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

Table 1

Non dimensional critical buckling loads (𝛼=𝑃𝐿²/𝐸𝐼) for clamped-clamped uniform homogeneous columns with continuous elastic restraint (𝛽=𝑘𝐿⁴/𝐸𝐼).

𝛽	Exact [8]	DQM 𝑁=21	DQM 𝑁=31	DQM 𝑁=41	LDQM 𝑁𝑥=11, 𝑁=21	LDQM 𝑁𝑥=11, 𝑁=31	LDQM 𝑁𝑥=11, 𝑁=41
0	39.47841760	39.47841735	39.46144027	—	39.47841219	39.47841756	39.47841760
50	43.26056590	43.26107726	38.55373074	—	43.26023292	43.26056213	43.26056583
100	47.00660086	47.00980042	37.89095672	—	47.00612534	47.00659571	47.00660072