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Optimal Shape of a Uniformly Convergent Column Subjected to a Load by the Follower Force Directed Towards the Positive Pole with Regard to the Condition of Permissible Stresses

Tomski L., Szmidla J., Yatsenko D.

Mechanics and Mechanical Engineering

2013

Vol. 17, nr 2

187--196

The results of theoretical research and numerical computations into the optimization of the shape of a cantilever column subjected to a load by the follower force directed towards the positive pole are presented in this paper. The equation of the bending line and the cross–section of the considered column were derived and an adequate boundary problem was formulated on the basis of the static criterion of stability. The additional condition of permissible stresses of an optimized column was assumed with regard to one of the three classes of the columns. The value of the critical load and optimum shape of the system, which fulfils the condition of compressive strength of the column rod for the chosen case of a load, were determined.

The free vibrations and optimization of the shape of a column subjected to a load by a follower force directed towards the positive pole applying the variational method

Szmidla J., Yatsenko D.

Vibrations in Physical Systems

2012

Vol. 25

393--398

The results of numerical computations and theoretical research into optimization of the shape and the free vibrations of a cantilever column subjected to a load by the follower force directed towards the positive pole are presented in this paper. The systems of equations: of motion and of cross-sectional area of the considered column were determined on the basis of the total mechanical energy and Hamilton’s principle. Taking into account the formulated boundary conditions, optimized shapes of the systems were determined for the chosen values of geometrical parameter of a head subjected to a load. The values of natural frequency of the considered system were obtained taking into account distribution of flexural rigidity along the column length while the values of critical load of optimized column were obtained on the basis of curves of changes in the basic natural frequency in relation to external load. The results of numerical computations were presented in the case of one from three classes of the systems – versatile uniformly convergence column for the assumed criterion of constant volume of the system.