Efficient Design of Thin Wall Seating Made of a Single Piece of Heavy-Duty Corrugated Cardboard
Abstract
:1. Introduction
1.1. Corrugated Cardboard
1.2. Thin-Wall Furniture
Corrugated Cardboard Furniture
1.3. Homogenization Techniques
1.4. Scope of the Study
2. Materials and Methods
2.1. Design Stages
2.2. Finite Element Models
2.2.1. Geometry
2.2.2. Material
2.2.3. Loads and Constraints
2.3. Homogenization Approach
3. Results and Discussion
3.1. Homogenized Material Properties
3.2. Parametric Study for α = 70° to 90°
3.3. Analysis of Designs with α = 80°
3.3.1. First Design for α = 80°
3.3.2. Second Design for α = 80°
3.3.3. Third Design for α = 80°
3.3.4. Fourth Design for α = 80°
3.3.5. Comparative Results for α = 80°
3.4. Summary Results
- Ply orientation. The vertical and longitudinal deflections are lower for orientation I, except for the first design, with slightly lower values for orientation I with bottom discontinuity.
- Discontinuity location. The vertical and longitudinal deflections are lower for designs with top discontinuity, because the seating surface is divided into two different panels with half the span of the whole seating surface.
- Bottom panel. We should keep the bottom panel, because it prevents longitudinal sliding between the lower edges of the front and rear panels.
- α angle: In the first three designs, α has little influence on the vertical deflections. However, in the fourth design, the lowest vertical deflections correspond to an intermediate angle of 80°. The best results correspond to those angles leading to a more uniform distribution of the seating surface. That is, for those designs with the inner panels dividing the seating surface into three zones of equal length, so that none of them tends to present more significant deflections than the others (see Figure 8).
4. Conclusions
4.1. Main Findings
4.2. Concluding Remarks
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Homogenized Stiffness Matrix
Appendix B. Transformation Matrices
Appendix B.1. Coordinate Transformation of a Generic Vector
Appendix B.2. Strain Transformations
Appendix B.3. Stresses Transformations
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Designation | Picture | Height (in) | Height (mm) | Flutes/m | Pitch (mm) | Take-Up Factor |
---|---|---|---|---|---|---|
A flute | | 1/4″ | 4.8 | 108 ± 10 | 8.0–9.5 | ≈1.50 |
B flute | | 1/8″ | 3.2 | 154 ± 10 | 5.5–6.5 | ≈1.40 |
C flute | | 11/64″ | 4.0 | 128 ± 10 | 6.8–7.9 | ≈1.45 |
E flute | | 1/16″ | 1.6 | 295 ± 13 | 3.0–3.5 | ≈1.25 |
F flute | | 1/32″ | 0.8 | 420 ± 13 | 1.9–2.6 | ≈1.25 |
Parameter | Unit | Heavy Duty | ||
---|---|---|---|---|
Outer Liner | Inner Liner | Fluting | ||
E1 | MPa | 8250 | 8180 | 4500 |
E2 | MPa | 2900 | 3120 | 4500 |
E3 | MPa | 2900 | 3120 | 3000 |
G23 | MPa | 70 | 70 | 35 |
G13 | MPa | 7 | 7 | 3.5 |
G12 | MPa | 1890 | 1950 | 1500 |
ν12 | - | 0.43 | 0.43 | 0.40 |
ν13 | - | 0.01 | 0.01 | 0.01 |
ν23 | - | 0.01 | 0.01 | 0.01 |
t | mm | 0.75 | 0.40 | 0.25 |
h | mm | - | - | 4.8 |
P | mm | - | - | 8.5 |
Qij | Unit | Outer Liner | Inner Liner | Fluting |
---|---|---|---|---|
Q11 | [MPa] | 8824.2 | 8801.4 | 146.2 |
Q12 | [MPa] | 1334.2 | 1444 | 59.807 |
Q13 | [MPa] | 44.361 | 48.01 | 145.44 |
Q22 | [MPa] | 3102 | 3357.2 | 361.6 |
Q23 | [MPa] | 35.71 | 39.08 | 59.755 |
Q33 | [MPa] | 2900.5 | 3120.6 | 146.14 |
Q44 | [MPa] | 70 | 70 | 4.5198 |
Q55 | [MPa] | 7 | 7 | 0.90365 |
Q66 | [MPa] | 1890 | 1950 | 5.9147 |
Design | Area (m2) | w (mm) | u (mm) | σxx (MPa) | σyy (MPa) |
---|---|---|---|---|---|
1st | 0.87 | 0.9 | 0.2 | 15.3 | 8.9 |
2nd | 0.83 | 1.1 | 0.3 | 1.4 | 2.6 |
3rd | 0.79 | 6.0 | 1.9 | 3.2 | 8.4 |
4th | 0.57 | 0.6 | 1.2 | 1.5 | 2.9 |
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Suarez, B.; Muneta, L.M.; Romero, G.; Sanz-Bobi, J.D. Efficient Design of Thin Wall Seating Made of a Single Piece of Heavy-Duty Corrugated Cardboard. Materials 2021, 14, 6645. https://doi.org/10.3390/ma14216645
Suarez B, Muneta LM, Romero G, Sanz-Bobi JD. Efficient Design of Thin Wall Seating Made of a Single Piece of Heavy-Duty Corrugated Cardboard. Materials. 2021; 14(21):6645. https://doi.org/10.3390/ma14216645
Chicago/Turabian StyleSuarez, Berta, Luisa M. Muneta, Gregorio Romero, and Juan D. Sanz-Bobi. 2021. "Efficient Design of Thin Wall Seating Made of a Single Piece of Heavy-Duty Corrugated Cardboard" Materials 14, no. 21: 6645. https://doi.org/10.3390/ma14216645