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

Table 10

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-F boundary condition.

𝛽	𝑐ℎ		𝑐𝑏
			0	0.2	0.4	0.6	0.8
0	0	Reference [15]	3.1177	2.9497	2.7676	2.5652	2.3285
		LDQM	3.117663	2.949668	2.767637	2.565141	2.328495
	0.2	Reference [15]	2.6225	2.4638	2.2915	2.0992	1.8725
		LDQM	2.622455	2.463779	2.291515	2.099165	1.872518
	0.4	Reference [15]	2.1054	1.9585	1.7988	1.6200	1.4074
		LDQM	2.105415	1.958547	1.798693	1.619887	1.407356
	0.6	Reference [15]	1.5522	1.4217	1.2798	1.1208	0.9309
		LDQM	1.552205	1.421546	1.279989	1.120782	0.930901
	0.8	Reference [15]	0.9245	0.8217	0.7109	0.5883	0.4441
		LDQM	0.924469	0.821641	0.710897	0.588251	0.444050
50	0	LDQM	10.969897	10.399534	9.730454	8.911626	7.828378
	0.2	LDQM	9.235948	8.649698	7.968922	7.148865	6.086033
	0.4	LDQM	7.195173	6.631250	5.989832	5.235064	4.284203
	0.6	LDQM	4.857766	4.387832	3.866699	3.271051	2.544323
	0.8	LDQM	2.344717	2.062718	1.758631	1.421514	1.024155
100	0	LDQM	15.525762	14.520910	13.367622	11.997451	10.254518
	0.2	LDQM	12.557084	11.612707	10.545695	9.300364	7.742857
	0.4	LDQM	9.374096	8.560820	7.656126	6.617654	5.337232
	0.6	LDQM	6.093411	5.484473	4.816329	4.058816	3.136808
	0.8	LDQM	2.854117	2.516107	2.150262	1.741823	1.254405