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

Table 12

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

𝛽	𝑐ℎ		𝑐𝑏
			0	0.2	0.4	0.6	0.8
0	0	Reference [15]	14.5112	13.1398	11.6969	10.1451	8.3957
		LDQM	14.511250	13.139786	11.696914	10.145084	8.395671
	0.2	Reference [15]	10.6860	9.5971	8.4543	7.2284	5.8498
		LDQM	10.686041	9.597121	8.454289	7.228449	5.849840
	0.4	Reference [15]	7.2831	6.4715	5.6228	4.7164	3.7019
		LDQM	7.283103	6.471476	5.622776	4.716370	3.701880
	0.6	Reference [15]	4.3287	3.7892	3.2283	2.6338	1.9748
		LDQM	4.328693	3.789166	3.228315	2.633792	1.974761
	0.8	Reference [15]	1.8667	1.5950	1.3157	1.0239	0.7075
		LDQM	1.866691	1.595022	1.315685	1.023937	0.707517
50	0	LDQM	19.549179	18.192929	16.760939	15.207995	13.417864
	0.2	LDQM	15.752005	14.659979	13.503215	12.238938	10.750059
	0.4	LDQM	12.298411	11.454703	10.551443	9.542443	8.289481
	0.6	LDQM	9.058173	8.426077	7.721329	6.876642	5.694553
	0.8	LDQM	5.246198	4.728938	4.126561	3.402176	2.479665
100	0	LDQM	24.581143	23.242950	21.824406	20.269884	18.419554
	0.2	LDQM	20.817957	19.721682	18.544637	17.218652	15.521898
	0.4	LDQM	17.286073	16.384686	15.372020	14.125521	12.234643
	0.6	LDQM	13.406960	12.499393	11.357450	9.833780	7.688312
	0.8	LDQM	6.909430	6.121287	5.250381	4.263196	3.070432