# Optimization of the Cross-Sectional Geometry of Auxetic Dowels for Furniture Joints

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

- ▪
- Analyzing the system;
- ▪
- Identifying constraints;
- ▪
- Identifying variables;
- ▪
- Introducing the target (target function selection);
- ▪
- Choosing the most appropriate optimization method;
- ▪
- Control of the system.

- ▪
- Size optimization: in other words, it can be described as sizing optimization, which deals with the cross-sectional areas of structures or cross-sectional areas of members of structures as the design variables;
- ▪
- Shape optimization: Additionally, it can be described as configuration optimization, which deals with the nodal coordinates of structures as the design variables;
- ▪
- Topology optimization: this optimization is the aim to delete needless structural members to reach the optimum design values;
- ▪
- Multi-objective optimization: using two or more of the above optimization methods at the same time to produce better optimization results.

## 2. Materials and Methods

#### 2.1. Design of the Auxetic Dowels

#### 2.2. Optimization of the Cross-Sectional Geometry of Auxetic Dowels

_{A}, fiA (φ), T

_{wd}and T

_{d}, respectively (Figure 4a). Minimum and maximum levels of those parameters were chosen to find optimum levels. The calculated dimensions for the auxetic pattern of dowels by using algorithm were shown in Figure 4b.

_{A}, fiA, T

_{wd}and T

_{d}are parameters to constrain the optimization equation (Figure 4a). After determining the maximum and minimum limit of parameters, all dimensions needed for producing the optimum cross-section of a dowel were determined (Figure 4b).

_{B}, so the first limit criterion is related to the compression of this part of the section (Equation (1)).

_{A/B}vector that can be written for the moment arm. The coordinates of point A can be represented as in Equations (2) and (3):

_{c}) and shear (τ) components created by the F force at the B point are considered together, the constraints that can be written to maximize the Poisson effect (ϑ) are expressed as follows (Equations (17) and (18)).

_{A}, t

_{B}and φ.

#### 2.3. Numerical Model and Analyses of Auxetic Dowels

#### 2.4. Production and Experimental Tests of the Dowels

## 3. Results and Discussion

#### 3.1. Optimization Results for Cross-Section of Auxetic Dowels

#### 3.2. Comparison of the Experimental Results, Numerical Analyses and Analytical Calculations

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Example auxetic patterns. (

**a**) Hexagonal unit cell, (

**b**) 3-star, (

**c**) 4-star and (

**d**) 2D hexachiral [49].

**Figure 3.**(

**a**) Frame joints with the first type of auxetic dowel, (

**b**) panels joint with the second type of auxetic dowel.

**Figure 4.**(

**a**) Parameters whose determined minimum and maximum level for optimization; (

**b**) dimensions calculated by using algorithm for auxetic pattern of dowels (mm).

**Figure 8.**(

**a**) Production process with 3D printer technology, (

**b**) test setup for determining Poisson’s ratio.

Parameters | 1st Dowel Type | 2nd Dowel Type | ||
---|---|---|---|---|

Minimum Level | Maximum Level | Minimum Level | Maximum Level | |

${t}_{A}$ | 1 mm | 2 mm | 1 mm | 2 mm |

${\phi}_{A}$ | 15° | 40° | 15° | 40° |

${T}_{wd}$ | 1 mm | 2 mm | 1 mm | 2 mm |

${T}_{d}$ | 15 mm | 10 mm | ||

Length | 50 mm | 40 mm |

Parameters | 1st Dowel Type | 2nd Dowel Type |
---|---|---|

${t}_{A}$ | 1.03 mm | 1 mm |

${\phi}_{A}$ | 17.53° | 15.87° |

${T}_{wd}$ | 1.72 mm | 1 mm |

${T}_{d}$ | 15 mm | 10 mm |

Length | 50 mm | 40 mm |

Dowel Type | Dowel Diameter (mm) | Dowel Length (mm) | Poisson’s Ratios | MOE (MPa) | ||
---|---|---|---|---|---|---|

Experimental | Numerical | Analytical | ||||

1st type | 15 | 50 | −0.273 (0.054) * | −0.309 | −0.302 | 155.54 |

2nd type | 10 | 40 | −0.287 (0.065) | −0.313 | −0.341 | 436.76 |

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**MDPI and ACS Style**

Kuşkun, T.; Kasal, A.; Çağlayan, G.; Ceylan, E.; Bulca, M.; Smardzewski, J.
Optimization of the Cross-Sectional Geometry of Auxetic Dowels for Furniture Joints. *Materials* **2023**, *16*, 2838.
https://doi.org/10.3390/ma16072838

**AMA Style**

Kuşkun T, Kasal A, Çağlayan G, Ceylan E, Bulca M, Smardzewski J.
Optimization of the Cross-Sectional Geometry of Auxetic Dowels for Furniture Joints. *Materials*. 2023; 16(7):2838.
https://doi.org/10.3390/ma16072838

**Chicago/Turabian Style**

Kuşkun, Tolga, Ali Kasal, Gökhan Çağlayan, Erkan Ceylan, Murat Bulca, and Jerzy Smardzewski.
2023. "Optimization of the Cross-Sectional Geometry of Auxetic Dowels for Furniture Joints" *Materials* 16, no. 7: 2838.
https://doi.org/10.3390/ma16072838