# A New Model for Optimal Mechanical and Thermal Performance of Cement-Based Partition Wall

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Geometry of the Partition Wall

^{3}, the elastic modulus is 2.2 × 10

^{4}N/mm

^{2}and Poisson’s ratio is 0.16. To study the eccentricity and the porosity effect on the mechanical-thermal properties, 13 specimens for the numerical simulations are designed, and the dimensions are shown in Table 1.

#### 2.2. Boundary Conditions for the Numerical Analysis

_{min}), as in Figure 2e. The boundary conditions in Figure 2a–f are as follows: Figure 2a–c demonstrate that one side is applied uniform displacement while the other side is fixed; Figure 2d demonstrates that the top side is applied with uniform pressure in a simply supported beam boundary condition; Figure 2e demonstrates that one side is fixed, while the screw is under a point load.

_{min}is used to evaluate the thermal performance. The numerical details are discussed in the following section.

#### 2.3. Numerical Methods

#### 2.3.1. Materials Response in the Uniaxial Tests

_{c}is taken as 7.2 MPa in our simulation. The Mazars model [41] (as shown in Figure 3) is used for uniaxial tensile response of the material, which is given as:

_{T}≤ 1, 10

^{4}≤ B

_{T}≤ 10

^{5}, and in this simulation, A

_{T}= 0.9, B

_{T}= 2 × 10

^{4}, ε

_{f}= 5.8 × 10

^{−5}.

#### 2.3.2. Elastic Finite Element Method

_{j}is the normal vector. The weak form of the governing Equation (3) can be expressed as:

_{i}is expressed via the element node displacement u

_{i}

^{n}as:

#### 2.3.3. The Incremental Elastic-Plastic Constitutive Model

_{ijkl}is the stiffness tensor, which is given as:

_{0}and v are the Young’s modulus and Poisson’s ratio, respectively. Following the plasticity theory, the relationship of the stress increment and the total strain increment for the Von Mises material can be written as:

_{σ}and T

_{i}are the area and boundary stress vectors, respectively. Again, Equation (13) is discretized into a number of elements and follows the procedure to establish the finite element model. Equation (13) is readily solved by the commercial finite element software ABAQUS.

#### 2.3.4. Computational Contact Theory

_{n}is the gap between the contact solids and σ

_{n}is the contact pressure. Then, the weak form of the governing Equation (3) is changed to the following form:

#### 2.3.5. Thermal Analysis

^{3}); and c is the specific heat capacity (920 J/(kg·K)). If the temperature is uniform along the height direction, then the three-dimensional (3D) problem can be reduced to a 2D problem. The boundary condition for the heat exchange is as follows:

## 3. Results and Discussions

#### 3.1. Mechanical Properties

#### 3.1.1. Effect of the eccentricity

#### 3.1.2. Effect of porosity

#### 3.2. Thermal Performance

_{min}increases with the minimum width and decreases with the porosity. For a given boundary condition (heat transfer coefficient and temperature difference), it is observed that the heat flow is almost linearly related to the minimum width and porosity. However, this may be affected by the boundary condition, since the heat flux is not uniformly distributed along with the width (in Figure 10c,d) and it can be affected by different boundary conditions. For the same porosity, the minimum width in the proposed model is smaller (the heat flow lower) than that of the cylinder cavity model, which indicates that the thermal performance is better. In particular, at a porosity of 35%, the heat flux in the proposed model (e = 0.77) is 10% lower than that of the cylinder cavity model, which indicates that the proposed model demonstrates an approximately 10% energy savings. As the eccentricity increases, the proposed model has better thermal performance than that of the circular cavity partition wall at the same porosities, as shown in Table 5. The numerical results show a good agreement with the numerical and the experimental results in the literature [44,45,46]. Generally, for the optimum design, a smaller porosity leads to smaller weight but weaker strength of the partition wall. Once the porosity and the packing strength (loading of Figure 2c) have been determined, a larger eccentricity leads to a better mechanical and thermal performance.

## 4. Conclusions

## Supplementary Materials

Supplementary File 1## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Dimensions of the partition wall (in mm): (

**a**) current model used in the building industry; (

**b**) proposed model; and, (

**c**) microstructure of the cement-based materials.

**Figure 2.**Boundary conditions of the partition wall (load 2a–load 2f): (

**a**–

**c**) uniformed loading in different directions; (

**d**) bending under the uniformed loads; (

**e**) hanging test boundary condition; and, (

**f**) heat transfer boundary condition.

**Figure 4.**Finite element (FE) models for the partition walls: (

**a**) Circular cavity panel in a three-dimensional (3D) view of the FE model; (

**b**) Elliptical cavity panel in a 3D view of the FE model; (

**c**) FE model of hanging test; and, (

**d**) two-dimensional (2D) FE model of thermal analysis.

**Figure 5.**Finite element model for the contact of a screw and the wall during hanging: (

**a**) screw located at the most disadvantageous position (at location H

_{min}); and, (

**b**) equilibrium of the contact force and the external force.

**Figure 6.**Effect of the eccentricity on the mechanical properties: (

**a**) maximum stress comparison under elastic loading, and (

**b**) ultimate strength comparison under failure simulation.

**Figure 7.**Stress distribution at the failure simulation (in MPa): (

**a**–

**e**) stress contours under failure simulation for the five loading conditions, according to Figure 2a–e.

**Figure 8.**Comparison of the stress concentration factor under different porosities: (

**a**–

**d**) stress concentration factor according to the loading cases in Figure 2b–e.

**Figure 9.**Comparison of the ultimate strength under different porosities: (

**a**–

**d**) ultimate strength according to the loading cases in Figure 2b–e.

**Figure 10.**Porosity and minimum width effect on the heat flux and heat flow (in J/s): (

**a**) porosity effect on the heat flow; (

**b**) minimum width effect on the heat flow; and, (

**c**,

**d**) contour of the heat flux distribution.

Specimen | CP | CP1 | CP2 | CP3 | CP4 | EP | EP1 | EP2 | EP3 | EP4 | CP5 | EP5 | EP6 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

major axis (mm) | 29 | 25 | 27 | 31 | 35 | 43 | 37 | 40 | 46 | 52 | 35 | 49 | 39 |

minor axis (mm) | 29 | 25 | 27 | 31 | 35 | 28 | 24 | 26 | 30 | 33 | 35 | 25 | 31 |

eccentricity | 0 | 0 | 0 | 0 | 0 | 0.77 | 0.77 | 0.77 | 0.77 | 0.77 | 0 | 0.87 | 0.60 |

porosity | 35% | 25% | 30% | 40% | 50% | 35% | 25% | 30% | 40% | 50% | 35% | 35% | 35% |

number of cavities | 7 | 7 | 7 | 7 | 7 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |

minimum width (mm) | 190 | 253 | 220 | 161 | 109 | 168 | 235 | 200 | 138 | 84 | 253 | 109 | 212 |

Specimen | CP | EP | CP5 | EP5 | EP6 |
---|---|---|---|---|---|

eccentricity | 0 | 0.77 | 0 | 0.87 | 0.6 |

porosity | 35% | 35% | 35% | 35% | 35% |

stress concentration factor (load 2a) | 2.01 | 2.04 | 1.99 | 2.07 | 2.02 |

Normalized Ratio (load 2a) | 1.00 | 1.02 | 0.99 | 2.07 | 2.05 |

ultimate strength (load 2a) (MPa) | 4.68 | 4.67 | 4.68 | 4.65 | 4.67 |

Normalized Ratio (load 2a) | 1.00 | 1.00 | 1.00 | 0.99 | 1.00 |

stress concentration factor (load 2b) | 5.39 | 4.42 | 6.91 | 3.39 | 5.65 |

Normalized Ratio (load 2b) | 1.00 | 0.84 | 1.28 | 0.63 | 1.08 |

ultimate strength (load 2b) (MPa) | 3.08 | 3.25 | 1.99 | 3.84 | 2.74 |

Normalized Ratio (load 2b) | 1.00 | 1.06 | 0.65 | 1.25 | 0.89 |

stress concentration factor Ratio (load 2c) | 4.08 | 4.98 | 3.31 | 6.83 | 3.79 |

Normalized Ratio (load 2c) | 1.00 | 1.22 | 0.81 | 1.67 | 0.93 |

ultimate strength (load 2c) (MPa) | 3.27 | 2.90 | 4.05 | 1.89 | 3.59 |

Normalized Ratio (load 2c) | 1.00 | 0.89 | 1.24 | 0.58 | 1.10 |

Stress under bending (load 2d) (MPa) | 0.64 | 0.63 | 0.69 | 0.62 | 0.65 |

Normalized Ratio (load 2d) | 1.00 | 0.98 | 1.07 | 0.97 | 1.02 |

ultimate bending load (load 2d) (N·m) | 941.25 | 977.92 | 905.67 | 1001.85 | 936.59 |

Normalized Ratio (load 2d) | 1.00 | 1.04 | 0.96 | 1.06 | 0.99 |

contact stress (MPa) (load 2e) | 13.65 | 12.62 | 18.01 | 8.33 | 15.43 |

Normalized Ratio (load 2e) | 1.00 | 0.90 | 1.29 | 0.60 | 1.11 |

the ultimate contact strength (load 2e) (N) | 52.75 | 57.05 | 39.98 | 86.49 | 46.66 |

Normalized Ratio (load 2e) | 1.00 | 1.11 | 0.78 | 1.68 | 0.91 |

Specimen | CP | CP1 | CP2 | CP3 | CP4 | EP | EP1 | EP2 | EP3 | EP4 |
---|---|---|---|---|---|---|---|---|---|---|

eccentricity | 0 | 0 | 0 | 0 | 0 | 0.77 | 0.77 | 0.77 | 0.77 | 0.77 |

porosity | 35% | 25% | 30% | 40% | 50% | 35% | 25% | 30% | 40% | 50% |

stress concentration factor (load 2a) | 2.01 | 1.78 | 1.88 | 2.2 | 2.64 | 2.04 | 1.78 | 1.9 | 2.22 | 2.62 |

stress concentration factor (load 2b) | 5.39 | 3.69 | 4.34 | 6.19 | 8.32 | 4.42 | 3.49 | 3.79 | 4.86 | 6.76 |

stress concentration factor (load 2c) | 4.08 | 3.06 | 3.43 | 4.59 | 6.57 | 4.98 | 3.61 | 4.41 | 6.02 | 9.41 |

maximum stress under bending (kN·m) | 0.64 | 0.68 | 0.67 | 0.63 | 0.59 | 0.63 | 0.66 | 0.65 | 0.60 | 0.55 |

contact stress (MPa) | 13.65 | 11.73 | 12.31 | 16.11 | 22.96 | 12.62 | 10.85 | 11.20 | 14.86 | 20.68 |

Specimen | CP | CP1 | CP2 | CP3 | CP4 | EP | EP1 | EP2 | EP3 | EP4 |
---|---|---|---|---|---|---|---|---|---|---|

eccentricity | 0 | 0 | 0 | 0 | 0 | 0.77 | 0.77 | 0.77 | 0.77 | 0.77 |

porosity | 35% | 25% | 30% | 40% | 50% | 35% | 25% | 30% | 40% | 50% |

ultimate strength (load 2a) (MPa) | 4.68 | 5.42 | 5.05 | 4.33 | 3.59 | 4.67 | 5.40 | 5.03 | 4.31 | 3.60 |

ultimate strength (load 2b) (MPa) | 3.08 | 4.06 | 3.54 | 2.54 | 1.82 | 3.25 | 4.09 | 3.64 | 2.89 | 2.07 |

ultimate strength (load 2c) (MPa) | 3.27 | 4.52 | 3.92 | 2.68 | 1.55 | 2.90 | 4.24 | 3.52 | 2.32 | 1.34 |

ultimate bending load (N·m) | 941.25 | 1046.85 | 977.64 | 913.52 | 819.67 | 977.92 | 1057.66 | 1011.18 | 944.96 | 960.78 |

the ultimate contact strength (N) | 52.75 | 61.38 | 58.49 | 44.69 | 31.36 | 57.05 | 66.36 | 64.29 | 48.45 | 34.82 |

Specimen | CP | CP1 | CP2 | CP3 | CP4 | EP | EP1 | EP2 | EP3 | EP4 | CP5 | EP5 | EP6 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

eccentricity | 0 | 0 | 0 | 0 | 0 | 0.77 | 0.77 | 0.77 | 0.77 | 0.77 | 0 | 0.87 | 0.6 |

porosity | 35% | 25% | 30% | 40% | 50% | 35% | 25% | 30% | 40% | 50% | 35% | 35% | 35% |

Heat flow (J/s) | 106.25 | 124.89 | 119.37 | 96.94 | 75.63 | 95.50 | 116.47 | 108.09 | 83.75 | 59.05 | 115.01 | 79.78 | 111.04 |

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**MDPI and ACS Style**

Huang, S.; Hu, M.; Huang, Y.; Cui, N.; Wang, W. A New Model for Optimal Mechanical and Thermal Performance of Cement-Based Partition Wall. *Materials* **2018**, *11*, 615.
https://doi.org/10.3390/ma11040615

**AMA Style**

Huang S, Hu M, Huang Y, Cui N, Wang W. A New Model for Optimal Mechanical and Thermal Performance of Cement-Based Partition Wall. *Materials*. 2018; 11(4):615.
https://doi.org/10.3390/ma11040615

**Chicago/Turabian Style**

Huang, Shiping, Mengyu Hu, Yonghui Huang, Nannan Cui, and Weifeng Wang. 2018. "A New Model for Optimal Mechanical and Thermal Performance of Cement-Based Partition Wall" *Materials* 11, no. 4: 615.
https://doi.org/10.3390/ma11040615