Twisted Rods Research Articles

Necessary and sufficient conditions for one-dimensional variational problems with applications to elasticity

This paper deals with necessary and sufficient conditions for weak and strong minimizers of functionals Φ ( u ) = ∫ a b f ( x , u ( x ) , u ′ ( x ) ) d x , where u ∈ C 1 ( [ a , b ] , R N ) . We first derive conditions which are simpler than the known ones, and then apply them to several particular problems, including stability problems in the elasticity theory. In particular, we solve some open problems in [A. Majumdar, A. Raisch: Stability of twisted rods, helices and buckling solutions in three dimensions, Nonlinearity 27(2014), 2841–2867] by finding optimal conditions for the stability of a naturally straight Kirchhoff rod under various types of endpoint constraints.

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The Problem of Modeling the Geometry of Twisted Fuel Rods with X-Type Cross Section in the Performance of Thermohydraulic Calculations

For creating computational models of processes affecting the safety of nuclear facilities, in accordance with the federal rules and regulations in the field of atomic energy use, the selected modeling methods, as well as the accepted approximations and assumptions shall be justified. The paper considers the issues of taking into account the specifics of modeling the geometry of twisted fuel rods with x-type cross section using nodalization software, as well as possible approaches to describing the geometry of such fuel rods during thermohydraulic calculations. The paper defines a preferred method for specifying geometry, which allows to correctly take into account the maximum value of the heat flux from the surface of the twisted fuel rods with x-type cross section when calculating temperatures in the core and the possibility of a heat exchange crisis on the surface of such fuel rods in case of violations of normal operation.

Creep relaxation in nonlinear viscoelastic twisted rods

AbstractThe solution to the problem of stress relaxation in a twisted nonlinear viscoelastic isotropic incompressible rod is presented. We address the multiplicative decomposition of the deformation gradient into reversible (elastic) and irreversible (creep) parts. The elastic potential and the creep potential can be chosen arbitrarily. In particular, the creep law can take into account both the nonlinearity of the relationship between the strain rate and the effective stress, and time‐hardening or softening. We consider two variants of creep constitutive relations. One is based on the Tresca equivalent stress, the other is based on the von Mises equivalent stress. The first of them leads to a significant simplification of the governing equations because in this case a radial elastic strain vanishes. In this framework, we obtain a closed‐form solution in elementary functions for the coupling of Mooney–Rivlin elastic model and linear creep law. For the von Mises material, numerical‐analytical results are obtained. The results are compared with the known small‐strain solutions.

Stability optimization for a simultaneously twisted and compressed rod

PurposeThe authors 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. The authors study the cross-sections with equal principal 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.Design/methodology/approachThe optimization problems for stability of twisted and compressed rods are studied 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).FindingsFor determining the optimal solution, the authors 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.Research limitations/implications(1) The linear stability equations are applied. (2) No nonlinear or postbuckling effects were accounted. (3) The moment-free, ideal boundary conditions on both ends of the rod assumed.Practical implicationsOne of the most common design cases in mechanical engineering is the concurrent compression and twisting of the straight members. The closed-form solution allows the immediate estimation of the optimization effect for axes and rotors in industrial and automotive engineering.Social implicationsThe application of lighter and material-saving structural elements allow the saving fabrication resources, reducing the mass of vehicles and industry machines. The systematic usage of material optimized structural elements assists the stabilization of global energy balance of Earth.Originality/valueAlbeit the governing ordinary differential equations are linear, the application of the optimality conditions leads to the nonlinearity of the final optimization equations. The search of closed form solution of the nonlinear differential equations is one of the mathematically hardest tasks in engineering mathematics. The closed-form solution presents in terms of higher transcendental functions.

Numerical investigation on thermohydraulic performance of high temperature hydrogen in twisted rod channels

Nuclear thermal propulsion (NTP) is one of the most promising approaches for deep space exploration and manned interstellar voyage. As the propellant and coolant of NTP reactors, hydrogen provides higher specific impulse. In this paper, the thermohydraulic performance of high temperature hydrogen flowing through the twisted rod bundles were investigated numerically by contrasting with the cruciform rod bundles and the circular rod bundles. The heat transfer models were validated by literature data and the relative errors are within 20%. Twisted rods could enhance lateral mixing and heat transfer since the twisted lobes and valleys could enhance radial heat transfer and produce a strong rotational flow near the walls disturbing boundary layer, which reduces hot spot factors and assures the thermal safety. The largest relative difference of the JF factor between the twisted and other non-twisted channels are 28.0% and 6.1% respectively in this model.

Buckling of a twisted rod with centralizers in a tubing

A lot of research work has been done on the buckling of compressed rods with connectors in cylinders. However, very limited investigations on the buckling of a twisted sucker rod with centralizers in the progressing cavity pump well has been carried out so far. In our present study, a numerical computational strategy is proposed to investigate this highly important buckling problem. Firstly, a twisted sucker rod with or without centralizers is selected for finite element simulation and calculation, which verifies our solution method. Following that, the effects of centralizer number, centralizer spacing, sucker rod diameter and tubing diameter on the critical torque are analyzed. It is found that the clearance ratio, i.e., the ratio of the clearance between the centralizer and the tubing to the clearance between the sucker rod and the tubing, is the only factor that affects the dimensionless critical torque. With a centralizer, the critical rod length is usually reduced by 25% compared to the case of a rod with hinged restraint.

Irregular and suppressed elastic deformation by a structural twist in cellulose nanofibre models

The elastic responsiveness of single cellulose nanofibres is important for advanced analysis of biological tissues and their use in sophisticated functional materials. However, the mechanical responsiveness derived from the twisted structure of cellulose nanofibres (CNFs) has remained unexplored. In this study, finite element simulations were applied to characterize the deformation response derived from the torsional structure by performing tensile and bending tests of an unconventionally very long and twisted rod model, having the known dimensional parameters and properties of CNFs. The antagonistic action of two types of structural elements (a contour twist and a curvilinear coordinate) was found to result in an irregular deformation response but with only small fluctuations. The contour twist generated rotational displacements under tensile load, but the curvilinear coordinate suppressed rotational displacement. Under bending stress, the contour twist minimized irregular bending deformation because of the orthotropic properties and made the bending stress transferability a highly linear response.

Preparation and characterization of Mg alloy rods with gradient microstructure by torsion deformation

Extruded AZ31 Mg alloy rods were subject to free-end torsion deformation at room temperature. The microstructure features of the torsion deformed samples were characterized using electron backscatter diffraction technique. Mg rods with gradient microstructure can be fabricated by torsion deformation. Inhomogeneous distribution of microstructure along the radial direction of the twisted rods is attributed to the linearly increasing strain accumulation and strain rate from core to surface. With increasing equivalent strain, both the amount of {10-12} twins and dislocation density increase and the c-axes of texture tend to rotate towards torsion axis. Although both dislocation slips and {10-12} twinning can be activated during torsion, dislocation slips are considered as the dominated deformation mechanism and responsible for the change of macro-texture for present torsion deformation. {10-12} twins and dislocations in the twisted samples can generate refinement hardening and dislocation hardening, respectively, to increase the hardness value.

Application of the Lagrange-Ritz-Kantorovich Method to the Vibration Analysis of Turbine Blades

The purpose of this effort is the method of vibration analysis. Object of research is turbine blade. A calculation method based on Lagrange equations is proposed. Blade is assumed to be an elastic rectilinear twisted rod. Linear theory is used which means that translational and angular displacements, as well as the loads, are supposed to be small. Deflections are approximated using the method of Ritz. The coordinate functions correspond to the boundary conditions. The coefficients of approximation are time dependent parameters according to the method of Kantorovich. These coefficients are generalized coordinates. Lagrange equations are solved numerically by means of computer mathematics system (MathCAD). This method enables us to calculate natural frequencies and modes of blade and analyze unsteady free vibrations and forced ones.

Experimental investigation of turbulent heat transfer performance in internal flow using a star shape cross sectioned twisted rod inserts

In the present investigation, the heat transfer and pressure drop characteristics of a circular tube fitted with a new 5 point star shape cross sectioned twisted rod inserts are experimentally reported for fully developed turbulent flow regime. Test runs were conducted in a concentric double pipe heat exchanger in the Reynolds number (Re) range of 8000–32,000 with water as a working fluid. For different investigated geometries of insert, the average Nusselt number ratio ( $${\text{Nu}}_{\text{a}} /{\text{Nu}}_{\text{p}}$$ ) and average friction factor ratio ( $${\text{f}}_{\text{a}} /{\text{f}}_{\text{p}}$$ ) with and without inserts are reported to be in the range of 1.79–2.79 and 2.44–4.17 respectively. The Nusselt number ratio ( $${\text{Nu}}_{\text{a}} /{\text{Nu}}_{\text{c}}$$ ) based on equal pumping power is also reported and found to be in the range of 0.94–1.24. The effects of varying pitch to length of insert ratio (p/l) and diameter of insert to the inner diameter of tube ratio (d/Di) on heat transfer and pressure drop are reported and empirical correlation is given for Nusselt number in terms of Reynolds number (Re), pitch to length of insert ratio (p/l), insert diameter to inner diameter of tube ratio (d/Di) and Prandtl number (Pr).

Preliminary Report on the Middle Neolithic Well from Sajószentpéter (North-Eastern Hungary)

In November 2012, during a preventive archaeological excavation necessitated by the construction of a new highway bypassing Sajószentpéter (Borsod-Abaúj-Zemplén county, North-Eastern Hungary), a Middle Neolithic water well with astonishing wooden lining was uncovered by the archaeologists of Herman Ottó Museum, Miskolc. The 60 cm high remains of the tube-like wooden structure was made from a single oak tree with a total diameter of 90 cm. The trunk had been initially cut into four pieces (panels) that were later bond together with trusses of twisted rods. The wooden structure had amazing tool-marks on the entire surface that could be related to at least 3 different chisels/axes and bear fundamental information regarding the chaine opératoire.

Synthesis of twisted ribbon-like carbon, carbon microtubes and carbon rod from mercerized cotton fiber

In this study, we used mercerized cotton fibers as carbonization precursors to fabricate carbon materials having different structures. The morphologies of the synthesized carbon materials were successfully controlled by varying the mercerization time. Twisted ribbon-like carbon structures, carbon microtubes, and carbon rods could be synthesized by carbonizing non-mercerized cotton fibers, cotton fibers mercerized for 40min, and fully mercerized cotton fibers (i.e., fibers mercerized for 60min), respectively. Interestingly, along with the morphological changes, the specific surface areas of these carbon materials were also changed to 203.7, 726, and 276.7m2/g, respectively. This method of fabricating carbon materials should lead to the synthesis of novel, structured carbon materials with various functionalities as it exploits both the natural structure of cotton fibers and artificial chemical processes.

Stability of twisted rods, helices and buckling solutions in three dimensions

We study stability problems for equilibria of a naturally straight, inextensible, unshearable Kirchhoff rod allowed to deform in three dimensions (3D), subject to terminal loads. We investigate the stability of the twisted, straight state in 3D for three different boundary-value problems, cast in terms of Dirichlet and Neumann boundary conditions for the Euler angles, with and without isoperimetric constraints. In all cases, we obtain explicit stability estimates in terms of the twist, external load and elastic constants and in the Dirichlet case, we compute bifurcation diagrams for the Euler angles as a function of the external load. In the same vein, we obtain explicit stability estimates for a family of prototypical helical equilibria in 3D and demonstrate that they are stable for a range of tensile and compressive forces. We propose a numerical L2-gradient flow model to study the stability and dynamical evolution (in viscous model situations) of Kirchhoff rod equilibria. In Nizette and Goriely 1999 J. Math. Phys. 40 2830–66, the authors construct a family of localized buckling solutions. We apply our L2-gradient flow model to these localized buckling solutions, demonstrate that they are unstable, study their evolution and the simulations demonstrate rich spatio-temporal patterns that strongly depend on the boundary conditions and imposed isoperimetric constraints.

Geometrical model for malaria parasite migration in structured environments.

Malaria is transmitted to vertebrates via a mosquito bite, during which rodlike and crescent-shaped parasites, called sporozoites, are injected into the skin of the host. Searching for a blood capillary to penetrate, sporozoites move quickly in locally helical trajectories, that are frequently perturbed by interactions with the extracellular environment. Here we present a theoretical analysis of the active motility of sporozoites in a structured environment. The sporozoite is modelled as a self-propelled rod with spontaneous curvature and bending rigidity. It interacts with hard obstacles through collision rules inferred from experimental observation of two-dimensional sporozoite movement in pillar arrays. Our model shows that complex motion patterns arise from the geometrical shape of the parasite and that its mechanical flexibility is crucial for stable migration patterns. Extending the model to three dimensions reveals that a bent and twisted rod can associate to cylindrical obstacles in a manner reminiscent of the association of sporozoites to blood capillaries, supporting the notion of a prominent role of cell shape during malaria transmission.

Homoclinic complexity in the localised buckling of an extensible conducting rod in a uniform magnetic field

We study the localised buckling of an extensible conducting rod subjected to end loads and placed in a uniform magnetic field. The trivial straight but twisted rod is described by a fixed point of a four-dimensional Hamiltonian system of equations previously shown to be chaotic. Localised solutions are given by homoclinic orbits to this fixed point and we explore the spatial complexity of localised rod configurations by means of shooting and parameter continuation methods that exploit the reversibility of the system of equations. Unlike in localisation studies of non-magnetic rods we find that for certain parameter values multiple Hamiltonian–Hopf bifurcations occur. Where these collide as parameters are varied, solutions exhibit delocalisation–relocalisation behaviour. Our results predict buckling instabilities and post-buckling behaviour of rods under combined mechanical and magnetic loads, which are relevant for electrodynamic space tethers and potentially for conducting nanowires in future electromechanical devices.

Investigation of Bed Joint Reinforcement Influence on Mechanical Properties of Masonry under Compression

The results of investigations of compressed reinforced masonry walls subjected to axial compression are presented. Tests were carried out using specimens made of clay bricks and cement-lime mortar. As reinforcement, smooth and spiral twisted longitudinal rods, two types of structural wire mesh and truss type reinforcement were used. Two percentages of bed joint reinforcement, about 0.1% and 0.05% were applied. For each type of reinforcement, three masonry walls were tested. Additionally, nine unreinforced models were also tested. The main aim of the investigations presented is to determine the effect of different types of reinforcement on the load capacity and failure. Measurement of the strains of reinforcing bars permitted the recording of the strain level at the moment of crack appearance and also at the moment of failure.

Transverse-Weld Tensile Properties of a New Al-4Cu-2Si Alloy as Filler Metal

AA2195, an Al-Cu-Li alloy in the T8P4 age-hardened condition, is a candidate aluminum armor for future combat vehicles, as this material offers higher static strength and ballistic protection than current aluminum armor alloys. However, certification of AA2195 alloy for armor applications requires initial qualification based on the ballistic performance of welded panels in the as-welded condition. Currently, combat vehicle manufacturers primarily use gas metal arc welding (GMAW) process to meet their fabrication needs. Unfortunately, a matching GMAW consumable electrode is currently not commercially available to allow effective joining of AA2195 alloy. This initial effort focused on an innovative, low-cost, low-risk approach to identify an alloy composition suitable for effective joining of AA2195 alloy, and evaluated transverse-weld tensile properties of groove butt joints produced using the identified alloy. Selected commercial off-the-shelf (COTS) aluminum alloy filler wires were twisted to form candidate twisted filler rods. Representative test weldments were produced using AA2195 alloy, candidate twisted filler rods and gas tungsten arc welding (GTAW) process. Selected GTA weldments produced using Al-4wt.%Cu-2wt.%Si alloy as filler metal consistently provided transverse-weld tensile properties in excess of 275 MPa (40 ksi) UTS and 8% El (over 25 mm gage length), thereby showing potential for acceptable ballistic performance of as-welded panels. Further developmental work is required to evaluate in detail GMAW consumable wire electrodes based on the Al-Cu-Si system containing 4.2-5.0 wt.% Cu and 1.6-2.0 wt.% Si.

Application of topological conservation to model key features of zero-torque multi-ply yarns

During yarn formation by ring spinning, fibres are bent into approximately helical shapes and torque or twist-liveliness is created. The yarn torque causes yarn instability, manifested as snarling or entanglements, and this instability must be controlled during manufacturing processes. Generally, the torque depends on yarn geometric factors such as the yarn twist, linear density and the fibre properties. A practical solution to the problem of twist-liveliness is the formation of a two-fold yarn. This twisting or plying process produces a yarn structure where the energy of the system is determined by purely geometrical constraints of the plied structure and consequently when an energy minimum is reached the plied yarn obtained from the process is torsionally balanced and torque-free. In the present paper, the stability of plied textile yarns will be evaluated using the Topological Conservation law (Fuller, F. B., 1971, Proc. Nat. Acad. Sci. USA, 68, 815–819.) developed to study the post-buckling behaviour of twisted rods by Van der Heijden et al. (Int. J. Mech. Sci., 45, 161–196, 2003). The present work considers the equilibrium configuration of a series of multi-ply twisted yarns (2, 4, and 6 strands) of finite length. Several structural and mechanical properties are highlighted: (i) the influence of structural properties (the number of strands, the strand linear density and strand twist) and the ratio of the torsional and bending stiffnesses of the strands on the balance point in multi-ply yarns. The topological invariant of the twisted yarn (link) is used to calculate the ply and strand properties (writhe) and compared with experimental results obtained at CSIRO. The inter-strand pressure between strands of a multi-ply yarn, a feature of interest for fibre interactions in yarn structures, is also calculated at the balance situation across a range of structural and mechanical conditions.

Integrability of a conducting elastic rod in a magnetic field

We consider the equilibrium equations for a conducting elastic rod placed in a uniform magnetic field, motivated by the problem of electrodynamic space tethers. When expressed in body coordinates the equations are found to sit in a family of non-canonical Hamiltonian systems involving an increasing number of vector fields. These systems, which include the classical Euler and Kirchhoff rods, are shown to be completely integrable in the case of a transversely isotropic rod; they are in fact generated by a Lax pair. For the magnetic rod this gives a physical interpretation to a previously proposed abstract nine-dimensional integrable system. We use the conserved quantities to reduce the equations to a four-dimensional canonical Hamiltonian system, allowing the geometry of the phase space to be investigated through Poincaré sections. In the special case where the force in the rod is aligned with the magnetic field the system turns out to be superintegrable, meaning that the phase space breaks down completely into periodic orbits, corresponding to straight twisted rods.