Figure 1.
Functionally graded (FG) nanoporous metal foam nanoplate and three types of porosity distribution, namely (1) uniform distribution (UD), (2) non-uniform distribution 1 (NUD1) (symmetric), and (3) non-uniform distribution 2 (NUD2) with (a) coating on substrate, (b) nanoplate model, (c) cross section.
Figure 1.
Functionally graded (FG) nanoporous metal foam nanoplate and three types of porosity distribution, namely (1) uniform distribution (UD), (2) non-uniform distribution 1 (NUD1) (symmetric), and (3) non-uniform distribution 2 (NUD2) with (a) coating on substrate, (b) nanoplate model, (c) cross section.
Figure 2.
Variation of buckling load ratio with a non-local small-scale parameter for a rectangular homogeneous nanoplate (m = n = 1, a = 10 nm, b = 5 nm).
Figure 2.
Variation of buckling load ratio with a non-local small-scale parameter for a rectangular homogeneous nanoplate (m = n = 1, a = 10 nm, b = 5 nm).
Figure 3.
Variation of buckling load ratio with a non-local small-scale parameter for a square homogeneous nanoplate (a = b = 5 nm).
Figure 3.
Variation of buckling load ratio with a non-local small-scale parameter for a square homogeneous nanoplate (a = b = 5 nm).
Figure 4.
Variation of the non-dimensional buckling load with a mode number n of square FG nanoporous nanoplate (m = 1, h = 5 nm, ζ = 1, la = lb = 50 nm, λ = 0.5): (a) UD, (b) NUD1, (c) NUD2.
Figure 4.
Variation of the non-dimensional buckling load with a mode number n of square FG nanoporous nanoplate (m = 1, h = 5 nm, ζ = 1, la = lb = 50 nm, λ = 0.5): (a) UD, (b) NUD1, (c) NUD2.
Figure 5.
Variation of non-dimensional critical buckling load with a small-scale parameter g: (a) square nanoplate (la = lb = 50 nm), (b) rectangular nanoplate (la = 50 nm, lb = 75 nm).
Figure 5.
Variation of non-dimensional critical buckling load with a small-scale parameter g: (a) square nanoplate (la = lb = 50 nm), (b) rectangular nanoplate (la = 50 nm, lb = 75 nm).
Figure 6.
Variation of non-dimensional critical buckling load with a porosity coefficient λ (m = n = 1, h = 5 nm, la = lb = 50 nm, ζ = 1): (a) UD, (b) NUD1, (c) NUD2.
Figure 6.
Variation of non-dimensional critical buckling load with a porosity coefficient λ (m = n = 1, h = 5 nm, la = lb = 50 nm, ζ = 1): (a) UD, (b) NUD1, (c) NUD2.
Figure 7.
Variation of non-dimensional critical buckling load with a length-to-thickness ratio of square FG nanoporous nanoplate (m = n = 1, h = 5 nm, la = lb, ζ = 1, λ = 0.5): (a) UD, (b) NUD1, (c) NUD2.
Figure 7.
Variation of non-dimensional critical buckling load with a length-to-thickness ratio of square FG nanoporous nanoplate (m = n = 1, h = 5 nm, la = lb, ζ = 1, λ = 0.5): (a) UD, (b) NUD1, (c) NUD2.
Figure 8.
Variation of the non-dimensional critical buckling load with the axial compression ratio ζ of the square FG nanoporous nanoplate (m = n = 1, h = 5 nm, la = lb = 50 nm, g = 0.5): (a) UD, (b) NUD1, (c) NUD2.
Figure 8.
Variation of the non-dimensional critical buckling load with the axial compression ratio ζ of the square FG nanoporous nanoplate (m = n = 1, h = 5 nm, la = lb = 50 nm, g = 0.5): (a) UD, (b) NUD1, (c) NUD2.
Figure 9.
Variation of the non-dimensional buckling load with mode number m (ζ = 1, h = 5 nm, g = 0.5, la = lb = 50 nm, λ = 0.5): (a) UD, (b) NUD1, (c) NUD2.
Figure 9.
Variation of the non-dimensional buckling load with mode number m (ζ = 1, h = 5 nm, g = 0.5, la = lb = 50 nm, λ = 0.5): (a) UD, (b) NUD1, (c) NUD2.
Table 1.
The non-dimensional buckling loads with different mode numbers, small scale parameters and porosity distributions of square FG nanoporous nanoplate (la = lb = 50 nm, h = 5 nm, ζ = 1, λ = 0.5).
Table 1.
The non-dimensional buckling loads with different mode numbers, small scale parameters and porosity distributions of square FG nanoporous nanoplate (la = lb = 50 nm, h = 5 nm, ζ = 1, λ = 0.5).
Mode | Solid Metal | UD | NUD1 | NUD2 |
---|
g = 0 | g = 0.5 | g = 0 | g = 0.5 | g = 0 | g = 0.5 | g = 0 | g = 0.5 |
---|
m = 1, n = 1 | 18.636 | 18.600 | 12.334 | 12.310 | 14.965 | 14.936 | 13.176 | 13.150 |
m = 2, n = 2 | 63.870 | 63.370 | 42.272 | 41.941 | 48.965 | 48.582 | 44.777 | 44.426 |
m = 3, n = 3 | 116.14 | 114.12 | 76.869 | 75.527 | 84.672 | 83.194 | 80.648 | 79.241 |
m = 4, n = 4 | 163.06 | 158.07 | 107.92 | 104.61 | 113.99 | 110.50 | 112.29 | 108.85 |
m = 5, n = 5 | 201.03 | 191.57 | 133.05 | 126.79 | 136.20 | 129.79 | 137.56 | 131.09 |
Table 2.
The non-dimensional buckling loads with different mode numbers, small scale parameters and porosity distributions of rectangular FG nanoporous nanoplate (la = 50 nm, lb = 75 nm, h = 5 nm, ζ = 1, λ = 0.5).
Table 2.
The non-dimensional buckling loads with different mode numbers, small scale parameters and porosity distributions of rectangular FG nanoporous nanoplate (la = 50 nm, lb = 75 nm, h = 5 nm, ζ = 1, λ = 0.5).
Mode | Solid Metal | UD | NUD1 | NUD2 |
---|
g = 0 | g = 0.5 | g = 0 | g = 0.5 | g = 0 | g = 0.5 | g = 0 | g = 0.5 |
---|
m = 1, n = 1 | 13.672 | 13.652 | 9.0485 | 9.0357 | 11.036 | 11.020 | 9.6751 | 9.6613 |
m = 2, n = 2 | 48.709 | 48.432 | 32.238 | 32.055 | 37.915 | 37.700 | 34.244 | 34.050 |
m = 3, n = 3 | 92.762 | 91.587 | 61.394 | 60.616 | 69.135 | 68.259 | 64.687 | 63.867 |
m = 4, n = 4 | 135.87 | 132.84 | 89.926 | 87.921 | 97.284 | 95.114 | 94.015 | 91.919 |
m = 5, n = 5 | 173.37 | 167.40 | 114.74 | 110.79 | 120.14 | 116.00 | 119.18 | 115.08 |
Table 3.
The non-dimensional critical buckling loads with different surface areas, small scale parameters and porosity distributions of square nanoplate (m = n = 1, h = 5 nm, ζ = 1, λ = 0.5).
Table 3.
The non-dimensional critical buckling loads with different surface areas, small scale parameters and porosity distributions of square nanoplate (m = n = 1, h = 5 nm, ζ = 1, λ = 0.5).
Surface Area | Solid Metal | UD | NUD1 | NUD2 |
---|
g = 0 | g = 0.5 | g = 0 | g = 0.5 | g = 0 | g = 0.5 | g = 0 | g = 0.5 |
---|
la = lb =30 nm | 16.956 | 16.863 | 11.222 | 11.161 | 13.220 | 13.148 | 11.924 | 11.859 |
la = lb =40 nm | 18.069 | 18.014 | 11.959 | 11.922 | 14.364 | 14.320 | 12.752 | 12.713 |
la = lb =50 nm | 18.636 | 18.600 | 12.334 | 12.310 | 14.965 | 14.936 | 13.176 | 13.150 |
la = lb =60 nm | 18.960 | 18.934 | 12.549 | 12.531 | 15.313 | 15.292 | 13.419 | 13.400 |
la = lb =70 nm | 19.161 | 19.141 | 12.681 | 12.669 | 15.531 | 15.515 | 13.569 | 13.556 |
Table 4.
The non-dimensional critical buckling loads with different thicknesses, small scale parameters and porosity distributions of square nanoplate (la = lb = 50 nm, m = n = 1, ζ = 1, λ = 0.5).
Table 4.
The non-dimensional critical buckling loads with different thicknesses, small scale parameters and porosity distributions of square nanoplate (la = lb = 50 nm, m = n = 1, ζ = 1, λ = 0.5).
h | Solid Metal | UD | NUD1 | NUD2 |
---|
g = 0 | g = 0.5 | g = 0 | g = 0.5 | g = 0 | g = 0.5 | g = 0 | g = 0.5 |
---|
h = 5 nm | 18.636 | 18.600 | 12.334 | 12.310 | 14.965 | 14.936 | 13.176 | 13.150 |
h = 6 nm | 18.190 | 18.154 | 12.039 | 12.015 | 14.491 | 14.463 | 12.842 | 12.817 |
h = 7 nm | 17.689 | 17.654 | 11.707 | 11.684 | 13.969 | 13.941 | 12.469 | 12.444 |
h = 8 nm | 17.145 | 17.111 | 11.347 | 11.325 | 13.411 | 13.385 | 12.064 | 12.040 |
h = 9 nm | 16.568 | 16.535 | 10.965 | 10.944 | 12.832 | 12.806 | 11.637 | 11.614 |
Table 5.
The non-dimensional critical buckling loads with different thicknesses, small scale parameters and porosity distributions of rectangular nanoplate (la = 50 nm, lb = 75 nm, m = n = 1, ζ = 1, λ = 0.5).
Table 5.
The non-dimensional critical buckling loads with different thicknesses, small scale parameters and porosity distributions of rectangular nanoplate (la = 50 nm, lb = 75 nm, m = n = 1, ζ = 1, λ = 0.5).
h | Solid Metal | UD | NUD1 | NUD2 |
---|
g = 0 | g = 0.5 | g = 0 | g = 0.5 | g = 0 | g = 0.5 | g = 0 | g = 0.5 |
---|
h = 5 nm | 13.672 | 13.652 | 9.0485 | 9.0357 | 11.036 | 11.020 | 9.6751 | 9.6613 |
h = 6 nm | 13.430 | 13.411 | 8.8883 | 8.8757 | 10.776 | 10.761 | 9.4936 | 9.4801 |
h = 7 nm | 13.155 | 13.136 | 8.7062 | 8.6939 | 10.484 | 10.469 | 9.2879 | 9.2747 |
h = 8 nm | 12.851 | 12.833 | 8.5053 | 8.4932 | 10.167 | 10.152 | 9.0614 | 9.0485 |
h = 9 nm | 12.524 | 12.506 | 8.2887 | 8.2769 | 9.8297 | 9.8157 | 8.8179 | 8.8053 |
Table 6.
The non-dimensional critical buckling loads with different aspect ratios, small scale parameters and porosity distributions of nanoplate (m = n = 1, la = 50 nm, h = 5 nm, ζ = 1, λ = 0.5).
Table 6.
The non-dimensional critical buckling loads with different aspect ratios, small scale parameters and porosity distributions of nanoplate (m = n = 1, la = 50 nm, h = 5 nm, ζ = 1, λ = 0.5).
lb/la | Solid Metal | UD | NUD1 | NUD2 |
---|
g = 0 | g = 0.5 | g = 0 | g = 0.5 | g = 0 | g = 0.5 | g = 0 | g = 0.5 |
---|
0.5 | 42.994 | 42.783 | 28.456 | 28.316 | 33.662 | 33.497 | 30.259 | 30.110 |
1 | 18.6364 | 18.600 | 12.334 | 12.310 | 14.965 | 14.936 | 13.176 | 13.150 |
1.5 | 13.672 | 13.652 | 9.0485 | 9.0357 | 11.036 | 11.020 | 9.6751 | 9.6613 |
2 | 11.897 | 11.882 | 7.8739 | 7.8642 | 9.6215 | 9.6097 | 8.4219 | 8.4116 |
2.5 | 11.069 | 11.056 | 7.3258 | 7.3174 | 8.9597 | 8.9494 | 7.8369 | 7.8280 |