The author deals with a slender column which is subjected to an axial compressive load p which may cause it to buckle. The governing differential equation for the displacement w(x) from its straight equilibrium position is left bracket EI(x)w double prime (x) right bracket double prime plus Pw double prime (x) equals 0, where x is the distance measured from one end of the column, E is the modulus of elasticity, and I(x) equals 1/Q(x) is the moment of inertia of the cross section of the column about a line passing through its centroid but perpendicular to the plane of buckling. We assume that E is constant, I(x) is a function of x, and all cross sections are similar.
ASJC Scopus subject areas
- Applied Mathematics