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

Table 9

Non dimensional critical buckling loads (𝛼=𝑃𝐿²/𝐸₀𝐼) for the axially functionally graded uniform columns with continuous elastic restraint (𝛽=𝑘𝐿⁴/𝐸₀𝐼) for exponential law gradient assumption (𝐸(𝜉)=𝐸₀𝑒^𝜇𝜉).

BC	𝛽	𝜇=−1	𝜇=−0.5	𝜇=0.5	𝜇=1
C-F	0	1.782102	2.112127	2.844778	3.241181
	50	6.272146	7.534741	10.200538	11.507320
	100	8.112043	9.940415	14.224745	16.544646
P-P	0	5.826546	7.634493	12.587151	15.838195
	50	10.824282	12.684208	17.638042	20.845819
	100	15.772528	17.725908	22.685148	25.842687
C-P	0	11.988386	15.639912	25.782548	32.554915
	50	15.640533	19.528086	30.050913	36.962919
	100	19.113129	23.299501	34.275138	41.344887
C-C	0	23.490038	30.598353	50.448156	63.852545
	50	27.172950	34.353512	54.212593	67.556554
	100	30.785108	38.059830	57.948273	71.236233
C-G	0	5.972525	7.682708	12.666644	16.235007
	50	16.438031	19.863476	27.642188	32.240813
	100	21.152920	26.511574	39.345458	46.225436