Wyboczenie Prętów Prostych o Zmiennych Sztywnościach Zginania - Mazurkiewicz, Z. (Engineering Transactions, 2015)
The paper is devoted to the solution of the elastic buckling problem of straight bars with flexuralrigidity varying in an arbitrary manner, supported with various boundary conditions and subjected to the action of a constant axial force. Simply supported and rigidly or elastically clamped bars are considered. The solution (using the Galerkin orthogonalization method) is reduced to an infinite set of homogeneous linear algebraic equations with the Fourier coefficients as unknowns. Setting the principal determinant of this set of equations equal to zero we obtain the condition for calculating the critical force. In view of the fact that the sum of any series in the set of equations thus obtained can be expressed in the form of an integral the solution obtained may be of considerable practical importance. The paper contains some concrete examples of computing the critical force for bars of variable flexural rigidity, simply supported or rigidly clamped at both ends.