Deformation Of Rod Research Articles

Analysis and experimental validation of the load characteristics of the hydraulic rod in a shearer

AbstractThe joint surface of the preloaded structure of the hydraulic rod in a shearer is prone to bending and slitting. In this study, to systematically evaluate this phenomenon, critical load characterization parameters of the hydraulic rod are first determined based on its critical load, preload, working load, and residual preload. A critical load equation of the hydraulic rod is further established based on the principle of compatibility of small deformation. Finally, the integral solution method is used to solve the load equation of the hydraulic rod of the shearer by combining the deflection and rotation equation of the fuselage and the hydraulic rod on the upper side of the coal wall to obtain the deformation and load value of the hydraulic rod. The results show that the maximum load applied on the upper hydraulic rod on the coal wall, lower hydraulic rod on the coal wall, lower hydraulic rod on the gob side, and upper hydraulic rod on the gob side are 538.15, 500.3, 445.95, and 375.15 kN, respectively. The corresponding maximum deformation of the upper hydraulic rod on the coal wall, lower hydraulic rod on the coal wall, and lower hydraulic rod on the gob side are 2.4696, 1.653, and 0.9652 mm, respectively. Compressive deformation occurred on the upper hydraulic rod on the gob side with a magnitude of −1.6346 mm. Results of numerical calculations agree well with instantaneous measurements of the load in the hydraulic rod in a shearer using wireless sensing technology. The maximum error between the calculation and measurement is less than 4%, thus validating the accuracy of the proposed load model. Using the proposed load model, we further analyzed the load characteristics of the hydraulic rod under straight cutting working conditions with different pitch and roll angles. Our findings provide an important basis for understanding the load characteristics of the entire shearer, optimizing the structure of the hydraulic rod, and improving the lifetime of the shearer.

Double restabilization and design of force–displacement response of the extensible elastica with movable constraints

A highly deformable rod, modelled as the extensible elastica, is connected to a movable clamp at one end and to a pin sliding along a frictionless curved profile at the other. Bifurcation analysis shows that axial compliance provides a stabilizing effect in compression, but unstabilizing in tension. Moreover, with varying the contraint’s curvature at the origin and the axial vs bending rod’s stiffness, in addition to possible buckling in tension, the structure displays none, two, or even four bifurcation loads, the last two associated only to the first buckling mode in compression. Therefore, the straight configuration may lose and recover stability one or two times, thus evidencing single and double restabilization, a feature never observed before. By means of the closed-form solution for the extensible elastica, the quasi-static behaviour of the structure is analytically described under large rotations and axial strain. The presented solution is exploited, together with an ad hoc developed optimization algorithm, to design the shape of the constraint’s profile necessary to obtain a desired force–displacement curve, so to realize a force-limiter or a mechanical device capable of delivering a complex force response upon application of a continuous displacement in both positive and negative direction.

Bending-active kirigami

Kirigami techniques use prescribed arrangements of cuts and fold lines to transform 2D sheet materials into complex 3D forms. These sheet transformations occur via elastic deformations, rigid folding motions, and/or pop-up mechanisms; design techniques for kirigami patterns are correspondingly based on mechanics, kinematics, and physical prototyping. This paper proposes a new family of pop-up kirigami patterns termed ‘bending-active kirigami’, which transform flat sheets into approximated double-curved surfaces using a simple 1-DOF actuation mechanism. A pattern design technique is first developed from a combination of the well-known ‘elastica’ solution for the large elastic deformation of slender rods, with the kinematic constraints imposed by a kirigami pop-up mechanism. This combination creates a rapid and intuitive design method for specification of a formed surface and its constituent kirigami pattern. An extended family of patterns are then developed based on other elastica solutions and pop-up mechanism types. Finally, a bending-active kirigami pattern is applied to the design of a deployable structure, with measurements of a physical prototype used to verify the developed design method.

Microstructure evolution and process optimization of molybdenum rods during loose tooling forging

Defects such as abnormal grain growth and cracking are easy to occur in the process of loose tooling forging of large-size molybdenum rods prepared by powder metallurgy. In this work, the forging process of molybdenum rods was simulated, which were heated to 1350 °C, and one end of them was subjected to loose tooling forging with deformation of 20%, 30% and 40%, and then they were subjected to secondary heating at 1200 °C, 1250 °C, 1300 °C and 1350 °C for 60 min. The microstructure of the molybdenum rods was characterized by optical microscope (OM), and the equivalent stress, equivalent strain and damage distribution characteristics of during the forging process were calculated by Deform-3D finite element software. The microstructure evolution law and crack formation mechanism during deformation were analyzed. The results show that when the two ends of the molybdenum rods were separately forged and heated, incomplete static recrystallization was easy to occur in the middle gradient deformation zone due to the uneven distribution of stress and strain, resulting in the abnormal growth of local grains. In the subsequent forging process, the surface of the molybdenum rods was cracked due to the excessive stress at the grain boundary of the coarse grains in the transition zone. The initial temperature and softening temperature of static recrystallization in tempering process were different with the deformation of molybdenum rods. Finally, the process optimization of molybdenum rods forging was put forward.

INFLUENCE OF POSITION ERRORS ON THE STABILITY OF A LOADBEARING VERTICAL ROD OF GREAT FLEXIBILITY

Many building structures are considered as rod systems. Bearing elements of rod systems are under load and experience large stresses and deformations. When external loads increase, these stresses and strains also increase. There may come a point where some elements lack strength, stiffness or stability. Such cases may arise due to uneven settlement and roll of the structure in conjunction with errors in the manufacture and installation of structures, insufficient development of projects, etc. One of the main measures for the timely prevention of emergency situations is the properly organized monitoring of the stress-strain state of the elements. In this paper, we consider a model of stressed structure, which combines elements in the form of flexible deformable rods and elements acting on them, represented by force vectors. As an example, we consider a structure of two vertical rectilinear rods pointing along one plumb line and connected in a node. The lower rod is pinched in the base and is a load bearing element. The upper rod is an external load for the lower one and is represented by the equivalent force vector. In theory, the lines of action of forces lie on one vertical line, so there are no other forces and moments besides axial longitudinal forces; the forces are applied at one point with given coordinates. When constructing the rod system, each rod must be set to a given design position. There will be position errors of the elements during the installation phase of the structure. Position errors are generally represented by errors in the specified angles of inclination of the rods and errors in the position of the ends of the rods in the assembly. In a stressed structure, these errors are equivalent to the errors of the force vectors. A modified system of force vectors arises. In such a system, due to position errors, a horizontal force arises which has the main influence on the stability of the supporting flexible rod when the external load increases.

Study on the effect of flow blockage due to rod deformation in QUENCH experiment

During a loss-of-coolant accident (LOCA) in the pressurized water reactor (PWR), there is a possibility that high temperature and internal pressure of the fuel rods lead to ballooning of the cladding, which causes a partial blockage of flow area in a subchannel. Such flow blockage would influence the core coolant flow, thus affecting the core heat transfer during a reflooding phase and subsequent severe accident. However, most of the system analysis codes simulate the accident process based on the assumed channel blockage ratio, resulting in the fact that the simulation results are not consistent with the actual situation. This paper integrates the developed core Fuel Rod Thermal-Mechanical Behavior analysis (FRTMB) module into the self-developed severe accident analysis code ISAA. At the same time, the existing flow blockage model is improved to make it possible to simulate the change of flow distribution due to fuel rod deformation. Finally, the ISAA-FRTMB is used to simulate the QUENCH-LOCA-0 experiment to verify the correctness and effectiveness of the improved flow blockage model, and then the effect of clad ballooning on core heat transfer and subsequent parts of core degradation is analyzed.

Reduced theory for hard magnetic rods with dipole–dipole interactions

Hard magnetic elastomers are composites of soft elastic foundations and magnetic particles with high coercivity. We formulate a theoretical framework to predict the large deformation of a hard magnetic elastomeric rod. In the previous work, the magnetic Kirchhoff rod equations, which constitute a framework for analyzing instabilities for hard magnetic rods, have been developed and validated experimentally for negligible dipole–dipole interactions. Building on previous studies, we derive the magnetic Kirchhoff rod equations with dipole–dipole interactions. The derived equations are integro-differential equations, representing the force and moment balance along the rod centerline that include long-ranged dipole-magnetic force and torque. On the basis of its discrete numerical simulation, we systematically study the effect of the the dipole–dipole interactions strength on the large deformation of hard magnetic rods. In addition, we find that our theory can predict previous experimental results without any adjustable parameters.

Research on the nuclear fuel rods melting behaviors by alternative material experiments

In a light water reactor, nuclear fuel element melting is critical. This paper will introduce the experimental studies on the melting and relocation behaviors of the single fuel rod and 3 × 3 fuel bundle imitators based on aluminum and zinc as alternative materials. The eutectic reaction can occur between Al and Zn. Moreover, the lower melting points of Al and Zn allow us to observe the experimental phenomena directly. In this paper, three single-rod experiments and a rod bundle experiment are discussed in detail. The results of the experiments are analyzed at both macro and micro levels. In the experiments of slowly increasing temperature, the melting phenomena of fuel rod imitators mainly include rod deformation, eutectic reaction, melting, erosion, and molten materials relocation. Among them, the existence of a eutectic reaction between materials will make the materials melt under their melting point, which significantly influences the melting time and behavior of the rod. Through this study, the nuclear fuel rods melting and relocation behaviors under the influence of the eutectic reaction can be observed, and the experimental results can provide data support for the development of related models.

Investigation on the modeling capability of ALPHA code for fuel rod deformation

Fuel pin cells/assemblies deformations are observed phenomena, which can cause reactivity feedback. To model the deformed geometry and considering the geometry modeling flexibility of method of characteristic (MOC), a complex geometry supported MOC ray-tracing toolkit is implemented on ALPHA (Advanced Lattice Physics code based on Heterogeneous Architecture), which employs the MOC with the axial flux expansion (MOC-EX) to perform 3D problem. Three different types of deformed geometry are calculated to investigate the capability of performing the neutronic simulation of the fuel rod deformation. The numerical results of the ALPHA code show a good agreement with the results of OpenMC, which indicate that the ALPHA code based on the MOC-EX method and complex geometry toolkit are capable to deal with the fuel rod deformation.

Integrable hard-rod deformation of the Heisenberg spin chains.

We present integrable models of interacting spin-1/2 chains which can be interpreted as hard-rod deformations of the XXZ Heisenberg chains. The models support multiple particle types: Dynamical hard rods of length ℓ and particles with lengths ℓ^{'}<ℓ that are immobile except for the interaction with the hard rods. We encounter a remarkable phenomenon in these interacting models: Exact spectral degeneracies across different deformations and volumes. The algebraic integrability of these systems is also treated using a recently developed formalism for medium-range integrable spin chains. We present the detailed Bethe Ansatz solution for the case ℓ=2.

Rod-removal technique for flexible-rods in the framework of semi-recursive multibody formulation

The slender rods experience mechanical deformation in most practical cases. The deformation should be modeled numerically since it affects the dynamics of the entire system. This paper models flexible slender-rods in a closed-loop multibody system by considering rods as variable-length constraint equations, and updating the positions and velocities. The principle behind this method is to use the rod-removal technique and the 3D semi-recursive multibody formulation. When applying the rod-removal technique, the rods-associated second-derivative-based inertial forces and velocity-dependent inertial forces and external forces must be calculated and assembled in the whole system. If consider the rod-flexibility, the stiffness equations of the removed flexible-rods, in turn, can be formulated based on beam finite elements. The finite element equations can be combined with the multibody equations of motion to perform the simulation of rigid–flexible multibody system. Two simple multibody systems with a flexible rod are employed to verify the effectiveness of the presented flexible-rod removal technique. A rigid–flexible vehicle model is taken as an example to investigate the effects of flexible-rods towards vehicle dynamics, where different initial velocities, sprung masses, and rod materials are considered. The numerical results describe how the dynamics of multibody systems changes when the deformation of flexible rods is considered. It proves that the effects of rod-flexibility must be taken into account for multibody systems especially in worse cases.

The algorithm for generating the training set for the problem of elastoplastic deformation of the metal rod

The paper proposes an algorithm for forming a small training set, which will provide a reasonable quality of a surrogate ML-model for the problem of elastoplastic deformation of a metal rod under the action of a longitudinal load pulse. This dynamic physical problem is computationally simple and convenient for testing various approaches, but at the same time it is physically quite complex, because it contains a significant range of effects. So, the methods tested on this problem can be further applied to other areas. This work demonstrates the possibility of a surrogate ML-model to provide a reasonable prediction quality for a dynamic physical problem with a small training set size.

Integrable spin chain with Hilbert space fragmentation and solvable real-time dynamics.

We revisit the so-called folded XXZ model, which was treated earlier by two independent research groups. We argue that this spin-1/2 chain is one of the simplest quantum integrable models, yet it has quite remarkable physical properties. The particles have constant scattering lengths, which leads to a simple treatment of the exact spectrum and the dynamics of the system. The Hilbert space of the model is fragmented, leading to exponentially large degeneracies in the spectrum, such that the exponent depends on the particle content of a given state. We provide an alternative derivation of the Hamiltonian and the conserved charges of the model, including an alternative interpretation of the so-called "dual model" considered earlier. We also construct a nonlocal map that connects the model with the Maassarani-Mathieu spin chain, also known as the SU(3) XX model. We consider the exact solution of the model with periodic and open boundary conditions, and also derive multiple descriptions of the exact thermodynamics of the model. We consider quantum quenches of different types. In one class of problems the dynamics can be treated relatively easily: we compute an example for the real-time dependence of a local observable. In another class of quenches the degeneracies of the model lead to the breakdown of equilibration, and we argue that they can lead to persistent oscillations. We also discuss connections with the TT[over ¯] and hard rod deformations known from quantum field theories.

COMPUTER SIMULATION IN THE PROBLEMS OF STABILITY OF THIN-WALLED RODS OF AN OPEN PROFILE WITH SHAPE IMPERFECTIONS

The presented numerical methodology is based on the finite element method (FEM) and computational procedures of the NASTRAN software package. It allows to investigate the influence of geometric imperfections in the shape of thin-walled rods of open profile on the critical values of the load, the shape of the stability loss and the stress-strain state. It has been developed an algorithm for computer modeling of initial imperfections in the shape of thin-walled rods, which is implemented in the NASTRAN software package using a neutral NASTRAN PC file and a specially developed program written in FORTRAN language and adapted to this software package. Geometric imperfections of the rods can be represented as their form of loss of stability or the form of deformation from the action of the load with the possibility of varying the maximum value of the imperfections amplitude. Computational procedures for solving the Lanczos stability problem and the geometrically nonlinear static problem by the Newton-Rafson method can be used to model imperfections. The program developed by the authors allows to form new nodal coordinates of a finite-element model of rods and to visualize geometric imperfections in a given scale. The article provides a step-by-step description of finite-element construction models of thin-walled rod of open profile with an ideal surface and taking into account the imperfection of the form, which is presented as the first form of loss of rod stability from longitudinal load applied with eccentricity. With the help of the FEMAP NASTRAN preprocessor is forming the geometry of the middle surface of an ideal rod, and setting the mechanical characteristics of the material, boundary conditions and load. The middle surface of the rod is fed as a set of flat quadrangular finite elements with six degrees of freedom in the node. In the article, a linear calculation of the stability by the Lanzosch method is performed to obtain the form of rod geometric imperfection. Setting the maximum amplitude of imperfections was performed using the program developed by the authors. Using the Newton-Rafson method, the geometrically nonlinear problem of rod statics with a given shape imperfection is solved, the critical value of the longitudinal load is determined, and the corresponding form of the rod stability loss is obtained. The presented numerical technique and the developed algorithm of computer modeling of shape imperfections allow to investigate in nonlinear formulation the stability of open profile thin-walled rods taking into account geometric imperfections of different amplitude as different forms of rod deformation, including the form of stability loss, to assess the impact of imperfections on the critical value of the load, the form of stability loss and stress-strain state. The presented algorithm and numerical technique can be used to study the stability of such thin-walled structural elements as shells, plates and others.

Decreased biofilm formation in Proteus mirabilis after short-term exposure to a simulated microgravity environment

BackgroundMicrobes threaten human health in space exploration. Studies have shown that Proteus mirabilis has been found in human space habitats. In addition, the biological characteristics of P. mirabilis in space have been studied unconditionally. The simulated microgravity environment provides a platform for understanding the changes in the biological characteristics of P. mirabilis.ObjectiveThis study intends to explore the effect of simulated microgravity on P. mirabilis, the formation of P. mirabilis biofilm, and its related mechanism.MethodsThe strange deformable rods were cultured continuously for 14 days under microgravity simulated in high-aspect rotating vessels (HARVs). The morphology, growth rate, metabolism, and biofilm formation of the strain were measured, and the phenotypic changes of P. mirabilis were evaluated. Transcriptome sequencing was used to detect differentially expressed genes under simulated microgravity and compared with phenotype.ResultsThe growth rate, metabolic ability, and biofilm forming ability of P. mirabilis were lower than those of normal gravity culture under the condition of simulated microgravity. Further analysis showed that the decrease of growth rate, metabolic ability, and biofilm forming ability may be caused by the downregulation of related genes (pstS, sodB, and fumC).ConclusionThe simulated microgravity condition enables us to explore the potential relationship between bacterial phenotype and molecular biology, thus opening up a suitable and constructive method for medical fields that have not been explored before. It provides a certain strategy for the treatment of P. mirabilis infectious diseases in space environment by exploring the microgravity of P. mirabilis.

Revealing deformation of segments and their supports in a hydrostatic segmental bearing

At present, there are theoretical and experimental studies of such bearings without taking into account the elastic deformation of the bearing segments. The rotor bearings of powerful turbines at nuclear power plants are subjected to loads as high as tens of tons. One of the important issues in designing segmental bearings operating under these conditions consists in taking into account elastic deformations of the segments. A schematic diagram of a segmental hydrostatic bearing was presented and the principle of its operation was described. When determining the deformation of spherical support, a formula of change in volume of a solid steel ball subjected to uniform pressure was applied. To determine the segment deformation in the axial direction, differential equation of bending of the strip beam as the initial one. The basic equation of deformation of rods with a curved axis acting in the plane of curvature was taken as a starting point of determining the segment deformation in the circumferential direction. It was found in the studies that the maximum deformation of the segment is 4.5 % of radial clearance at a feed pressure of 5 MPa and can affect the bearing characteristics. A substantially nonlinear character of deformations along the segment axis was revealed. It was found that the pressure of the working fluid significantly affects the segment thickness. With an increase in feeding pressure from 1 MPa to 10 MPa, the thickness of the steel segment increased more than 2 times and the thickness of the bronze segment increased more than 3 times. It was established that the pressure of the working fluid exceeding 10 MPa substantially affects the deformation of the spherical support and the bearing clearance. The study results will make it possible to determine more accurately the main characteristics of the segmental bearing and design it more efficiently.

Tensile and shear behavior of box connector for precast concrete shear walls

As precast concrete (PC) shear walls have been widely used in housing industrialization, reliable connections are important to ensure structural integrity of prefabricated shear walls. In the present study, a pair of innovative steel sleeve and box connections were proposed for rapid installation of fully assembled PC shear walls. Pull-out tests were performed on six PC specimens with sleeve and box connectors. Further, monotonic and cyclic lateral loading tests were performed on eight PC wall-ground beam joints. The test parameters were the configuration of connectors in the pull-out tests, and screw bolt strength, axial compression ratio (ACR), and loading type in the lateral loading tests. The test results showed that early pull-out failure occurred in the embedded sleeve due to flexural deformation of the horizontal pin rod, while fracture of the screw bolt occurred in the box component. Shear strength of the wall joint was developed by adhesive/interlock action, dowel action, and shear friction action. As screw bolt strength and ACR increased, the shear strength increased. To investigate the characteristic failure behavior of the connector and wall joint specimens, nonlinear finite element analysis (FEA) was conducted using ABAQUS program. A parametric study was performed to investigate the effect of design parameters on the pull-out and shear strength of the wall joint. Further, the test results were compared with the current design code requirements. Finally, an improved connection was suggested to increase the structural performance of the wall joint.

Experimental and analytical investigations on hysteretic behavior of assembled mild steel rod energy dissipaters

Metallic dampers have been widely used in engineering structures to absorb seismic energy and protect primary structure members, while conventional large-scale metallic dampers have the inherent disadvantages of space-occupying and poor post-earthquake replacement performance, resulting in expensive repairing cost and long downtime. The miniature energy dissipaters featuring relatively low bearing capacity and light-weight property seem to offer a feasible way to solve this dilemma. Existing dissipaters failed to form a reasonable anti-buckling mechanism for the inner yielding core, bringing problems as difficult grouting or large buckling deformation. Besides, low-cycle fatigue performance of such dissipaters was not quantitatively investigated in previous research. In this paper, a novel fuse-type miniature damper named assembled steel rod energy dissipater (ASRED) and free of welding and grouting was developed, which uses an equally divided metallic tube to fill the space between the core rod and the restraining tube. Experimental studies were conducted on two types of specimens with different lengths to investigate the low-cycle fatigue performance and deformation ability of the proposed ASRED. The test results showed all specimens exhibited satisfactory deformation performance, and stable hysteretic loops were obtained with no fluctuation in the compressive excursion. The lateral deformation of the inner rods was very small which guarantees an excellent low-cycle fatigue performance for the dissipaters. Besides, a hysteretic model was proposed to reproduce the cyclic behavior of the dissipaters. Finally, the commonly used Manson-Coffin equation was applied to predict the fracture cycle number of ASRED, and the proposed strain amplitude modifying method successfully eliminated the difference in low-cycle fatigue performance between the dissipaters and the mild steel making it.

Stability analysis of wooden arches with account for nonlinear creep

Introduction. The paper deals with the calculation of wooden arches taking into account the nonlinear relationship between stresses and instantaneous deformations, as well as creep and geometric nonlinearity, are considered. The analysis is based on the integral equation of the viscoelastoplastic hereditary aging model, originally proposed by A.G. Tamrazyan [1] to describe the nonlinear creep of concrete. Materials and Methods. The creep measure is taken in accordance with the work of I.E. Prokopovich and V.A. Zedgenidze [2] as a sum of exponential functions. The transition from the integral form of the creep law to the differential form is shown. The relationship between stresses and instantaneous deformations for wood under compression is determined from the Gerstner formula, and elastic work is assumed under tension. The solution is carried out using the finite element method in combination with the Newton-Raphson method and the Euler method according to the scheme that involves a stepwise increase in the load with correction of the stiffness matrix taking into account the change in the coordinates of the nodes with the sequential calculation of additional displacements of the nodes, which are due to the residual forces. The proposed approach for increasing the accuracy of determination of creep deformations at each step provides using the fourth-order Runge-Kutta method instead of the Euler method. Results. Based on the Lagrange variational principle, expressions are obtained for the stiffness matrix and the vector of additional dummy loads due to creep. The method developed by the authors is implemented in the form of a program in the MATLAB environment. Calculation examples are given for parabolic arches simply supported at the ends without an intermediate hinge and with an intermediate hinge in the middle of the span under the action of a uniformly distributed load. The results obtained are compared in the viscoelastic and viscoelastic formulation. The reliability of the results is validated through the calculation in the elastic formulation in the ANSYS software package. Discussion and Conclusions. For the arches considered, it is found that even with a load close to the instant critical, the growth of time travel is limited. Thus, the nature of their work under creep conditions differs drastically from the nature of the deformation of compressed rods.

A magnetoelastic theory for Kirchhoff rods having uniformly distributed paramagnetic inclusions and its buckling

We present a theory for finite and spatial elastic deformation of rods under the influence of arbitrary magnetic field and boundary condition. The rod is modeled as a Kirchhoff rod and is assumed to have uniformly distributed array of uniaxial spheroidal paramagnetic inclusions embedded in it all pointing in the same direction in the undeformed state. The governing equations of the magnetoelastic rod are derived which are further non-dimensionalized and linearized to investigate buckling in such rods. Analytical expressions for the onset of buckling from the rod’s trivial state are obtained in terms of loading parameters (applied magnetic field, axial load, torque) as well as geometric (inclusion orientation in the undeformed state) and material (ratio of bending and torsional stiffnesses) parameters for different combinations of boundary conditions. The buckled shape of the rod at the onset of buckling is also examined. The presented work can be useful in simulation and design of magnetic soft continuum robots.