TY - JOUR
T1 - Exact solutions for the generalized euler's problem
AU - Li, Q. S.
PY - 2009
Y1 - 2009
N2 - This paper is concerned with buckling analysis of a nonuniform column with classical/ nonclassical boundary conditions and subjected to a concentrated axial force and distributed variable axial loading, namely, the generalized Euler's problem. Exact solutions are derived for the buckling problem of nonuniform columns with variable flexural stiffness and under distributed variable axial loading expressed in terms of polynomial functions. Then, more complicated buckling problems are considered such as that the distribution of flexural stiffness of a nonuniform column is an arbitrary function, and the distribution of axial loading acting on the column is expressed as a functional relation with the distribution of flexural stiffness and vice versa. The governing equation for such problems is reduced to Bessel equations and other solvable equations for seven cases by means of functional transformations. A class of exact solutions for the generalized Euler's problem involved a nonuniform column subjected to an axial concentrated force and axially distributed variable loading is obtained herein for the first time in literature. © 2009 by ASME.
AB - This paper is concerned with buckling analysis of a nonuniform column with classical/ nonclassical boundary conditions and subjected to a concentrated axial force and distributed variable axial loading, namely, the generalized Euler's problem. Exact solutions are derived for the buckling problem of nonuniform columns with variable flexural stiffness and under distributed variable axial loading expressed in terms of polynomial functions. Then, more complicated buckling problems are considered such as that the distribution of flexural stiffness of a nonuniform column is an arbitrary function, and the distribution of axial loading acting on the column is expressed as a functional relation with the distribution of flexural stiffness and vice versa. The governing equation for such problems is reduced to Bessel equations and other solvable equations for seven cases by means of functional transformations. A class of exact solutions for the generalized Euler's problem involved a nonuniform column subjected to an axial concentrated force and axially distributed variable loading is obtained herein for the first time in literature. © 2009 by ASME.
KW - Buckling
KW - Exact solution
KW - Nonuniform column
KW - Structural stability
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U2 - 10.1115/1.2937151
DO - 10.1115/1.2937151
M3 - 21_Publication in refereed journal
VL - 76
SP - 1
EP - 9
JO - Journal of Applied Mechanics, Transactions ASME
JF - Journal of Applied Mechanics, Transactions ASME
SN - 0021-8936
IS - 4
ER -