Elastic Analysis of Three-Layer Concrete Slab Based on Numerical Homogenization with an Analytical Shear Correction Factor
Abstract
:1. Introduction
2. Materials and Methods
2.1. Basic Assumptions
2.2. Finite Difference in Variational Form
2.3. Numerical Homogenization
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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( | ( | ( | ||
---|---|---|---|---|
300 | 180 | 5 | 8 | 10 |
External layers | 0.2 | ||
Middle core | 6 | 3 | 0 |
Stiffness | Homogenization Method | CLPT Method |
---|---|---|
MPa mm) | 2.7359 | 2.7088 |
MPa mm) | 0.5688 | 0.5417 |
MPa mm) | 2.7359 | 2.7088 |
MPa mm) | 1.0836 | 1.0835 |
MPa mm) | 1.2125 | 1.2007 |
MPa mm) | 0.2519 | 0.2401 |
MPa mm) | 1.2125 | 1.2007 |
MPa mm) | 0.4803 | 0.4803 |
MPa mm) | 1.3203 | 1.2833 |
MPa mm) | 1.3203 | 1.2833 |
Name of Model | Value of Displacements (mm) |
---|---|
Analytical model | 9.82 |
Model 1 | 10.18 |
Model 2 | 9.93 |
Model 3 | 9.94 |
Model 4 | 17.43 |
Homogenization model | 9.71 |
CLPT model | 9.89 |
Grid Point No | Finite Difference Method in the Variational Approach [63] | Numerical Homogenization | ||
---|---|---|---|---|
mx (Nm/m) | Mx (Nm/m) | mx (Nm/m) | Mx (Nm/m) | |
12 | 3381 | 19,550 | 3214 | 18,753 |
18 | 3036 | 14,016 | 2963 | 13,507 |
24 | 2856 | 12,134 | 2731 | 11,834 |
30 | 2777 | 11,244 | 2663 | 10,868 |
36 | 2746 | 10,619 | 2615 | 10,054 |
42 | 2735 | 9865 | 2597 | 9352 |
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Staszak, N.; Szymczak-Graczyk, A.; Garbowski, T. Elastic Analysis of Three-Layer Concrete Slab Based on Numerical Homogenization with an Analytical Shear Correction Factor. Appl. Sci. 2022, 12, 9918. https://doi.org/10.3390/app12199918
Staszak N, Szymczak-Graczyk A, Garbowski T. Elastic Analysis of Three-Layer Concrete Slab Based on Numerical Homogenization with an Analytical Shear Correction Factor. Applied Sciences. 2022; 12(19):9918. https://doi.org/10.3390/app12199918
Chicago/Turabian StyleStaszak, Natalia, Anna Szymczak-Graczyk, and Tomasz Garbowski. 2022. "Elastic Analysis of Three-Layer Concrete Slab Based on Numerical Homogenization with an Analytical Shear Correction Factor" Applied Sciences 12, no. 19: 9918. https://doi.org/10.3390/app12199918
APA StyleStaszak, N., Szymczak-Graczyk, A., & Garbowski, T. (2022). Elastic Analysis of Three-Layer Concrete Slab Based on Numerical Homogenization with an Analytical Shear Correction Factor. Applied Sciences, 12(19), 9918. https://doi.org/10.3390/app12199918