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Steel and Composite Structures
  Volume 45, Number 4, November25 2022 , pages 547-554

Buckling of axially graded columns with varying power-law gradients
X.F. Li, L. Lu, Z.L. Hu, Y. Huang and B.J. Xiao

    This paper studies the static stability of an axially graded column with the power-law gradient varying along the axial direction. For a nonhomogeneous column with one end linked to a rotational spring and loaded by a compressive force, respectively, an Euler problem is analyzed by solving a boundary value problem of an ordinary differential equation with varying coefficients. Buckling loads through the characteristic equation with the aid of the Bessel functions are exactly given. An alternative way to approximately determine buckling loads through the integral equation method is also presented. By comparing approximate buckling loads with the exact ones, the approximate solution is simple in form and enough accurate for varying power-law gradients. The influences of the gradient index and the rotational spring stiffness on the critical forces are elucidated. The critical force and mode shapes at buckling are presented in graph. The critical force given here may be used as a benchmark to check the accuracy and effectiveness of numerical solutions. The approximate solution provides a feasible approach to calculating the buckling loads and to assessing the loss of stability of columns in engineering.
Key Words
    axially graded column; buckling; critical load; exact solution; power-law gradient
X.F. Li, L. Lu, Z.L. Hu, and B.J. Xiao:School of Civil Engineering, Central South University, Changsha 410075, China

Y Huang:School of Mathematics and Big Data, Foshan University, Foshan, Guangdong 528000, China

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