Buckling Analyses of Axially Functionally Graded Nonuniform Columns with Elastic Restraint Using a Localized Differential Quadrature Method

Table 11

Non dimensional critical buckling loads (𝛼=𝑃𝐿²/𝐸₀𝐼₀) for the axially functionally graded non-uniform columns with continuous elastic restraint (𝛽=𝑘𝐿⁴/𝐸₀𝐼₀) for C-C boundary condition.

𝛽	𝑐ℎ		𝑐𝑏
			0	0.2	0.4	0.6	0.8
0	0	Reference [15]	57.3940	51.7856	45.7356	38.9917	30.8922
		LDQM	57.393956	51.785589	45.735646	38.991689	30.892202
	0.2	Reference [15]	41.9169	37.6023	32.9638	27.8171	21.6802
		LDQM	41.916891	37.602328	32.963838	27.817083	21.680218
	0.4	Reference [15]	28.1794	25.0890	21.7813	18.1332	13.8242
		LDQM	28.179398	25.089039	21.781290	18.133162	13.824196
	0.6	Reference [15]	16.3412	14.3958	12.3266	10.0639	7.4275
		LDQM	16.341179	14.395830	12.326582	10.063919	7.427477
	0.8	Reference [15]	6.6801	5.7836	4.8399	3.8228	2.6649
		LDQM	6.680051	5.783574	4.839860	3.822760	2.664885
50	0	LDQM	61.166910	55.582013	49.557537	42.839820	34.759070
	0.2	LDQM	45.734227	41.416605	36.768958	31.599542	25.400286
	0.4	LDQM	31.958849	28.829688	25.466443	21.730794	17.253425
	0.6	LDQM	19.880964	17.847607	15.659665	13.222303	10.279687
	0.8	LDQM	9.367432	8.320721	7.182753	5.897801	4.324708
100	0	LDQM	64.914455	59.351070	53.349176	46.652798	38.579025
	0.2	LDQM	49.518379	45.193527	40.530226	35.326471	29.036478
	0.4	LDQM	35.683768	32.505243	29.069896	25.216920	20.502165
	0.6	LDQM	23.285078	21.132662	18.778906	16.088335	12.689894
	0.8	LDQM	11.549700	10.288383	8.886242	7.271719	5.279100