Optimum Column Buckling under an Axial Load and its Own Weight,
BAGHDAD UNIV (IRAQ)
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A vertical column of a given length made of an elastic homogeneous, and isotropic material, is to be designed with circular cross sections of varying radii or equivalently with any preassigned cross sections that are similar and similarly oriented. The lower end of the column is assumed to be built in, while a vertically copressive force is assumed to be acting on its free upper end. The optimum shape of the columns determined such that the weight of the column is minimum, and yet the column does not buckle under the action of the prescribed compressive force plus its own weight. The linear theory of elasticity is used to express the stress-strain relations, the energy method is applied to define the stability criterion, and calculus of variation is utilized to minimize the weight. The solution of the resulting non-linear two-point boundary value problem is found by a modified method of successive approximations.