A Study on the Applicability and Accuracy of the Discrete Element Method for Plates Based on Parameter Sensitivity Analysis
Abstract
:1. Introduction
2. Basic Theory of the DEM for a Plate
2.1. The Model of the DEM for a Plate
2.2. Calculation of Internal Forces in Contact Elements
3. Theory of Parameter Sensitivity Analysis
3.1. Single-Parameter Sensitivity Analysis
3.2. Multi-Parameter Sensitivity Analysis
3.2.1. Full Factorial Method
3.2.2. Orthogonal Design Method
4. Parameter Sensitivity Analysis
4.1. Influences of Single-Parameter Changes
4.1.1. Thickness-to-Width Ratio
4.1.2. Elastic Modulus
4.1.3. Poisson’s Ratio
4.2. Influences of Multi-Parameter Changes
4.2.1. Boundary Conditions
4.2.2. Plate Dimensions
4.2.3. Form of Loading
4.2.4. Thickness-to-Width Ratio
4.2.5. Elastic Modulus
4.2.6. Poisson’s Ratio
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Operating Combination | Parameter | |||
---|---|---|---|---|
A | B | C | D | |
1 | 1 | 1 | 1 | 1 |
2 | 1 | 2 | 2 | 2 |
3 | 1 | 3 | 3 | 3 |
4 | 2 | 1 | 2 | 3 |
5 | 2 | 2 | 3 | 1 |
6 | 2 | 3 | 1 | 2 |
7 | 3 | 1 | 3 | 2 |
8 | 3 | 2 | 1 | 3 |
9 | 3 | 3 | 2 | 1 |
Boundary | Fixed | Simply | Displacement Tracking Point | Position of Line Load | Position of Point Load |
---|---|---|---|---|---|
Cantilever plate | AB | \ | C | CD | C |
Two adjacent edges | AB | AD | C | CD | C |
Two opposite edges | AB | CD | E | FG | E |
Three edges | AB | AD, BC | H | CD | H |
Four edges | AB, CD | BC, AD | E | FG | E |
Material | E (GPa) | μ | Material | E (GPa) | μ |
---|---|---|---|---|---|
Alloy steel | 206 | 0.25–0.3 | Cast steel | 175 | 0.31–0.34 |
Lead | 170 | 0.42 | Aluminum alloy | 71 | 0.3 |
Rolled aluminum | 69 | 0.32–0.36 | Concrete | 14–23 | 0.1–0.18 |
Nylon | 2.83 | 0.4 | Rubber | 0.00784 | 0.48 |
Parameters | Level 1 | Level 2 | Level 3 | Level 4 | Level 5 | |
---|---|---|---|---|---|---|
1 | Boundary conditions | Cantilever plate | Two adjacent | Two opposite | Three edges | Four edges |
2 | Plate dimensions (m) | 0.3 × 0.3 | 1.2 × 0.6 | 2 × 2 | 4 × 1 | 10 × 10 |
3 | Form of loading | Uniformly distributed | Line load | Concentrated load | Impact | Harmonic |
4 | Thickness-to-width ratio | 0.01 | 0.04 | 0.1 | 0.16 | 0.2 |
5 | Elastic modulus (GPa) | 0.005 | 50 | 100 | 150 | 200 |
6 | Poisson’s ratio | 0.1 | 0.24 | 0.3 | 0.4 | 0.48 |
Operating Combination | Boundary | Dimension | Form of Loading | h/b | E | μ | Error * |
---|---|---|---|---|---|---|---|
Y (%) | |||||||
1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.239 |
2 | 2 | 2 | 2 | 2 | 2 | 2 | 0.918 |
3 | 3 | 3 | 3 | 3 | 3 | 3 | 1.063 |
4 | 4 | 4 | 4 | 4 | 4 | 4 | −2.342 |
5 | 5 | 5 | 5 | 5 | 5 | 5 | 2.002 |
6 | 1 | 2 | 3 | 4 | 5 | 1 | 0.838 |
7 | 2 | 3 | 4 | 5 | 1 | 2 | 1.359 |
8 | 3 | 4 | 5 | 1 | 2 | 3 | 3.102 |
9 | 4 | 5 | 1 | 2 | 3 | 4 | 4.212 |
10 | 5 | 1 | 2 | 3 | 4 | 5 | 2.805 |
11 | 1 | 3 | 5 | 2 | 4 | 1 | 0.187 |
12 | 2 | 4 | 1 | 3 | 5 | 2 | 0.474 |
13 | 3 | 5 | 2 | 4 | 1 | 3 | 2.762 |
14 | 4 | 1 | 3 | 5 | 2 | 4 | 1.623 |
15 | 5 | 2 | 4 | 1 | 3 | 5 | 0.424 |
16 | 1 | 4 | 2 | 5 | 3 | 1 | 0.460 |
17 | 2 | 5 | 3 | 1 | 4 | 2 | −2.884 |
18 | 3 | 1 | 4 | 2 | 5 | 3 | −1.736 |
19 | 4 | 2 | 5 | 3 | 1 | 4 | 0.865 |
20 | 5 | 3 | 1 | 4 | 2 | 5 | 1.747 |
21 | 1 | 5 | 4 | 3 | 2 | 1 | −2.652 |
22 | 2 | 1 | 5 | 4 | 3 | 2 | 1.538 |
23 | 3 | 2 | 1 | 5 | 4 | 3 | 0.546 |
24 | 4 | 3 | 2 | 1 | 5 | 4 | 4.121 |
25 | 5 | 4 | 3 | 2 | 1 | 5 | 2.559 |
Mean value1 ** (%) | 0.875 | 1.811 | 1.642 | 2.154 | 2.154 | 0.875 | |
Mean value2 ** (%) | 1.435 | 0.718 | 2.213 | 1.922 | 2.008 | 1.435 | |
Mean value3 ** (%) | 1.842 | 0.980 | 1.794 | 1.572 | 1.540 | 1.842 | |
Mean value4 ** (%) | 2.633 | 2.100 | 1.703 | 1.845 | 1.753 | 2.633 | |
Mean value5 ** (%) | 1.907 | 2.903 | 1.539 | 1.198 | 1.834 | 1.907 | |
Range *** (%) | 1.757 | 2.184 | 0.674 | 0.956 | 0.614 | 1.757 |
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Guo, F.; Ye, J. A Study on the Applicability and Accuracy of the Discrete Element Method for Plates Based on Parameter Sensitivity Analysis. Buildings 2023, 13, 1567. https://doi.org/10.3390/buildings13061567
Guo F, Ye J. A Study on the Applicability and Accuracy of the Discrete Element Method for Plates Based on Parameter Sensitivity Analysis. Buildings. 2023; 13(6):1567. https://doi.org/10.3390/buildings13061567
Chicago/Turabian StyleGuo, Fei, and Jihong Ye. 2023. "A Study on the Applicability and Accuracy of the Discrete Element Method for Plates Based on Parameter Sensitivity Analysis" Buildings 13, no. 6: 1567. https://doi.org/10.3390/buildings13061567