Numerical analysis of the critical force for a twisted rod in relation to the parameters of the problem

The stability of an elastic pillar under a longitudinal contracting force is considered for the case of a naturally twisted rod. The critical force increases due to twist by a factor depending on principal bending stiffnesses and on the angle of twist. It was previously believed that the dependence of this factor on the angle of twist is smooth and monotone. Our numerical experiments show that this dependence has “teeth” and “valleys”. Moreover, the notion of the “length coefficient” cannot be used in the case of three-dimensional deformation, as can be done in the flat case. Such conclusions are made on the basis of numerical studies of the critical force with the use of the L2 package developed for exact symbolic computing with piecewise polynomial functions. The values of critical forces are easily obtained under various conditions with guaranteed accuracy.