Optimization of concurrently compressed and torqued rod

The applications of this method for stability problems in the context of twisted and compressed rods are demonstrated in this manuscript. The complement for Euler’s buckling problem is Greenhill's problem, which studies the forming of a loop in an elastic bar under simultaneous torsion and compression (Greenhill, 1883). We search the optimal distribution of bending flexure along the axis of the rod. For the solution of the actual problem the stability equations take into account all possible convex, simply connected shapes of the cross-section. We study the cross-sections with equal principle moments of inertia. The cross-sections are similar geometric figures related by a homothetic transformation with respect to a homothetic center on the axis of the rod and vary along its axis. The cross section that delivers the maximum or the minimum for the critical eigenvalue must be determined among all convex, simply connected domains. The optimal form of the cross-section is known to be an equilateral triangle. The distribution of material along the length of a twisted and compressed rod is optimized so that the rod must support the maximal moment without spatial buckling, presuming its volume remains constant among all admissible rods. The static Euler’s approach is applicable for simply supported rod (hinged), twisted by the conservative moment and axial compressing force. For determining the optimal solution, we directly compare the twisted rods with the different lengths and cross-sections using the invariant factors. The solution of optimization problem for simultaneously twisted and compressed rod is stated in closed form in terms of the higher transcendental functions.

Winged artifacts

Winged artifacts aim at the imitation of nature’s ingenious method to produce thrust with slim and smart-shaped flapping surfaces—the bending-torsional drive. The kinematics of these surfaces shows, in three dimensions, a bending motion coupled with a simultaneous torsion. This chapter describes the design and development of the artificial bird SmartBird, which was introduced in 2011 on the occasion of the annual international industry fair Hannovermesse. This artwork with articulated wings received worldwide attention through its unprecedented agility. The efficient motion of bodies heavier than air rests on the optimization of target functions like total weight to be balanced by lift, flow resistance to be balanced by thrust, structural layout and reliability, energy storage and, last but not least, smart flight control. From the author’s point of view, the bending-torsional drive just has started its career as a new player in this optimization game.

Microstructure Evolution and Hardness Distribution in Al Wires Subjected to Simultaneous Tension-Torsion Deformation

Commercially pure Al wires are drawn through equal channel angular dies with simultaneous torsion. The wires are deformed up to an equivalent strain of 1 to 4 at room temperature after several passes. The microstructure evolution of the wires is investigated using optical microscopy at both longitudinal and transverse cross sections. A grain refinement to a mean grain size of 10 to 15 μm is achieved by using this process. Finer grain structure is observed at the edge area of the wires due to the non-uniform strain distribution. The micro-hardness measurement indicates that the hardness distribution is inhomogeneous and increasing from a minimum value at the wire centre to a maximum value at the wire edge. Finite element (FE) results show that by using a channel angel of 160° and an initial wire diameter of 4 mm during one pass, an equivalent plastic strain of about 0.4 at the wire centre and 0.9 at the wire edge can be achieved. The most important advantage of this process is the ability to impose continuous severe plastic deformation to wires. This new hybrid process could be used as an industrial method for continuous grain refinement of wires.