Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection
Table 2
Comparison of analytical approximations with the exact one for midspan deflections.
(a)
(b)
(c)
(d)
20°
0.1097
0.1097 (0.0000)
0.1097 (0.0000)
0.1097 (0.0000)
40°
0.2111
0.2111 (0.0000)
0.2111 (0.0000)
0.2112 (0.0474)
60°
0.2966
0.2965 (0.0337)
0.2967 (0.0337)
0.2968 (0.0674)
80°
0.3597
0.3592 (0.1390)
0.3601 (0.1112)
0.3606 (0.2502)
100°
0.3958
0.3945 (0.3285)
0.3965 (0.1769)
0.3981 (0.5811)
120°
0.4016
0.3993 (0.5727)
0.4019 (0.0747)
0.4051 (0.8715)
140°
0.3752
0.3731 (0.5597)
0.3735 (0.4531)
0.3641 (2.9584)
Number inside the bracket ( ) is the % relative error computed.
(a)Results by the exact theory [12].
(b)Results by the HPM truncated to the first order.
(c)Results by the HPM truncated to the second order.
(d)Results by the SAA.
