0 (Ceramic) |
Present (εz ≠ 0) |
FOSNDT |
0.7202 |
2.4808 |
3.0999 |
0.5474 |
|
Reddy (1984Reddy, J.N. (1984).A simple higher order theory for laminated composite plates. ASME Journal of Applied Mechanics51:745-752.) (εz = 0) |
PSDT |
0.7251 |
2.5020 |
3.0916 |
0.4769 |
|
Sayyad and Ghugal (2017bSayyad, A. S., and Ghugal, Y. M. (2017b). A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates. International Journal of Applied Mechanics 9(1): 1-36.) (εz = 0) |
TSDT |
0.7259 |
2.5016 |
3.0949 |
0.4920 |
|
Sayyad and Ghugal (2017bSayyad, A. S., and Ghugal, Y. M. (2017b). A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates. International Journal of Applied Mechanics 9(1): 1-36.) (εz = 0) |
HSDT |
0.7247 |
2.5003 |
3.0899 |
0.4739 |
|
Sayyad and Ghugal (2017bSayyad, A. S., and Ghugal, Y. M. (2017b). A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates. International Journal of Applied Mechanics 9(1): 1-36.) (εz = 0) |
ESDT |
0.7280 |
2.4974 |
3.1039 |
0.4871 |
|
Timoshenko (1921Timoshenko, S. P. (1921). On the correction for shear of the differential equation for the transverse vibration of prismatic bars. Philosophical Magazine 41:742-746.) (εz = 0) |
FSDT |
0.7129 |
2.5023 |
3.0396 |
0.3183 |
|
Bernoulli-Euler (εz = 0) |
CBT |
0.7129 |
2.2693 |
3.0396 |
--- |
1 |
Present (εz ≠ 0) |
FOSNDT |
1.7131 |
4.8452 |
4.7667 |
0.5225 |
|
Reddy [1984Reddy, J.N. (1984).A simple higher order theory for laminated composite plates. ASME Journal of Applied Mechanics51:745-752.] (εz = 0) |
PSDT |
1.7793 |
4.9458 |
4.7856 |
0.5243 |
|
Sayyad and Ghugal (2017Sayyad, A. S., and Ghugal, Y. M. (2017b). A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates. International Journal of Applied Mechanics 9(1): 1-36.b) (εz = 0) |
TSDT |
1.7806 |
4.9451 |
4.7912 |
0.5331 |
|
Sayyad and Ghugal (2017bSayyad, A. S., and Ghugal, Y. M. (2017b). A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates. International Journal of Applied Mechanics 9(1): 1-36.) (εz = 0) |
HSDT |
1.7517 |
4.9257 |
4.7165 |
0.6025 |
|
Sayyad and Ghugal (2017bSayyad, A. S., and Ghugal, Y. M. (2017b). A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates. International Journal of Applied Mechanics 9(1): 1-36.) (εz = 0) |
ESDT |
1.7819 |
4.9432 |
4.7964 |
0.5430 |
|
Timoshenko (1921Timoshenko, S. P. (1921). On the correction for shear of the differential equation for the transverse vibration of prismatic bars. Philosophical Magazine 41:742-746.) (εz = 0) |
FSDT |
1.7588 |
4.8807 |
4.6979 |
0.5376 |
|
Bernoulli-Euler (εz = 0) |
CBT |
1.7588 |
4.5528 |
4.6979 |
--- |
5 |
Present (εz ≠ 0) |
Present |
2.7339 |
7.5452 |
6.3352 |
0.5026 |
|
Reddy (1984Reddy, J.N. (1984).A simple higher order theory for laminated composite plates. ASME Journal of Applied Mechanics51:745-752.) (εz = 0) |
PSDT |
2.8644 |
7.7723 |
6.6057 |
0.5314 |
|
Sayyad and Ghugal (2017bSayyad, A. S., and Ghugal, Y. M. (2017b). A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates. International Journal of Applied Mechanics 9(1): 1-36.) (εz = 0) |
TSDT |
2.8671 |
7.7792 |
6.6172 |
0.5144 |
|
Sayyad and Ghugal (2017bSayyad, A. S., and Ghugal, Y. M. (2017b). A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates. International Journal of Applied Mechanics 9(1): 1-36.) (εz = 0) |
HSDT |
2.8641 |
7.7715 |
6.6047 |
0.5332 |
|
Sayyad and Ghugal (2017bSayyad, A. S., and Ghugal, Y. M. (2017b). A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates. International Journal of Applied Mechanics 9(1): 1-36.) (εz = 0) |
ESDT |
2.8697 |
7.7830 |
6.6281 |
0.5022 |
|
Timoshenko (1921Timoshenko, S. P. (1921). On the correction for shear of the differential equation for the transverse vibration of prismatic bars. Philosophical Magazine 41:742-746.) (εz = 0) |
FSDT |
2.8250 |
7.5056 |
6.4382 |
0.9942 |
|
Bernoulli-Euler (εz = 0) |
CBT |
2.8250 |
6.8994 |
6.4382 |
--- |
10 |
Present (εz ≠ 0) |
FOSNDT |
2.8969 |
8.5103 |
7.8979 |
0.4431 |
|
Reddy (1984Reddy, J.N. (1984).A simple higher order theory for laminated composite plates. ASME Journal of Applied Mechanics51:745-752.) (εz = 0) |
PSDT |
2.9989 |
8.6530 |
7.9080 |
0.4226 |
|
Sayyad and Ghugal (2017bSayyad, A. S., and Ghugal, Y. M. (2017b). A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates. International Journal of Applied Mechanics 9(1): 1-36.) (εz = 0) |
TSDT |
3.0022 |
8.6561 |
7.9195 |
0.4392 |
|
Sayyad and Ghugal (2017bSayyad, A. S., and Ghugal, Y. M. (2017b). A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates. International Journal of Applied Mechanics 9(1): 1-36.) (εz = 0) |
HSDT |
2.9986 |
8.6527 |
7.9070 |
0.4211 |
|
Sayyad and Ghugal (2017bSayyad, A. S., and Ghugal, Y. M. (2017b). A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates. International Journal of Applied Mechanics 9(1): 1-36.) (εz = 0) |
ESDT |
3.0054 |
8.6547 |
7.9301 |
0.4558 |
|
Timoshenko (1921Timoshenko, S. P. (1921). On the correction for shear of the differential equation for the transverse vibration of prismatic bars. Philosophical Magazine 41:742-746.) (εz = 0) |
FSDT |
2.9488 |
8.3259 |
7.7189 |
1.2320 |
|
Bernoulli-Euler (εz = 0) |
CBT |
2.9488 |
7.5746 |
7.7189 |
--- |
∞ (Metal) |
Present (εz ≠ 0) |
FOSNDT |
3.9097 |
13.505 |
3.0999 |
0.5474 |
|
Reddy (1984Reddy, J.N. (1984).A simple higher order theory for laminated composite plates. ASME Journal of Applied Mechanics51:745-752.) (εz = 0) |
PSDT |
3.9363 |
13.582 |
3.0916 |
0.4769 |
|
Sayyad and Ghugal (2017bSayyad, A. S., and Ghugal, Y. M. (2017b). A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates. International Journal of Applied Mechanics 9(1): 1-36.) (εz = 0) |
ESDT |
3.9444 |
13.574 |
3.0980 |
0.5072 |
|
Timoshenko (1921Timoshenko, S. P. (1921). On the correction for shear of the differential equation for the transverse vibration of prismatic bars. Philosophical Magazine 41:742-746.) (εz = 0) |
FSDT |
3.8702 |
12.552 |
3.0396 |
0.3183 |
|
Bernoulli-Euler (εz = 0) |
CBT |
3.8702 |
12.319 |
3.0396 |
---- |