewski9 examined the mechanical properties of frame furniture joints using FEM. Kiliç et al.10 investigated the impact of tenon size on the static load of wooden chairs. Tankut et al.11 explored the application of FEM in analyzing wood structure products in furniture. Chen and Wu8 focused on optimizing the design of modified wood in furniture tenon and tenon structures using FEM. Yu et al.12 studied the mechanical and fatigue characteristics of wood chair structures using FEM. Optimizing key nodes in furniture design is crucial as they represent the overall safety and structural strength of the chair13. These nodes are particularly vulnerable to fractures or damage due to stress concentration14.

Injection molding is the primary production process for plastic chairs, which are widely used in daily life15. However, there is often variation in part tolerance during the injection molding process, and no unified standard exists. Dents in plastic products are a common issue that can be addressed by improving the structure of metal injection molds and optimizing the injection process. This ultimately leads to optimization in product structure design16,17. Additionally, there is limited research on the structural and mechanical analysis of plastic chairs, and previous studies have not explored the effects of impact forces on chair products.

Therefore, it is crucial to employ a scientific approach to enhance the mechanical properties of plastic chairs, prolong their fatigue life, and minimize plastic waste. It is equally important to ensure that these improvements are made while preserving the artistic form and structural integrity of the product. This research aims to contribute to the innovation, creation, and design of furniture that promotes a more rational and comfortable lifestyle for individuals.

In the production process of plastic chairs, it is important to adhere to the principles of component simplification and safety. This includes considerations such as ease of manufacturing, uniform wall thickness, and high strength and stiffness. Additionally, incorporating a stiffener into the shell structure is a commonly utilized technique to enhance critical load capacity, distribute stress, and improve the mechanical properties of the chair. This approach helps to prevent warping deformation without the need to increase the wall thickness18.

Following the design principles, the chair in question has a main reference size of 510 mm (length)×510 mm (width)×825 mm (height), with a seat and back thickness of 5 mm, as depicted in Fig. 1a. The detailed structure of the chair model can be seen in Fig. 1b. The plastic chair analyzed in this study was manufactured using polypropylene (PP) material. The specific properties of the PP utilized include a Poisson’s ratio of 0.39, a density of 1.04 g/cm3, and a yield strength of 41.4 MPa. This PP material was sourced from Fengxian, Shanghai, China, and its physical parameters were tested by Hebei Yishi Enterprise, China.

Parameter pictures: (a) Structural parameter, (b) Structure detail.

Injection molding is the primary method used to manufacture most types of plastic chairs19. To ensure more accurate analytical results, it is important to create every part of the chair during the modeling process to better align with the actual construction. This will enable more precise FEM20. To achieve this, we utilized Ansys software to establish a three-dimensional solid model of the plastic chair and conducted mechanical properties simulation force analysis. The quality of mesh division plays a crucial role in the accuracy of stress analysis and fatigue life prediction for the chair components21,22. Therefore, it was necessary to create virtual topologies of several curved surfaces to enhance the accuracy of force analysis23,24. This process is illustrated in Fig. 2a, with the progress of virtual topology shown in the color section of Fig. 2b, and a comparison of grid divisions after setting the virtual topology shown on Fig. 2c. For more accurate mechanical analysis results, a larger number of contact units were included in the FE model25. We adopted the hexahedron meshing method26,27,28 and used different mesh sizes for solution and convergence studies. When the FE model’s mesh size was set at 5 mm, the force solution process appeared to converge, with an average mesh mass of 0.9836, which was sufficient for analysis (Fig. 2d). The meshing diagram of the FE model for the plastic chair is presented in Fig. 2e. To realistically simulate the chair’s behavior when subjected to forces, the chair legs were fixedly constrained while various types of loads were applied. Only the chair was allowed to compress and deform along the loading direction, with zero moving deformation allowed in other directions (Fig. 2e).

FE model mesh processing for plastic chair: (a) Pre-processing model, (b) Virtual topology processing, (c) Meshing comparison, (d) The meshing quality diagram, (e) Chair meshing diagram.

Previous studies have highlighted the global trend of increasing average weight among populations in various countries. Therefore, it is crucial to fully consider the weight of the user when calculating and adjusting the furniture design4,29. In order to cater to a wider range of users, the strength, durability, and impact of plastic chairs are evaluated according to the GB/T 10357.3–2013 fifth-level experimental standard. This standard involves applying a load of 2000 N and 950 N to the front edge of the chair seat at a distance of 100 mm, with 10 and 2 × 106 tests, respectively. Additionally, a drop test is conducted by repeatedly dropping a 25 kg impactor 10 times from a height of 300 mm directly onto this position. The loading diagram for the chair during testing is depicted in Fig. 3.

Schematic diagram of experimental loading of plastic chair: (a) Strength testing, (b) Fatigue testing, (c) Impact testing.

The evaluation of overall product design heavily relies on the structural safety of each component30. When designing the structure of furniture products, it is essential to consider not only the overall stability but also the local stability of individual components31. In the presence of stress, the safety evaluation of each component is calculated using the formula:

where σs represents the yield value, [σ] denotes the real stress value, n represents the safety factor, and K represents the safety margin.

By analyzing the forces acting on each component and considering the constraints, the deformation and stress experienced by the chair under external forces can be determined. This is illustrated in Fig. 4.

In Fig. 4a, it can be observed that the chair experienced a maximum deformation of 11.74 mm, primarily occurring at the loading position of the seat surface. Figure 4b indicates that the chair reached a maximum stress of 29 MPa, with the highest concentration observed at the lower end of the connection between the rear legs and the chair surface. This yielded a safety factor of 1.43 for the maximum equivalent stress, as depicted in Fig. 4c. Furthermore, Fig. 4d demonstrates a safety margin of 0.43 at the location with the minimum safety factor, followed by a symmetrical distribution of the minimum margin at the front end of the chair seat. Consequently, the strength analysis confirmed that the structural design of the chair complied with the testing standard.

Static analysis: (a) Deformation, (b) Stress, (c,d) Safety factor and margin.

The fatigue life of the chair is influenced not only by stress conditions but also by the number of use cycles32,33,34. Utilizing the FEM fatigue analysis program enables accurate prediction of component damage location12, while the Goodman theory provides precise estimation of the fatigue life of the analyzed entity. The governing equation for this theory is as follows:

where Sa represents the cyclic stress amplitude, S(R = − 1) represents the fatigue amplitude when the stress ratio equals 1, Sm denotes the average stress, and Sb represents the ultimate strength. The values of Sa and Sm can be calculated using the formulas:

where σmax refers to the maximum stress value, and σmin represents the minimum stress value.

The fatigue life of material components can be calculated using the following equation:

where N is the number of cycles, m and c are the relevant parameters of the PP, and a and b are calculated as: $a =\frac{{lg}{c}}{m}$ and $b =-\frac{1}{m}$.

For assessing the cumulative fatigue damage of components, the widely used theory is Palmgren-Miner’s linear cumulative fatigue damage theory32,33,35. The formula for damage assessment is calculated as:

where D represents the cumulative damage index of the material, ni is the actual number of stress cycles, and Ni is the number of cycles for the material to reach the stress amplitude.

Figure 5 presents the fatigue diagrams of the chair. In Fig. 5a, it is evident that the chair experienced a maximum deformation of 8.31 mm, primarily concentrated in the middle of the seat surface. Figure 5b illustrates the maximum stress under load, measuring 18.66 MPa, predominantly occurring at the connection point between the rear legs and the seat surface. Notably, the location with the minimum safety factor was determined to be 2.22 when the chair was loaded, as depicted in Fig. 5c. Figure 5d highlights the location of the minimum fatigue life, which was determined to be approximately 3.3677 × 106 cycles. Remarkably, this exceeds the standard number of cycles. Moreover, Fig. 5e indicates that the maximum fatigue damage value of the chair was 0.6, which is below 1. This maximum fatigue value was also observed at the location with the minimum fatigue life. Consequently, it can be concluded that the connection point between the rear legs and the seat surface is the most critical area where fatigue failure is likely to occur, representing the weakest point in terms of fatigue resistance.

Fatigue analysis diagrams: (a) Deformation, (b) Stress, (c) Safety factor, (d,e) Fatigue life and damage.

The structural behavior of a load-bearing structure can significantly differ when subjected to an impact load compared to a quasi-static load, even if the geometric configuration remains the same. The impact force exerted on the structure during impact loading is typically very high36. In accordance with the chair drop impact testing standard, the impactor’s velocity is set at 2.45 m/s when it collides with the chair, as determined by Eq. (6):

where h represents the drop height of the impactor, g denotes the acceleration due to gravity, t1 represents the drop time, and v represents the velocity of the impactor. The momentum generated by the impactor during the collision with the plastic chair is calculated as:

where P represents the momentum generated, and m represents the mass of the impactor.

The impulse produced during the collision of the chair can be calculated as:

where I represents the impulse, and t2 is the action time of the impactor, which is 0.1 s. The impulse is equivalent to the change in momentum (P) generated by the impactor. The force (F) exerted by the impactor on the chair is determined to be 612.5 N. This impact force (F) on the chair can be calculated as:

Figure 6 illustrates the deformation and stress patterns of the plastic chair when subjected to external forces. In Fig. 6a, it is evident that the maximum deformation observed was 16.26 mm, primarily concentrated in the middle of the seat surface. The deformation of the seat surface gradually increased over time, with a noticeable increase towards the end of the collision, as depicted in Fig. 6c. Additionally, Fig. 6b highlights that the maximum stress experienced by the seat surface under load was 32.59 MPa, predominantly concentrated in the middle of the seat surface. The stress variation of the seat surface corresponds to the deformation pattern, as shown in Fig. 6d. It can be observed from Fig. 6c, d that the deformation and stress reach their maximum values at the end of the impact on the seat surface. Figure 6e reveals that the deformation of the cross-section of the seat surface is symmetrically distributed, gradually decreasing from the center to the edge when impacted. Furthermore, Fig. 6f demonstrates that the changes in cross-sectional stress of the seat surface align with the deformation changes. Lastly, Fig. 6b indicates that during the drop impact analysis of the chair, the safety factor at the maximum stress was calculated to be 1.27, ensuring a safe state. This confirms that the structural design of the chair meets the necessary usage requirements.

Analysis of drop testing: (a,b) Deformation and Stress, (c,d) Deformation and Stress curve, (e,f) Deformation and Stress curve of seat surface section.

Based on the safety analysis and fatigue analysis discussed in Sections “Strength analysis” and “Impact resistance analysis”, it was determined that the rear legs and seat surface connection of the chair experienced the maximum stress and had the shortest fatigue life. To further comprehend the impact of wall thickness on this connection, the range of wall thickness was varied from 4 to 10 mm. Additionally, as highlighted in Section “Key structural mechanical analysis”, the center of the seat surface exhibited the maximum deformation and stress during drop testing of the chair. Accordingly, the thickness of the set surface was designed within the range of 4–8 mm.

Figure 7 presents the impact of wall thickness on the safety and fatigue characteristics of the chair. In Fig. 7a, it can be observed that increasing the wall thickness had minimal influence on the deformation experienced by the chair under load. However, it is noteworthy that the maximum stress experienced by the chair during loading reached 38.34 MPa when the wall thickness was 4 mm. In this case, the structural safety factor was determined to be 1.08, indicating that the chair’s structure was close to a damaged state and did not meet the design requirements (Fig. 7b). Figure 7c illustrates partial diagrams of the safety factor for the chair, comparing wall thicknesses of 4 mm, 5 mm, and 10 mm. The area representing the safe position of the chair under force was the smallest when the wall thickness was 4 mm, and this position was close to a damaged state. In Fig. 7d, it can be observed that increasing the wall thickness aided in reducing the deformation when the chair was loaded. Notably, the increase in deformation was more pronounced within the designated range when the wall thickness was 5 mm. Furthermore, Fig. 7e demonstrates that increasing the thickness improved the fatigue life of the chair under stress. However, at a wall thickness of 4 mm, the fatigue life of the chair was determined to be 1.6 × 106 cycles, which did not meet the testing standard.

Influence of wall thickness dimensions on chair safety and fatigue performance: (a,b) Deformation and Stress trend, (c) Partial safety diagram, (d,e) Deformation and Fatigue life of cyclic load.

Nevertheless, it is important to consider that the wall thickness of a plastic product should ideally be as thin as possible to meet the serviceability conditions and molding process requirements. Thinner walls contribute to shorter molding time cycles and lower raw material consumption. Consequently, based on the strength analysis and fatigue property analysis of the chair joint with different wall thicknesses, it is determined that the optimal size is 5 mm.

Prior research has demonstrated that dimensional parametric analysis is widely employed in the optimal design of FEM to effectively determine the momentum and impact range produced by an impactor. This enables the control and mitigation of structural damage in the event of a collision37. Figure 8 showcases the deformation and stress experienced by a seat surface when subjected to impact load, varying in thickness from 4 to 8 mm. Figure 8a depicts that as the thickness of the seat surface increased, the deformation in the middle region gradually decreased, along with a reduction in the area of action when force was applied. Overall, the trend exhibited a smooth progression. Notably, the seat surface with a 4 mm thickness was most influenced by the impactor, revealing the highest deformation and widest deformation range under load, with a maximum value of 20 mm in the middle region. Additionally, Fig. 8c indicates that increasing the thickness effectively reduced the maximum deformation in the middle section of the seating surface. Consequently, both Fig. 8a, c demonstrate that the deformation of the chair can be effectively minimized by augmenting the thickness of the seat surface. Figure 8d illustrates that the state with a 4 mm seat surface thickness had the largest area of maximum stress and the most significant sinkage. The maximum stress generated by the impactor was almost 40 MPa, which posed a severe risk of part failure. Interestingly, a comparison of the stress diagrams for seat thicknesses of 4 mm and 5 mm reveals that the safety area of the chair was significantly improved (Fig. 8d). Ultimately, it is evident from Fig. 8d that an increase in thickness can alleviate the concentration of stress in the cross-section, reducing the stress generated on the seat surface during the stress process. This improvement in safety properties enhances the structural integrity of the chair.

Influence of seat thickness parameter: (a,b) Deformation and Stress of chair surface, (c,d) Deformation and Stress of cross-section.

The safety design of a structure should not solely rely on increasing dimensions to enhance material safety characteristics. It is essential to integrate safety considerations with the inherent properties of the material38. In line with this, the plastic chair in our study met the testing standard when the wall thickness and seat surface thickness were both 5 mm. Furthermore, adhering to the principle of consistent wall thickness in the production process of plastic parts, the dimensions of the chair presented in Fig. 1 can also be used as a reference for physical design and production. To validate the compliance of our designed plastic chair with relevant standards and ensure the accuracy of the FEM, mechanical tests were conducted using the KH-FM-8123 model Multi-purpose furniture mechanical testing machine, obtained from Suzhou Jianhao Science and Technology Company Limited in Jiangsu, China (Fig. S1a). The deformation values of the plastic chairs before and after the tests were recorded with a precision of 0.01 mm using a dislocator purchased in Guangzhou, China (Fig. S1c). Besides, in the chair for mechanical properties of experimental testing, to further reduce the experimental errors brought about by the differential deformation measurement instrument and the impact of its pointer debugging processing and the base is fixed. Strength, durability, and drop impact tests were performed on the chair in accordance with relevant mechanical test standards for chairs and stools (Fig. S1b). The plastic chair’s solid model, specimen loading, and testing process are depicted in Fig. S1c.

Figure 9 illustrates the relationship between the deformation and stress data obtained from the FEM and the experimental results of the chair. Fig. S2a reveals that the maximum deformation recorded during testing was 11.32 mm, and the FEM results were slightly higher than the experimental measurements, as depicted in Fig. 9a. However, the standard deviation between the two decreased as the load value increased, with a difference of 0.42 mm between the FEM and experimental results when the load reached 2000 N. Furthermore, Fig. 9b demonstrates that the stresses observed during the chair testing were higher than the results obtained from the simulated analysis. The stress experienced by the plastic chair during experimental loading was measured at 28.33 MPa. Surprisingly, the FEM results gradually approached the experimental values, and the discrepancy between them decreased as the load increased. Additionally, based on the strength test results of the plastic chair, the deformation and stress errors between the experimental and FEM values were determined to be 3.7% and 5.9%, respectively. This indicates the reliability of the FEM results. Importantly, these analyses confirm that no structural damage occurred to the chair during the experimental analysis.

Comparison pictures of strength testing: (a) Deformation, (b) Sress.

Figure 10 presents the fatigue testing results obtained from both the FEM and experimental testing of the chair. Fig. S2b shows that the maximum deformation value recorded during experimental testing was 8.62 mm, including a significant increase compared to the FEM results. However, the standard deviation between the two gradually decreased, with an error of 0.31 mm between the simulated analysis and experimental results when the load reached 950 N. Figure 10a displays the relative variations in deformation highlighting the decreasing trend of standard deviation. Similarly, Fig. 10b demonstrates that the stress generated during chair testing exceeded the stress values obtained from the FEM results. Nevertheless, the standard deviation between the two decreased over time, with the actual deflection differing by a range of 1.18 MPa to 0.41 MPa. From Fig. 10, it is evident that when subjected to cyclic loading fatigue, the deformation and stress errors between the analyzed values of the FE model and the experimental results were 3.6% and 3.2%, respectively. Furthermore, Fig. S2b confirms that the plastic chair does not exhibit structural damage at the end of the loading, thus meeting the experimental standard.

Comparison pictures of fatigue testing: (a) Deformation, (b) Stress.

Figure 11 showcases the drop impact testing results obtained from both the FEM and experimental testing of the chair. Figure 11a demonstrates that the deformation trend observed during testing aligned with the FEM results, with a maximum deformation of 14.5 mm. The maximum difference between the experimental and FEM results was 1.7 mm. Similarly, Fig. 11b reveals that the chair experienced a maximum stress of 30.6 MPa during testing, with a maximum difference of approximately 2 MPa between the experimental and FEM results. Figure 11c illustrates that although the difference between them gradually increased, the relative error values remained around 10%. Importantly, from Fig. 11, it can be inferred that when the plastic chair was subjected to impact loading, the deformation and stress errors between the analytical and experimental values of the FE model were 11.7% and 6.5%, respectively. This suggests a strong correlation between the FEM and experimental testing. Furthermore, as depicted in Fig. S3, the chair did not sustain structural damage at the conclusion of the experimental testing.

In summary, the strength testing, fatigue testing, and drop impact testing conducted on the plastic chair demonstrate that the error between the analytical results obtained from the FEM and the experimental results is within 12%. Furthermore, no structural damage was observed in the plastic chair throughout the experimental process. These findings affirm the reliability of the FEM results and confirm that the structural design of the chair complies with the experimental standards.

Comparative pictures of impact resistance testing: (a) Deformation, (b) Stress, (c) Error analysis.

In this study, a thin-walled plastic chair for home use was prepared by structural design, and then its mechanical properties such as strength, fatigue properties and impact resistance were analyzed using the FEM in order to find the key structure of the chair’s stresses, and then its parameters were studied and analyzed. Finally, in order to further verify the mechanical properties of the plastic chair and the reliability of the FEM analysis, the chair was prepared in kind for experimental verification. The main conclusions of this study are as follows:

(1) The analysis of the mechanical strength and fatigue properties of the chair revealed significant insights. During loading, the seat surface experienced the maximum deformation, while the lower end of the connection between the rear leg and seat exhibited the highest stress and minimum safety factor. Additionally, the drop impact analysis indicated that the point of impact on the chair experienced the greatest deformation and stress, with these values gradually increasing over time under the impact load. Through the simulation analysis using FEM, we ensured that our product design met the required test standards and aligned with typical usage conditions.

(2) The FEM analysis provided valuable insights into the mechanical properties of the plastic chair. It was determined that the thickness of the seat surface and the wall thickness of the connection between the seat surface and the back leg were key parameters influencing the chair’s mechanical strength. Consequently, different parametric analyses of the key structure of the chair under stress and based on the requirements of its one-piece molding process are carried out so as to further determine the optimal structural parameters of the chair. Then the chair was then manufactured and tested, with the results indicating deformation errors of 3.7%, 3.6%, and 11.7% in the FEM and experimental strength analysis, fatigue analysis, and drop impact analysis, respectively. Similarly, stress errors are 5.9%, 5.2%, and 6.5% were observed. These findings confirm the high reliability of the chair’s structural design. Importantly, no structural damage occurred during the testing process, further validating the robustness of the chair’s design.

(3) Furthermore, this study highlights that FEM is particularly effective in simulating the structural stress of curved shells. It provides valuable analytical insights for the structural design of new, comfortable curved furniture, improving design efficiency and facilitating research on reducing material usage in furniture design. This research bears significant scientific significance in these areas.

All the data will be available upon reasonable request to the corresponding author of the present paper.

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This work was supported by the Science and Technology Innovation Program of Hunan Province (Grant number 2021RC4062), the Scientifc Innovation Fund for Post-graduates of Central South University of Forestry and Technology (Grant number CX20220726).

College of Material Science and Engineering, Central South University of Forestry Technology, Changsha, Hunan, China

Ling Song, Minggong Yu & Delin Sun

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Ling Song: Conceptualization, Data curation, Methodology, Writing – original draft. Minggong Yu: Formal analysis, Investigation, Methodology. Delin Sun: Funding acquisition, Resources, Writing - Review & Editing.

Correspondence to Delin Sun.

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Song, L., Yu, M. & Sun, D. Structural design and experimental verification of a thin-walled plastic chairs based on the finite element method. Sci Rep 14, 22285 (2024). https://doi.org/10.1038/s41598-024-73499-1

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Received: 20 March 2024

Accepted: 18 September 2024

Published: 27 September 2024

DOI: https://doi.org/10.1038/s41598-024-73499-1

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