Buckling Of Rods Research Articles

Parametric studies and compressive performance of GH4169/K465 Kagome lattice structure prepared by selective laser melting

This paper is proposed a sufficient strategy to enhance the Kagome lattice structure by introducing sphere connections at the joints of the rods. Three types of lattice structures, namely single-cell Kagome, sandwich monocyte, and multi-layer sandwich GH4169/K465, were fabricated through the selective laser melting method. Experimental results demonstrated that the load peak value of the lattice structure increased gradually with variations in rod diameter and angle. When the rod diameter is 2 mm and the angle is 50°, the comprehensive performance is relatively excellent. Both the single-cell Kagome and sandwich monocyte structures exhibited a secondary load peak curve for the load versus displacement curve.The primary failure mode of the spherical connections Kagome structure is member fracture. For sandwich cell structures, when the rod diameter is 1.1 mm, the elastic modulus, yield strength and energy absorption of SRK are 412 MPa, 17.02 MPa and 8.05 MJ/mm3, respectively. When the rod diameter is increased to 1.7 mm, the properties of SRK are 561 MPa, 84.32 MPa and 35.49 MJ/mm3, respectively. The properties of SRK gradually increase with the increase of rod diameter. the elastic modulus, yield strength, and energy absorption of strut-reinforced Kagome with varying rod diameters surpass those of both the Kagome and spherical connections Kagome structures. The failure mode in strut-reinforced Kagome structures is primarily due to rod buckling. In the compressive stress-strain curve of the multi-layer sandwich structure,when the deformation amount is 0.2, SRK has a higher compressive strength than Kagome and SCK structure, which can reach about 350 MPa, while Kagome and SCK are lower than 200 MPa. demonstrated a gradual increasing trend in stress with increasing strain. In addition, the mechanical properties of the Kagome lattice structure are enhanced due to partial structural failure, with fracture occurring in certain members.

Buckling of Thin-Walled Cylinders from Three Dimensional Nonlinear Elasticity.

The famous bifurcation analysis performed by Flügge on compressed thin-walled cylinders is based on a series of simplifying assumptions, which allow to obtain the bifurcation landscape, together with explicit expressions for limit behaviours: surface instability, wrinkling, and Euler rod buckling. The most severe assumption introduced by Flügge is the use of an incremental constitutive equation, which does not follow from any nonlinear hyperelastic constitutive law. This is a strong limitation for the applicability of the theory, which becomes questionable when is utilized for a material characterized by a different constitutive equation, such as for instance a Mooney-Rivlin material. We re-derive the entire Flügge's formulation, thus obtaining a framework where any constitutive equation fits. The use of two different nonlinear hyperelastic constitutive equations, referred to compressible materials, leads to incremental equations, which reduce to those derived by Flügge under suitable simplifications. His results are confirmed, together with all the limit equations, now rigorously obtained, and his theory is extended. This extension of the theory of buckling of thin shells allows for computationally efficient determination of bifurcation landscapes for nonlinear constitutive laws, which may for instance be used to model biomechanics of arteries, or soft pneumatic robot arms.

Influence of Stacking Sequence on Strength and Stability of Suspension System Control Arm CFRP Laminate Rods.

The paper deals with buckling and strength analysis of suspension system rods made of carbon fibre reinforced polymer (CFRP) laminate. The whole suspension system of urban solar vehicle, Eagle Two, designed by Lodz University of Technology students was considered. The calculations and analysis focused on suspension rods, where the traditional metal material was replaced with CFRP laminate. The influence of layer arrangement on rod strength, static, and dynamic buckling were analysed. The research was conducted using numerical simulations employing finite element method software. The static and dynamic load was considered. The obtained results show that the plies’ order in the laminate influences both the strength and stiffness of the considered rod. The best results considering both failure force and longitudinal elasticity modulus were obtained for the stacking sequences with axially oriented (0°) plies on the outside of the rod.

Modeling cells spreading, motility, and receptors dynamics: a general framework

The response of cells during spreading and motility is dictated by several multi-physics events, which are triggered by extracellular cues and occur at different time-scales. For this sake, it is not completely appropriate to provide a cell with classical notions of the mechanics of materials, as for “rheology” or “mechanical response”. Rather, a cell is an alive system with constituents that show a reproducible response, as for the contractility for single stress fibers or for the mechanical response of a biopolymer actin network, but that reorganize in response to external cues in a non-exactly-predictable and reproducible way. Aware of such complexity, in this note we aim at formulating a multi-physics framework for modeling cells spreading and motility, accounting for the relocation of proteins on advecting lipid membranes.Graphic We study the mechanical response under compression/extension of an assembly composed of 8 helical rods, pin-jointed and arranged in pairs with opposite chirality. In compression we find that, whereas a single rod buckles (a), the rods of the assembly deform as stable helical shapes (b). We investigate the effect of different boundary conditions and elastic properties on the mechanical response, and find that the deformed geometries exhibit a common central region where rods remain circular helices. Our findings highlight the key role of mutual interactions in the ensemble response and shed some light on the reasons why tubular helical assemblies are so common and persistent.

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.

Buckling of chiral rods due to coupled axial and rotational growth

We present a growth model for special Cosserat rods that allows for induced rotation of cross-sections. The growth law considers two controls, one for lengthwise growth and another for rotations. This is explored in greater detail for straight rods with helical and hemitropic material symmetries by introduction of symmetry-preserving growth to account for the microstructure. The example of a guided-guided rod possessing a chiral microstructure is considered to study its deformation due to growth. We show the occurrence of growth-induced out-of-plane buckling in such rods.

Mechanics of tubular helical assemblies: ensemble response to axial compression and extension

Nature and technology often adopt structures that can be described as tubular helical assemblies. However, the role and mechanisms of these structures remain elusive. In this paper, we study the mechanical response under compression and extension of a tubular assembly composed of 8 helical Kirchhoff rods, arranged in pairs with opposite chirality and connected by pin joints, both analytically and numerically. We first focus on compression and find that, whereas a single helical rod would buckle, the rods of the assembly deform coherently as stable helical shapes wound around a common axis. Moreover, we investigate the response of the assembly under different boundary conditions, highlighting the emergence of a central region where rods remain circular helices. Secondly, we study the effects of different hypotheses on the elastic properties of rods, i.e., stress-free rods when straight versus when circular helices, Kirchhoff’s rod model versus Sadowsky’s ribbon model. Summing up, our findings highlight the key role of mutual interactions in generating a stable ensemble response that preserves the helical shape of the individual rods, as well as some interesting features, and they shed some light on the reasons why helical shapes in tubular assemblies are so common and persistent in nature and technology.Graphic We study the mechanical response under compression/extension of an assembly composed of 8 helical rods, pin-jointed and arranged in pairs with opposite chirality. In compression we find that, whereas a single rod buckles (a), the rods of the assembly deform as stable helical shapes (b). We investigate the effect of different boundary conditions and elastic properties on the mechanical response, and find that the deformed geometries exhibit a common central region where rods remain circular helices. Our findings highlight the key role of mutual interactions in the ensemble response and shed some light on the reasons why tubular helical assemblies are so common and persistent.

Mode Coarsening or Fracture: Energy Transfer Mechanisms in Dynamic Buckling of Rods

We present results of a hybrid experimental, theoretical, and simulation-based investigation of the postbuckling behavior of thin elastic rods axially impacted by a projectile. We find a new postbuckling mechanism: mode coarsening. Much akin to inverse energy cascade phenomena in other nonlinear dynamic systems, energy is transferred during mode coarsening from higher to lower wave numbers-unless the rod breaks, abruptly dissipating in the course of fracture the rod's strain energy. We derive a model that provides a predictive means to capture mode coarsening in the form of a nondissipative, purely geometric force relaxation mechanism, and validate the model by means of molecular dynamics (MD) based structural dynamics simulations for rods of wood and pasta considering different thermodynamic ensembles. The scalability of theory and simulation for engineering applications opens new venues toward safe design of engineering structures subject to impact-induced risks of buckling, ranging from skyscrapers, to aerospace structures, to the crashworthiness of vehicles, for example.

The quantum character of buckling instabilities in thin rods

Here the buckling of inextensible rods due to axial body forces is mapped to 1D, nonrelativistic, time-independent quantum mechanics. Focusing on the pedagogical case of rods confined to 2D, three simple and physically realizable applications of the mapping are given in detail; the quantum counterparts of these are particle in a box, particle in a delta-function well, and particle in a triangular well. A fourth application examines the buckling counterpart of a quantum many-body problem (in the Hartree approximation). Through a fifth application, given in the form of an exercise, the reader can explore the surprising consequences of adding a second transverse dimension to the rod buckling problem and imposing periodic boundary conditions.

SPE Strong: Strengthening Our Core: There Is No Silver Bullet: Strengthening the Fundamentals

President's column “Success is neither magical nor mysterious. Success is the natural consequence of consistently applying the basic fundamentals.” —Jim Rohn, American businessman and author This month’s column is dedicated to technology evaluation, an area where I have spent the majority of my career. For at least 2 decades, I have been approached almost weekly by either one of my engineers or an inventor who has found the “next best thing that will revolutionize our industry.” While I have been a champion for innovation and technology development, I have also applied critical thinking in forming my opinion of such claims. The first questions I always ask myself are: “Do I need this new technology?” and “Do I understand the root cause of the problem well enough to determine if applying existing technology and accepted practices cannot solve it?” To adequately answer these questions, a good understanding of the fundamentals, such as fluid or mechanical dynamics, is often needed. Is this new tool or method genuinely innovative, or has it been born out of engineering ignorance? “Being ignorant is not so much a shame, as being unwilling to learn.” —Benjamin Franklin For context, let me provide an example. The downhole rod-driven reciprocating pump has existed since the late 1800s (Beckwith 2014). For a century, the design practices for deter-mining the optimal tolerance between the downhole plunger and barrel were theoretical equations and often used rules of thumb. Too large of a tolerance would lead to excess fluid slip-page and decreasing efficiency of the pump. Too tight of a tolerance could lead to rod buckling and the inability to handle particulates such as sand. As an industry, we typically erred on the side of caution toward tighter tolerances, and many “gadgets” were invented to prolong the life of the downhole rods and pumps and to counter issues caused by this design practice. It wasn’t until the late 1990s when a group of operators in the Permian Basin began to question the validity of the existing equations and design philosophies. These Permian operators collectively funded research at Texas Tech University to understand the dynamics of the fluid slippage between a plunger and barrel under a variety of conditions. Through intensive research and experimentation of the fundamentals, they were able to develop a new equation, later named the Patterson Equation, which proved that larger tolerances did not lead to excess slippage (Nickens et al. 2005). The gained understanding of these previously accepted fundamentals had significant implications throughout the industry. Operators began to increase their plunger and barrel tolerances in their designs, and they no longer needed gadgets. As a result, the run life of the downhole equipment increased considerably. The value gained by those operating companies collaborating with the university far exceeded their original investment. However, the industry was the greatest benefactor of the publication of the research.

Features of compressed rods calculations with account of initial imperfections and creep effects

The article presents solutions to the problem of rod buckling, taking into account creep effects. Trigonometric series, the finite difference method in combination with the programming language MATLAB, as well as the finite element method in the ANSYS software package were used in the solutions. The behavior of the rods is researched for two types of relations between strain and stress during creep, with strains in an explicit and implicit form. When solving, the criterion of initial imperfections with their different values is used, as well as the tangential-modular theory. The results obtained for the two creep models are compared. The conclusion is made about the accuracy of the results of calculations in ANSYS with the presence of a combination of geometric and physical nonlinearity for various creep models.

РОЗРАХУНКОВА МОДЕЛЬ ПРОЦЕСУ СТИСНЕННЯ ПОВІТРЯ З РІДИНОЮ В ЦИЛІНДРІ ДВЗ

The paper discusses the features and performs a preliminary analysis of the symptoms and the causes of the connecting rod damage of an internal combustion engine caused by liquid entering the cylinder (hy­drolock). Object of the study is the cylinder of an internal combustion engine when liquid enters it. Purpose of the study is to research the mechanism of compression air with a liquid in the engine cyl­inder for identifying currently absent quantitative characteristics of the phenomenon of hydrolock, which causes deformation (buckling) and subsequent destruction of the connecting rod. Method of the study is theoretical, includes the development of a methodology for calculating the variation of the air parameters during compression air with a liquid. Based on simplifying assumptions, a system of differential equations for the pressure and temperature of the air with a liquid in a cylinder is ob­tained from the equations of gas state and energy. The system is solved by numerical integration over the crankshaft rotation angle with initial conditions were obtained using the standard ICE cycle calculation soft­ware. As a result, computation of the cylinder pressure in compression process by the crankshaft rotation angle depending on the filling ration of the combustion chamber with liquid was performed. The practical use of the methodology and the results obtained consists in their application in the problems of the engine damage simulation, including the calculations of the connecting rod buckling during hydrolock, as well as to clarify the symptoms and the causes of the damage. By calculation using the developed methodology, it was found that with an increase in the amount of a liquid, the maximum pressure in the internal combustion engine cylinder rapidly increases during compres­sion, starting with the combustion chamber filling ratio of 80%. With a further increase in liquid filling, commensurate with the volume of the combustion chamber, pressure rise in the final phase of the compres­sion stroke is possible tens or even hundreds of times, which determines the damage to the connecting rod during hydrolock. KEYWORDS: INTERNAL COMBUSTION ENGINE, ICE, CONNECTING ROD, CYLINDER, FAILURE, DAMAGE, HYDROLOCK, SIMULATION.

Stress-Strain State of the Bottom of the Casing String in the Horizontal Well

The purpose of the work is to develop the method for calculating the stress-strain state parameters of the bottom of the casing which is lowered into a horizontal well during its construction. When pushed into a well, a long casing string on the supports experiences cross bendings and bucklings which are caused by its own gravity and frictional forces created by axial forces of string compression. The latter are variables in length and depend on the reactions at the supports. The problem is solved by integrating the differential equation of the long rod buckling caused by its own gravity. In a first approximation, the reactions at the supports are found out disregard-ing the axial forces of friction. The author finds the general solution of the basic differential equation of horizontal pipe column deformations taking into account friction and axial forces acting during its lowering. It forms the basis for calculating bucklings and bendings, angles of rod rotation, its inner bending moments and cross forces at the sections between the supports. Geometric and power parameters of pipe deformations at the sections between the supports can be determined using the system of equations of the compatibleness of the angles of rotation and the support moments equilibrium. These equations contain axial force parameters, which can also be derived using the suggested system of algebraic equations. The solution of the problem becomes possible due to adding the transverse force equations to this system. These equations are obtained on the basis of the established relation between transverse and axial forces in the column and reactions and friction at the supports. It allows determining the axial compressive forces simultaneously. The method of linearization of the algebraic equations system and its iterative solution with high accuracy is developed. Due to the value of axial forces, calculated in a first approxi-mation, the system becomes linear, and its iterative solution allows finding the desired parameters with high accu-racy. The obtained results take into account the requirements to the construction technology of a horizontal well. The author considers the deviations of the well direction from the horizontal on the change of the stress-strain state of the casing. The paper offers the formulae to calculate the optimal distance between the casing centralizers as well as solves the problem of its reverse motion. The author takes into consideration additional moments of frictional forces affecting the casing centralizers. The obtained results might serve for the analysis of the stress-strain state of the casing column in the technological process of the horizontal well construction which makes it possible to increase its reliability and lifelength.

Bifurcation scenarios in helical buckling of slender rods using new FE

We develop a new Finite Element to accurately model twisting of rods and capture the bifurcation scenarios leading to helical buckling and various further post-buckling states. Since standard nonlinear beam elements do not account for nonlinearities in torsional modes, as well as for coupling between axial, lateral and torsional modes, we derive a new beam element, which allows us to describe complex helical buckling bifurcation scenarios of a rod subjected to a twisting load. The formulated beam element is systematically tested to assess its predictive capabilities in determining critical torsional buckling loads and its sensitivity to number of elements used. Once the model is validated against commercial FE software (Abaqus), we focus our attention on computing bifurcation scenarios to observe various complex helical configurations and transitions between them. The analysis reveals co-existence between helices with multiple loops for certain values of twisting load. Additionally, we trace the transition onsets between stable helical configurations. The developed FE can be applied to study complex buckling mechanics of engineering and biological structures.

Local and nonlocal buckling of Mooney-Rivlin rods

Closed-form solutions for the local and nonlocal buckling stretches and loads of Mooney-Rivlin rods for various (i) support conditions, (ii) values of the nonlocal parameter corresponding to (a) the assumption of linearly elastic material, (b) the nonlinear constitutive law of the Mooney-Rivlin material with first order and third order shear deformation theories for rubber-like materials are presented. A perturbation method is used for the solution corresponding to the third order shear deformation theory. Some of the solutions obtained in the current study are compared with those available in the relevant literature. Although the assumption of the linearly elastic behaviour of the material yields perfect local buckling stretch values interestingly (if the limitation on the magnitudes of strains were disregarded), it yields meaningless values for the local buckling loads; basing on the three-dimensional elasticity solution for the Mooney-Rivlin rods. Appealing results are obtained via the nonlinear constitutive law of the Mooney-Rivlin material.

Post-buckling analysis of compressed rods in cylinders by using dynamic relaxation method

Buckling of rods with cylindrical constraints is an essential problem in engineering and medical fields. Completely different to the buckling of classical Euler rods, the post-buckling modes for rods with cylindrical constraints involve highly complicated deformations and geometric configurations. In this paper, the rods are discretized into beam elements by finite element method, and the constraint relation between the rods and cylinders is described by gap element. A dynamic relaxation method for static buckling of compressed rods in cylinders is introduced. Numerical simulations have been carried out to investigate the effects of damping, element length, initial contact stiffness and penetration on post-buckling, etc. The characteristic buckling modes include deflection curves with single point, two points, three points and point-line-point contact. For the helical buckling, it is found that the transition section consists of two noncontact sections only, while the perturbed-helix section does not exist. Except the critical load and shear force of helical buckling, numerical simulation results are in good agreement with the analytical solution. By using the dynamic relaxation method, stable helical buckling modes can be obtained directly without undergoing sinusoidal buckling deformation under given compressive loads.

Numerical Study on Dynamic Buckling of Composite Bar with One Edge Simply Supported and Opposite Edge Clamped

Considering the stress wave effect, the dynamic buckling problem of a composite rod with one side fixed on one side being axially impacted by a rigid mass is studied. Based on the Hamilton principle and the axial inertia and rotational inertia, the dynamic buckling control equation is derived. For the dimensionless, the central differential method is used to solve the governing equation. The buckling mode of the composite bar with different initial deflections under different impact mass, impact velocity, critical length and layup mode is obtained by B-R criterion. The results show that the impact velocity, impact mass, critical length and layup mode have an effect on the dynamic buckling of composite rods, and the initial deflection changes have a significant effect on the buckling mode.

Diffusion-driven swelling-induced instabilities of hydrogels

Under a variety of external stimuli, hydrogels can undergo coupled solid deformation and fluid diffusion and exhibit large volume changes. The numerical analysis of this process can be complicated by numerical instabilities when using mixed formulations due to the violation of the inf-sup condition. In addition, the large deformations produce complex instability patterns causing singularities in the underlying set of equations. For these reasons, the experimentally observed complex patterns remain elusive and poorly understood. Furthermore, a stability criterion suitable to detect critical conditions and predict post-instability patterns is lacking for hydrogel simulations. Here we investigate the stability criterion for coupled problems with a saddle point nature and propose a generic framework to study diffusion-driven swelling-induced instabilities of hydrogels. Adopting a numerically stable subdivision-based mixed isogeometric analysis, we show that the proposed framework for stability analysis accurately captures instability points during the transient swelling of hydrogels. The influence of geometrical and material parameters on the critical conditions are also presented in stability diagrams for two useful problems involving the buckling of hydrogel rods and the wrinkling on the surface of hydrogel bilayers. The results show that the short-time response of hydrogels immersed in water are highly unstable. We believe that this generic scheme provides a theoretical and computational foundation to study the morphogenesis in nature, and it also paves the way to create functional materials and design novel hydrogel devices through stability diagrams.

Studying buckling of composite rods made of hybrid carbon fiber/carbon nanotube reinforced polyimide using multiscale FEM

In this paper, the buckling behavior of rods made of carbon fiber/carbon nanotube-reinforced polyimide (CF/CNT-RP) under the action of axial load is investigated based on a multiscale finite element method. A dual-step procedure is first adopted to couple the influences of micro- and nano-scale in order to obtain the equivalent elastic properties of CF/CNT-RP for various volume fractions of CF and CNT. The interphase effect between CNTs and the polymer matrix is taken into consideration. Also, dispersion of CF/CNT into the polymer matrix is assumed to be random. Then, rods with square and circular cross sections are considered whose stability characteristics are analyzed. The finite element modeling is performed using two models including a 3D brick model and a 2D beam model. Selected numerical results are given to study the effects of volume fraction of CNT/CF, interphase and geometrical properties on the axial buckling response of multiscale composite rods.

Post-Buckling Analysis of a Rod Confined in a Cylindrical Tube

Understanding the buckling and post-buckling behavior of rods confined in a finite space is of both scientific and engineering significance. Under uniaxial compression, an initially straight and slender rod confined in a tube may buckle into a sinusoidal shape and subsequently evolve into a complicated, three-dimensional (3D) helical shape. In this paper, we combine theoretical and numerical methods to investigate the post-buckling behavior of confined rods. Two theoretical models, which are based on the inextensible and extensible rod theories, respectively, are proposed to derive the analytical expressions for the axial compressive stiffness in the sinusoidal post-buckling stage. The former is concise in formulation and can be easily applied in engineering, while the latter works well in a broader scope of post-buckling analysis. Both methods can give a good approximation to the sinusoidal post-buckling stiffness and the former model is proved to be a zeroth-order approximation of the latter. The flexible multibody dynamics method based on the Timoshenko's geometrically exact beam theory is used to examine the accuracy of the two models. The methods presented in this work can be used in, for example, drilling engineering in oil and gas industries.