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

Table 6

Non dimensional critical buckling loads (𝛼=𝑃𝐿²/𝐸𝐼₀) for the columns of parabolic varying width and constant height (𝐼(𝜉)=𝐼₀(1+𝑎𝜉)²) with continuous elastic restraint (𝛽=𝑘𝐿⁴/𝐸𝐼₀).

BC	𝑎=−0.5			𝑎=0.5			𝑎=1
	𝛽=25	𝛽=50	𝛽=100	𝛽=25	𝛽=50	𝛽=100	𝛽=25	𝛽=50	𝛽=100
C-F	4.341228	5.715021	7.305691	7.704323	11.199778	15.954946	8.844363	13.022270	19.259820
F-C	4.814955	6.692851	8.861021	8.038782	10.842500	14.737209	10.168566	13.021924	17.364909
P-P	7.672218	10.127971	14.937938	17.585157	20.097766	25.116851	23.271880	25.748067	30.688871
C-P	12.293759	14.009160	17.265144	32.912173	35.092823	39.430646	44.369842	46.626819	51.129119
P-C	12.782280	15.020605	19.433707	32.627483	34.516476	38.249232	43.893645	45.666325	49.175037
C-C	22.316590	24.131698	27.694119	61.849231	63.721127	67.446145	83.766543	85.604838	89.266360
C-G	10.832136	14.608627	18.532817	23.114885	30.762149	44.091245	29.276062	37.551999	53.151712