Deformation Of Rod Research Articles

Tensile Buckling in Shear Deformable Rods

In the framework of the Reissner–Simo rod theory and following Haringx’ approach for studying axial buckling in shear deformable rods, we give a mechanical interpretation of tensile instability, together with its mathematical justification, and we perform a linearized eigenvalue buckling analysis for tense planar rods. Buckled shapes and critical loads are calculated for most usual boundary conditions.

On the line self-contact deformation of a clamped rod under combined edge thrust and twist

Abstract We study the deformation of a clamped-clamped rod under combined edge thrust and twist, with emphasis on the final deformation pattern involving line self-contact. Two types of loading combinations are considered, i.e., twist-shortening and shortening-twist. In twist-shortening, the rod is pre-rotated a specified angle and then the two ends are brought closer quasi-statically. Shortening-twist is the other way around. Continuation scheme based on shooting method is employed to study the rod deformation as the end twist and shortening vary. We first examine the deformation sequence when the two ends are brought to one half of the initial distance and then the twist angle is increased quasi-statically. The deformation jumps from free-of-contact to one-point contact, then jumps again to two-point, then evolves smoothly to three-point and then to point-line-point writhing. In the case of twist-shortening, a typical deformation sequence also includes free of self-contact, one-point, two-point, three-point, and point-line-point contact. The final stage of deformation when the two ends approach each other depends on the pre-rotation. For instance, when the rod is pre-rotated 7 π and beyond, the final deformation as the two ends approach each other is point-line-point self-contact. For pre-rotations 6 π , 5 π , and 4 π , the final deformations are three-point, two-point, and one-point self-contacts, respectively.

Animating elastic rods with sound

Sound generation methods, such as linear modal synthesis, can sonify a wide range of physics-based animation of solid objects, resolving vibrations and sound radiation from various structures. However, elastic rods are an important computer animation primitive for which prior sound synthesis methods, such as modal synthesis, are ill-suited for several reasons: large displacements, nonlinear vibrations, dispersion effects, and the geometrically singular nature of rods. In this paper, we present physically based methods for simultaneous generation of animation and sound for deformable rods. We draw on Kirchhoff theory to simplify the representation of rod dynamics and introduce a generalized dipole model to calculate the spatially varying acoustic radiation. In doing so, we drastically decrease the amount of precomputation required (in some cases eliminating it completely), while being able to resolve sound radiation for arbitrary body deformations encountered in computer animation. We present several examples, including challenging scenes involving thousands of highly coupled frictional contacts.

Modeling Study on Stiffness Characteristics of Hydraulic Cylinder under Multi-Factors

For a complex mechanical system driven by hydraulic cylinders, the dynamic response characteristics of the mechanical system are significantly affected by the stiffness characteristics of hydraulic cylinders. This paper comprehensively studies the impacts of various factors on the stiffness characteristics of the hydraulic cylinders, including the oil bulk modulus, the air content in the hydraulic oil, the axial deformation of the piston rod, the volume expansion of the cylinder barrel, the volume expansion of the metal pipes and the flexible hoses, and the deformation of the hydraulic cylinder sealing. By combining the theoretical analysis and the experimental results, the level of each impacting factor was quantified, and the stiffness model of the hydraulic cylinder was established. Finally, comparative analysis of the stiffness was conducted by taking the experimental hydraulic cylinder as an example; it was verified that the calculated results of the proposed hydraulic cylinder stiffness model approximated the experimental results. Compared with stiffness models presented in current literature, the average accuracy was improved by more than 15 %.

Study of static and dynamic stability of flexible rods in a geometrically nonlinear statement

We study static and dynamic stability problems for a thin flexible rod subjected to axial compression with the geometric nonlinearity explicitly taken into account. In the case of static action of a force, the critical load and the bending shapes of the rod were determined by Euler. Lavrent’ev and Ishlinsky discovered that, in the case of rod dynamic loading significantly greater than the Euler static critical load, there arise buckling modes with a large number of waves in the longitudinal direction. Lavrent’ev and Ishlinsky referred to the first loading threshold discovered by Euler as the static threshold, and the subsequent ones were called dynamic thresholds; they can be attained under impact loading if the pulse growth time is less than the system relaxation time. Later, the buckling mechanism in this case and the arising parametric resonance were studied in detail by Academician Morozov and his colleagues. In this paper, we complete and develop the approach to studying dynamic rod systems suggested by Morozov; in particular, we construct exact and approximate analytic solutions by using a system of special functions generalizing the Jacobi elliptic functions. We obtain approximate analytic solutions of the nonlinear dynamic problem of flexible rod deformation under longitudinal loading with regard to the boundary conditions and show that the analytic solution of static rod system stability problems in a geometrically nonlinear statement permits exactly determining all possible shapes of the bent rod and the complete system of buckling thresholds. The study of approximate analytic solutions of dynamic problems of nonlinear vibrations of rod systems loaded by lumped forces after buckling in the deformed state allows one to determine the vibration frequencies and then the parametric resonance thresholds.

A Highly Sensitive Transducer for Landslide Monitoring

The paper presents construction details and experimental characteristics of a transducer devoted to measuring soil displacement during landslides. It consists of a flexible rod on which special highly sensitive strain gages are glued so that rod deformation can be accurately measured. Beside its high sensitivity, the transducer is also characterized by the possibility of measuring soil levels displacements in depth, being thus useful for geologists to study the structure and dynamics of such a phenomenon. Article DOI: https://dx.doi.org/10.20319/mijst.2015.11.0111 This work is licensed under the Creative Commons Attribution-Non-commercial 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

Determinants of the biomechanical and radiological outcome of surgical correction of adolescent idiopathic scoliosis surgery: the role of rod properties and patient characteristics.

Aim of the study was to evaluate the role of the mechanical properties of the rod and of the characteristics of the patients (age, skeletal maturity, BMI, and Lenke type) in determining the deformity correction, its maintenance over time and the risk of mechanical failure of the instrumentation. From March 2011 to December 2014 120 patients affected by AIS underwent posterior instrumented fusion. Two 5.5-mm CoCr rods were implanted in all patients. For every patient, age, sex, Risser grade, Lenke type curve, flexibility of the main curve, body mass index (BMI), and percentage of correction were recorded. In all patients, the Cobb angle value and rod curvature angle (RC) were evaluated. RC changes were registered and correlated to each factor to establish a possible statistically significance in a multivariate analysis. A biomechanical model was constructed to study the influence of rod diameter and material as well as the density of the anchoring implants in determining stress and deformation of rods after contouring and implantation. Radiographic and biomechanical analysis showed a different mean rod deformation for concave and convex side: 7.8° and 3.9°, respectively. RC mean value at immediate follow-up was 21.8° for the concave side and 14.6° for the convex. At 2-year minimum follow-up, RC value increases 1.5° only for the concave side. At 3.5-year mean follow-up, RC value increases 2.7°, p=0.003, for the concave side and 1.3° for the convex, p=0.06. The use of the stiffest material as well as of the lowest diameter resulted in higher stresses in the rods. The use of either a low or a high instrumentation density resulted only in minor differences in the loss of correction. Rod diameter and material as well as patient characteristics such as BMI, age, and Risser grade play an important role in deformity correction and its maintenance over time.

Serpentine locomotion through elastic energy release.

A model for serpentine locomotion is derived from a novel perspective based on concepts from configurational mechanics. The motion is realized through the release of the elastic energy of a deformable rod, sliding inside a frictionless channel, which represents a snake moving against lateral restraints. A new formulation is presented, correcting previous results and including situations never analysed so far, as in the cases when the serpent's body lies only partially inside the restraining channel or when the body has a muscle relaxation localized in a small zone. Micromechanical considerations show that propulsion is the result of reactions tangential to the frictionless constraint and acting on the snake's body, a counter-intuitive feature in mechanics. It is also experimentally demonstrated that the propulsive force driving serpentine motion can be directly measured on a designed apparatus in which flexible bars sweep a frictionless channel. Experiments fully confirm the theoretical modelling, so that the presented results open the way to exploration of effects, such as variability in the bending stiffness or channel geometry or friction, on the propulsive force of snake models made up of elastic rods.

Dynamic Analysis of Composite Rods Under Thermal and Force Loads

We propose a general approach to the solution of direct dynamic problems of the numerical analysis of composite rods subjected to thermal and force loads for a large variety of their materials and loading conditions. We take into account the shear effects and interactions between the elements of structures and supporting media. The proposed inhomogeneous rods are regarded as elements of rod systems and characterized by higher parameters of strength and stiffness and lower costs of their production as compared with homogeneous elements. In the equations of motion and physical relations, we introduce four functional characteristics of stiffness and viscosity and three mass functional characteristics equivalently reflecting the dynamic deformation of composite rods with the help of a one-dimensional model. With the help of trigonometric Fourier series, the dynamic loads, displacements, and temperature are represented as products of functions of the coordinate and time. The solution of the homogeneous problem is obtained via the matrizant of the system of equations of the first order. Partial solutions for loads of various types and generalized temperature loads are obtained on the basis of approximation of given quantities and the required displacements by trigonometric series.

Thermal-Force Deformation of a Physically Nonlinear Three-Layer Stepped Rod

Consideration has been given to the thermal-force deformation of a three-layer plastoelastic rod with a stepped thickness of one supporting layer. The physical equations of state are consistent with the Il′yushin theory of small plastoelastic deformations. To describe the kinematics of a rod bundle nonsymmetric across the thickness, the authors adopted the broken-normal hypotheses. A system of equilibrium equations has been derived, and its general iterative solution in displacements has been obtained. A numerical parametric analysis of the rod′s stress–strain state has been made.

Effects of Multilevel Facetectomy and Screw Density on Postoperative Changes in Spinal Rod Contour in Thoracic Adolescent Idiopathic Scoliosis Surgery.

Flattening of the preimplantation rod contour in the sagittal plane influences thoracic kyphosis (TK) restoration in adolescent idiopathic scoliosis (AIS) surgery. The effects of multilevel facetectomy and screw density on postoperative changes in spinal rod contour have not been documented. This study aimed to evaluate the effects of multilevel facetectomy and screw density on changes in spinal rod contour from before implantation to after surgical correction of thoracic curves in patients with AIS prospectively. The concave and convex rod shapes from patients with thoracic AIS (n = 49) were traced prior to insertion. Postoperative sagittal rod shape was determined by computed tomography. The angle of intersection of the tangents to the rod end points was measured. Multiple stepwise linear regression analysis was used to identify variables independently predictive of change in rod contour (Δθ). Average Δθ at the concave and convex side were 13.6° ± 7.5° and 4.3° ± 4.8°, respectively. The Δθ at the concave side was significantly greater than that of the convex side (P < 0.0001) and significantly correlated with Risser sign (P = 0.032), the preoperative main thoracic Cobb angle (P = 0.031), the preoperative TK angle (P = 0.012), and the number of facetectomy levels (P = 0.007). Furthermore, a Δθ at the concave side ≥14° significantly correlated with the postoperative TK angle (P = 0.003), the number of facetectomy levels (P = 0.021), and screw density at the concave side (P = 0.008). Rod deformation at the concave side suggests that corrective forces acting on that side are greater than on the convex side. Multilevel facetectomy and/or screw density at the concave side have positive effects on reducing the rod deformation that can lead to a loss of TK angle postoperatively.

Intraoperative implant rod three-dimensional geometry measured by dual camera system during scoliosis surgery.

Treatment for severe scoliosis is usually attained when the scoliotic spine is deformed and fixed by implant rods. Investigation of the intraoperative changes of implant rod shape in three-dimensions is necessary to understand the biomechanics of scoliosis correction, establish consensus of the treatment, and achieve the optimal outcome. The objective of this study was to measure the intraoperative three-dimensional geometry and deformation of implant rod during scoliosis corrective surgery.A pair of images was obtained intraoperatively by the dual camera system before rotation and after rotation of rods during scoliosis surgery. The three-dimensional implant rod geometry before implantation was measured directly by the surgeon and after surgery using a CT scanner. The images of rods were reconstructed in three-dimensions using quintic polynomial functions. The implant rod deformation was evaluated using the angle between the two three-dimensional tangent vectors measured at the ends of the implant rod.The implant rods at the concave side were significantly deformed during surgery. The highest rod deformation was found after the rotation of rods. The implant curvature regained after the surgical treatment.Careful intraoperative rod maneuver is important to achieve a safe clinical outcome because the intraoperative forces could be higher than the postoperative forces. Continuous scoliosis correction was observed as indicated by the regain of the implant rod curvature after surgery.

Dynamics of a middle ear with fractional type of dissipation

In this paper, a model of spatial motion of the ossicular chain described as a system of two rigid bodies connected to the temporal bone through the system of particularly chosen massless viscoelastic rods was proposed. Several assumptions regarding the relative motion between incus and malleus, external loading force, distributed pressure of the perilymph on the stapes baseplate behind the oval window, and supporting ligaments were made. In order to avoid merging with fractional partial differential equations, the dissipation of energy due to the deformation of the eardrum is taken into account through deformation of its radial fibers while simple shear deformation pattern of the stapedial annular ligament was replaced by uniaxial deformation of viscoelastic rods. By use of the Gibbs–Appel approach and the complementary constitutive axioms corresponding to the fractional Kelvin–Zener model of viscoelastic body, the equations of motion were derived. The Cauchy problem given in terms of coupled fractional differential equations was transformed in the equivalent integer order form and solved numerically by standard numerical procedures. These results, obtained by means of the Atanackovic–Stankovic expansion formula, were compared with the ones received by use of Laplace’s transform and its numerical inversion. As a principal novelty, this model uses both fractional calculus and recently reported results on mechanical tests performed on human middle ear tissues. Thus, it can be used for either predicting of the middle ear behavior in normal and pathological conditions or simulations preceding implants design within restoration of the hearing function.

Large coupled bending and torsional deformation of an elastic rod subjected to fluid flow

In the present work, we seek to understand the fundamental mechanisms of three-dimensional reconfiguration of plants by studying the large deformation of a flexible rod in fluid flow. Flexible rods made of polyurethane foam and reinforced with nylon fibers are tested in a wind tunnel. The rods have bending–torsion coupling which induces a torsional deformation during asymmetric bending. A mathematical model is also developed by coupling the Kirchhoff rod theory with a semi-empirical drag formulation. Different alignments of the material frame with respect to the flow direction and a range of structural properties are considered to study their effect on the deformation of the flexible rod and its drag scaling. Results show that twisting causes the flexible rods to reorient and bend with the minimum bending rigidity. It is also found that the Vogel exponent of a reconfiguring rod is not affected by torsion. Finally, using a proper set of dimensionless numbers, the state of a bending and twisting rod is characterized as a beam undergoing a pure bending deformation.

On nonlinear deformations of nonlocal elastic rods

The nonlinear theory of Kirchhoff and Clebsch is extended to rods made of nonlocal materials; the motion equations are written and the balance of energy is proved. In view of application to the study of equilibrium configurations, by means of the usual assumptions of nonlocal elasticity the integro-differential equations of the theory are transformed into differential equations. Deformations of pure bending about a principal direction of inertia of rods subject to forces and couples applied at their ends are studied: equilibrium equations are integrated by means of elliptic functions, and solutions for rods made of nonlocal and classic elastic materials are compared. The curves formed in equilibrium by the axes of rods made of nonlocal materials are distinguished in inflexional and non-inflexional elastica. The equilibrium of cantilevers subject to a force applied at their free end is also examined: the results for rods of classic and nonlocal materials are discussed by regarding the deformed axial curve of a cantilever as a segment of an inflexional elastica.

Magnetooperated Polydisperse Granulated Magnetized Structures

The problem of influence of an external magnetic field on the torsional deformation of magnetic elastomers is considered. The magnetic elastomer is modeled by a structure consisting of polydisperse spherical two-phase cells of the same kind, each of which is a magnetized hard sphere with a shell of an easily deformable elastomer. Such сells continuously fill the volume of a hollow cylindrical rod, with smaller cells located in domains among larger ones. The problem is solved in a linear formulation for the micro- and macrolevels of magnetic and elastic strain fields which appear in the magnetic elastomer under the action of an external magnetic field. The volume fractions of magnetized spherical inclusions corresponding to the maximum torsional deformation of the composite rod are found.

Fabrication of triboelectric nanogenerator with textured surface and its electric output performance

Contact electrification between insulators, manifesting as static or triboelectricity is a well-known effect. The triboelectric nanogenerator (TENG) which is based on the contact triboelectricification and electrostatic induction provides a promising route for harvesting ambient mechanical energy and converting it into electric energy. The TENG which is due to its unique properties such as simple structures, low cost, high electric density etc., can offset or even replace the traditional power source for small portable electronics, sensors and so on. So far, the influence of factors on the output performance of TENG is still trapped in unsettled questions and under debate. In this paper, we prepare several textured polydimethylsiloxane (PDMS) films with micro rod array by model method and fabricate a TENG with a size of 2222 mm. The electric generation can be achieved with a cycled process of contact and separation between a polymer and metal electrode (PDMS and aluminum respectively in this study). Several influences as the surface structure and external load on the electrical output of the TENG are systematically studied by integrating use of experimenal tests and ANSYS simulation. Results show that the existence of micro rod array on the PDMS films effectively enlarges the contact area and provides more surfaces for charge storage and hence improve the output performance of TENG. When keeping the external load constant, the output increases with decreasing distance between micro rods. When the external load is 5 N and the distance is 15 m, the average output voltage and current as high as 88 V and 15 A can be achieved respectively, which is 1.5 times higher than the output generated when the distance is 50 m. The electrical output increases quasilinearly with the increase of the external load. Simulation results show that the micro rods of PDMS films are mainly compressed by normal load, which results in a bigger diameter of micro rods. The deformations of PDMS substrate leads to the lateral friction between the micro rods and the upper electrode, which produces more charges because of the friction. For 5 N normal load, the deformations of PDMS substrate and micro rods contribute to the sum of displacement vector and the deformations along Z-axis are 32.7 m and 21.3 m respectively, and are 4.96 and 5.04 times higher than the deformation at the load of 1 N. All the results in an enlarging surface area and the larger output correspondingly. Not only does this work present a new type of generator with micro rods on the PDMS surface, which can be an effective method to improve the electrical output of TENG, but also offers a unique point of view for further understanding of the working principle of TENG.

Нелинейное деформирование трехслойного металлополимерного стержня локальными нагрузками

Нелинейное деформирование трехслойного металлополимерного стержня локальными нагрузками

Behavior of asymmetric deformation of rod in locally-lateral upsetting

Behavior of asymmetric deformation of rod in locally-lateral upsetting

Deformation of a long thermoelastic rod of rectangular normal cross-section under mixed boundary conditions by boundary integrals

Abstract Using a well-known solution for steady temperature distribution in a rectangle, a boundary integral method is used to obtain an approximate solution for a plane problem of uncoupled thermoelasticity with mixed mechanical boundary conditions. The unknown functions in the cross-section are obtained in the form of series in Cartesian harmonics, enriched with harmonic functions that have a singular behavior at the transition points. The results are discussed and the functions of practical interest are represented on the boundary and also inside the domain. The locations where possible debonding may take place are noted.