Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection

Table 1

Comparison of analytical approximations with the exact one for buckling loads.

𝛼𝑇	𝑃exact/𝑃𝐸^(a)	𝑃HPM1/𝑃𝐸^(b)	𝑃HPM2/𝑃𝐸^(c)	𝑃SAA/𝑃𝐸^(d)
20°	1.0154	1.0152 (0.0197)	1.0155 (0.0098)	1.0155 (0.0098)
40°	1.0637	1.0609 (0.2632)	1.0648 (0.1034)	1.0647 (0.0940)
60°	1.1517	1.1371 (1.2677)	1.1567 (0.4341)	1.1576 (0.5123)
80°	1.2939	1.2437 (3.8797)	1.3056 (0.9042)	1.3164 (1.7389)
100°	1.5184	1.3808 (9.0622)	1.5318 (0.8825)	1.5890 (4.6496)
120°	1.8848	1.5483 (17.8534)	1.8615 (1.2362)	2.0821 (10.4680)

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.