Table 6 Thermal critical buckling load \({\mathcal{T}}_{cr}\) of square perfect and imperfect FG plates exposed to linear thermal loading for various values of plate thickness ratios \(a/h\), porosity parameter \(\tau\) and volume fraction indices \(\mathfrak{r}\).
\(\mathfrak{r}\) | \(a/h\) | Theory | \(\mathcal{q}\) | Perfect | Imperfect I (even) | Imperfect II (uneven) | Imperfect III (logarithmic-uneven) | |||
|---|---|---|---|---|---|---|---|---|---|---|
\(\tau =0\) | \(\tau =0.1\) | \(\tau =0.2\) | \(\tau =0.1\) | \(\tau =0.1\) | \(\tau =0.1\) | \(\tau =0.2\) | ||||
0 | 5 | HPT18 | \(=0\) | 11159.22 | 14046.50 | 18946.93 | 12555.54 | 14274.56 | 12518.32 | 14096.82 |
Present | \(=0\) | 11156.80 | 14043.45 | 18942.82 | 12553.96 | 14274.27 | 12516.72 | 14096.39 | ||
Present | \(\ne 0\) | 11744.80 | 14783.46 | 19940.81 | 13211.59 | 15017.18 | 13172.50 | 14830.50 | ||
10 | HPT18 | \(=0\) | 3227.50 | 4064.41 | 5484.84 | 3643.99 | 4158.39 | 3632.87 | 4105.13 | |
Present | \(=0\) | 3227.36 | 4064.23 | 5484.60 | 3643.93 | 4158.46 | 3632.81 | 4105.18 | ||
Present | \(\ne 0\) | 3278.75 | 4128.90 | 5571.82 | 3701.77 | 4224.26 | 3690.48 | 4170.16 | ||
20 | HPT18 | \(=0\) | 833.07 | 1051.01 | 1420.91 | 942.47 | 1077.71 | 939.54 | 1063.70 | |
Present | \(=0\) | 833.07 | 1051.00 | 1420.89 | 942.46 | 1077.72 | 939.54 | 1063.71 | ||
Present | \(\ne 0\) | 836.59 | 1055.44 | 1426.87 | 946.44 | 1082.25 | 943.50 | 1068.18 | ||
1 | 5 | HPT18 | \(=0\) | 5001.89 | 5474.11 | 6019.52 | 5341.39 | 5711.79 | 5332.82 | 5675.72 |
Present | \(=0\) | 5000.95 | 5473.12 | 6018.49 | 5341.07 | 5712.37 | 5332.48 | 5676.19 | ||
Present | \(\ne 0\) | 5365.35 | 5899.26 | 6530.35 | 5735.74 | 6141.16 | 5726.37 | 6101.61 | ||
10 | HPT18 | \(=0\) | 1413.02 | 1539.29 | 1681.31 | 1514.01 | 1624.97 | 1511.45 | 1614.13 | |
Present | \(=0\) | 1412.96 | 1539.23 | 1681.26 | 1514.01 | 1625.05 | 1511.45 | 1614.20 | ||
Present | \(\ne 0\) | 1473.78 | 1615.64 | 1780.54 | 1582.32 | 1702.19 | 1579.57 | 1690.45 | ||
20 | HPT18 | \(=0\) | 358.71 | 390.86 | 426.74 | 385.24 | 414.45 | 384.57 | 411.59 | |
Present | \(=0\) | 358.71 | 390.85 | 426.73 | 385.24 | 414.46 | 384.57 | 411.60 | ||
Present | \(\ne 0\) | 370.96 | 407.02 | 448.74 | 399.31 | 430.69 | 398.59 | 427.61 | ||
5 | 5 | HPT18 | \(=0\) | 3902.54 | 3949.18 | 3624.56 | 4037.93 | 4122.04 | 4035.12 | 4117.49 |
Present | \(=0\) | 3908.08 | 3956.99 | 3634.52 | 4048.61 | 4141.72 | 4045.63 | 4136.07 | ||
Present | \(\ne 0\) | 4190.70 | 4284.42 | 4014.10 | 4347.69 | 4454.78 | 4344.32 | 4448.01 | ||
10 | HPT18 | \(=0\) | 1160.21 | 1170.98 | 1057.33 | 1218.81 | 1269.84 | 1217.45 | 1265.62 | |
Present | \(=0\) | 1160.75 | 1171.71 | 1058.23 | 1219.85 | 1271.79 | 1218.47 | 1267.46 | ||
Present | \(\ne 0\) | 1219.95 | 1250.28 | 1162.30 | 1287.90 | 1350.29 | 1286.29 | 1344.91 | ||
20 | HPT18 | \(=0\) | 298.67 | 301.50 | 270.71 | 315.74 | 331.60 | 315.33 | 330.22 | |
Present | \(=0\) | 298.70 | 301.55 | 270.77 | 315.81 | 331.74 | 315.40 | 330.357 | ||
Present | \(\ne 0\) | 311.98 | 320.42 | 297.24 | 331.66 | 350.80 | 331.18 | 349.07 | ||
