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

Table 7

Non dimensional critical buckling loads (𝛼=𝑃𝐿²/𝐸𝐼₀) for the columns of constant width and linearly varying height (𝐼(𝜉)=𝐼₀(1+𝑎𝜉)³) with continuous elastic restraint (𝛽=𝑘𝐿⁴/𝐸𝐼₀).

	𝑎=−0.5				𝑎=0.5				𝑎=1
	𝛽=0	𝛽=25	𝛽=50	𝛽=100	𝛽=0	𝛽=25	𝛽=50	𝛽=100	𝛽=0	𝛽=25	𝛽=50	𝛽=100
C-F	1.336426	3.406304	4.350010	5.487807	3.551010	8.394751	12.332922	18.020661	4.612119	10.082221	14.934526	22.864147
F-C	0.576515	4.175688	5.657646	7.558428	5.811363	9.281395	12.095892	16.252824	10.691414	13.774455	16.483421	20.954255
P-P	3.627812	6.022524	8.352143	12.576225	18.375617	20.866994	23.355361	28.321680	29.022499	31.437359	33.847167	38.650332
C-P	7.362241	8.951802	10.460281	13.205198	37.498111	39.736262	41.969764	46.421968	58.957688	61.272201	63.584952	68.205009
P-C	7.369711	9.677768	11.969157	16.483968	37.490417	39.306827	41.110477	44.677867	58.897925	60.520678	62.134215	65.333104
C-C	14.348488	16.093293	17.802510	21.098101	73.217187	75.065707	76.908867	80.578722	114.787912	116.546905	118.302355	121.800784
C-G	3.757964	8.394621	10.934803	13.536789	18.603820	26.955608	35.048357	49.998675	30.063711	38.940072	47.723673	64.917551