Rod Elements Research Articles

Theoretical Studies of Bounce in Rod-Type Microswitches

To improve reliability of microswitches, it is necessary to carry out theoretical studies of the switching process both at the moment of switching and at the moment of bouncing. The article presents a dynamic model of microswitches with elastic rod elements, which allows at the design stage to evaluate such basic performance characteristics as response time and contact bounce time. The proposed technique is based on representation of the solution to the differential equation of vibrations of an elastic element in the form of a linear combination of eigenforms and the application of the Bubnov-Galerkin method. Theoretical studies of bounce in a rod microswitch are carried out. It is shown that breakdown precursors of the spacer spring are an increase in the switching time and the time of the first separation in case of bouncing.

General case of reinforced concrete rod elements calculation using the diagram method

In ВС 63.13330 the general calculation case for the diagram method is oblique off-center compression, which takes into account only three components of internal force factors in the cross section: the longitudinal force - Nz– and two bending moments relative to the corresponding axes – Mxand My. The other three components-the QX and Qy transfer forces and the MZ torque – are left out of consideration. In addition, for this case, the search in the available literature, including the founders of the diagram method, for the output of calculation formulas, was not successful – in all sources they are given in ready-made form without evidence. This article is intended to try filling in these gaps. For this purpose, based on the expressions for rod displacements that are generally accepted in mechanics, in particular on the Mora integral of displacements, the resolving expressions of the diagram method are obtained in the most general form.

Скорости деформаций в сечении пространственно криволинейного стержня при различных допущениях

The article considers incremental relations connecting the changes in the kinematic parameters of the rod cross section with the deformation rate. These relations allow assessing the deformation rate on the elemental areas of a spatially curved rod, as well as considering the distortion of cross-section in its plane due to shear and torsion. Assessment of such relations between deformation rates and the rates of kinematic parameters allows developing the method of nonlinear calculation of rod systems based on integral expressions. Subsequently, these relations will be used for assessing the tangential stiffness of the rod element cross-section subjected to elastic-plastic calculation.

Модернизация программы конечно-элементного анализа стержневых систем FESTA-2020 для использования в автоматизированной системе проектирования судовых конструкций «АЛМАЗ-К»

This paper describes the efforts of St. Petersburg State Marine Technical University in development of Almaz-K CAD system for structural ship design and in the upgrade of FESTA-2020 FEM-based package for rod element analysis to be applied in Almaz-K.

Two-node method for the effective elastic properties of periodic cellular truss materials and experiment verification via stereolithography

A two-node method is proposed in this paper to predict the effective elastic properties of periodic cellular truss materials based on the traditional representative volume element (RVE) method. Through the two-node method, the original unit cell with multiple boundary nodes is transformed into a new equivalent unit cell with only two boundary nodes, and the effective elastic properties of the original unit cell can be indirectly obtained by the new equivalent unit cell. The accuracy of the present method is theoretically and numerically validated by using the asymptotic homogenization (AH) method and experimentally validated by the quasi-static uniaxial compression tests of the 3D printed cellular structures. Both theoretical and numerical results show that the present two-node method is more accurate and easier to implement than the traditional RVE method and the AH method when the size of the unit cell is negligible relative to the size of the macrostructure. For periodic cellular truss materials with rod elements, the present method can provide results with the same accuracy as the AH method but with more efficiency. For periodic cellular materials with beam elements, the present method can provide more accurate lower bound of the effective elastic properties than the traditional RVE method. The uniaxial compression tests results show that the elastic modulus of the equivalent structure obtained by the two-node method is almost the same as its original structures and is in good agreement with the calculation results obtained by the AH method.

Study of post-impact behaviour of thin hybrid carbon/epoxy and glass/epoxy woven composite laminates under fatigue tensile loading – Part II: Numerical study

This article concerns the modelling of post-impact damage propagation in thin carbon/epoxy and glass/epoxy hybrid woven composite laminates loaded in fatigue tension. The modelling is based on the semi-continuous approach implemented into the explicit finite element code RADIOSS. The bundles are modelled with rod elements and the resin is modeled with a specific damageable shell element, used to stabilize the bundles. This approach is extended to post-impact fatigue tensile loadings. Resin damaging is implemented for the shell elements through two fatigue laws Yxy-Nresina and Yxy-Nresinb based on thermodynamical forces and identified through the experimental results obtained in Part I. Fiber breakage is introduced for rod elements through Basquin curves based on tensile and compressive strains. The damage accumulation is taken into account by a Miner’s rule. For several impact energies and amplitude of fatigue loading, the modelling well correlates the experimental results in terms of damage propagation scenario, path and speed.

Development of Force Limiters in Mobile Rod Structures of Demountable Type

Large-scale mass events (sports, entertainment, etc.) require safe and high-quality organization of the visual and stage sector, so there is a need for pre-fabricated and mobile rod structures. To solve such problems, it is convenient to use the Layher system of modular building structures. The criterion for design failure is the failure of one of the most loaded elements, even when the entire system as a whole still has some resource. Compensating devices can be a solution to this problem. This study solves the problem of redistribution of forces in the rods using compensating devices, taking into account the stress state of the rod system. In the event of failure of one or more elements, their internal forces are redistributed between adjacent elements in proportion to their stiffness, so spatial rod systems can fairly well resist progressive destruction. However, the destroyed element does not carry any further load and adjacent elements can also fail. Compensating devices leave overstressed rods in operation and thus increase the load-bearing capacity of the rod system. The invention relates to the field of construction and mechanical engineering, namely to rod metal structures and their elements that work on tension or compression, primarily in statically indeterminate systems. The purpose of the invention is to obtain stable axial forces in a limited range separately for compression and stretching with the possibility of adjusting their size and length of the element. This goal is achieved by the fact that in the process of manufacturing the force limiter, which includes coaxial rod elements with a collet clip, the contact surfaces are made with ring waves (teeth), which can have a sinusoidal, triangular and trapezoidal profile with different angles of inclination of the sides. The height and pitch of the ring waves are assigned from the conditions for performing the calculated range and speed of loads, and the angle of inclination of the profiles from the conditions for ensuring different rates of change in forces (compression/stretching). Arbitrary schemes have been studied, the use of compensating devices in which allows reducing the metal content of the structure by 20%. A compensating device was developed and calculated. An experiment was conducted to identify the redistribution of forces between elements when using compensating devices: the results generally coincide with theoretical calculations.

A Three-Dimensional Model for Strength Assessment of Type-C Independent Cargo Tank Structures

For the analysis of the arrangement and strength of Type-C independent cargo tank structures, the linear spring or rod elements are usually used to model supporting woods, in which one-dimensional and linear contact behaviors are assumed. This study aimed at developing a three-dimensional model for achieving more accurate strength assessment. In the model, solid elements are modeled to simulate the supporting woods. The nonlinear contact between the cargo tanks and the supporting woods is taken into account through LS-DYNA software. Numerical simulations of a 22,000-m3 liquefied petroleum gas carrier are carried out using both one-dimensional and three-dimensional models. Three load cases including one static and two dynamic cases are considered to assess the strength of the tank structures and supporting woods. The results obtained by the proposed model are compared with the results on the basis of spring elements. It is found that this new model can provide more reasonable strength predictions of the tank structures and the supporting woods. The method based on spring elements underestimates the wood stress, which indicates that it may be not conservative. Some discussions and suggestions are presented.

Microstructure and Properties of Tungsten Heavy Alloy Connections Formed during Sintering with the Participation of the Liquid Phase.

Tungsten heavy alloys (THA) are used in the defense industry for subcaliber bullet cores due to their high density and strength. Typically methods of joining tungsten rod elements include: soldering, friction welding or threaded sleeve splicing. The properties of the joints were tested for three types of material containing 90.8, 96.2 and 98.2 wt.%. tungsten, density from 17.3 to 18.4 g/cm3 and strength range 400–1000 MPa. Combination in the liquid phase at the sintering temperature was carried out in a vacuum furnace at a temperature of 1520 °C in a hydrogen atmosphere, and tests used pairs of both identical and dissimilar materials. After that, some of the bars were subjected to additional heat treatment at 1100 °C for 3 h. The tests of the mechanical properties in the static tensile test and the measurement of impact strength showed that the obtained strength of the joints was comparable to that of the parent material. The microstructure analysis showed that the resulting joint area, while maintaining the appropriate roughness of the joined end faces of the bars, is homogeneous without areas of the solidified matrix of the joint line. Research showed that it is possible to bond under sintering conditions with the participation of a solid liquid phase of homonymous and dissimilar THA materials. The strength of joints in dissimilar materials was comparable to a tungsten heavy alloy material with lower strength in the bonded pair while homonymous materials were comparable to the original material. The test results provided a good basis for further research in which the obtained pairs of joints will be subjected to plastic working processes.

On the Determination of the Mechanical Characteristics of Rod Elements Made of Functionally Graded Materials

The determining problem of the variable characteristics of an elastic rod made of a functionally graded material based on acoustic sounding data is considered. The amplitude-frequency characteristics of the rod during longitudinal and bending vibrations are used as additional information. A system of nonlinear integral equations is derived, the solution of which is based on an iterative scheme. The conditions under which the reconstruction is carried out in a unique way are presented. The results of computational experiments are discussed.

Analytical calculation of deformations of a truss for a long span covering

Introduction. The method of induction based on the number of panels is employed to derive formulas designated for deflection of a square in plan hinged rod structure, which has supports on its sides and which consists of individual pyramidal rod elements. The truss is statically determinable and symmetrical. Some features of the solution are identified on the curves constructed according to derived formulas.
 Materials and methods. The analysis of forces arising in the rods of the covering is performed symbolically using the method of joint isolation and operators of the Maple symbolic math engine. The deflection in the centre of the covering is found by the Maxwell–Mohr’s formula. The rigidity of truss rods is assumed to be the same. The analysis of a sequence of analytical calculations of trusses, having different numbers of panels, is employed to identify coefficients, designated for deflection and reaction at the supports, in the final design formula. The induction method is employed for this purpose. Common members of sequences of coefficients are derived from the solution of linear recurrence equations made using Maple operators.
 Results. Solutions, obtained for three types of loads, are polynomial in terms of the number of panels. To illustrate the solutions and their qualitative analysis, curves describing the dependence of deflection on the number of panels are made. The author identified the quadratic asymptotics of the solution with respect to the number of panels. The quadratic asymptotics is linear in height.
 Conclusions. Formulas are obtained for calculating deflection and reactions of covering supports having an arbitrary number of panels and dimensions if exposed to three types of loads. The presence of extremum points on solution curves is shown. The dependences, identified by the author, are designated both for evaluating the accuracy of numerical solutions and for solving problems of structural optimization in terms of rigidity.

A numerical and scaled experimental study on ride comfort enhancement of a high-speed rail vehicle through optimizing traction rod stiffness

In this research, the effect of rail vehicle carbody’s flexural modes on the ride comfort of an example high-speed railway vehicle is investigated. The vehicle is modeled as a rigid multi-body system, where the rigid body vertical, longitudinal, pitch, and roll degrees of freedom of the carbody and bogie frames and the rigid body vertical and roll degrees of freedom of the wheelsets are considered. An Euler–Bernoulli beam theory is used to account for the flexural motion of the carbody. The longitudinal interaction between carbody and bogie through the traction rod is modeled as a nonlinear spring element. The corresponding equations of motion of the system in the frequency domain are obtained by using the equivalent linearization method. The effect of the traction rod is explored by using this model. Also, the optimal stiffness of the traction rod element that minimizes the flexural vibrations of the carbody is obtained through a genetic algorithm. With the optimal stiffness for the traction rod, the ride quality index at the center of the carbody floor is improved by 41% at a speed of 300 km/h. For the validation of numerical results, a scaled model of the vehicle with a scale factor of 24.5 was constructed, and its associated results are presented. The model was excited by random input signals, which were generated based on the power spectral density of the track irregularity function. The agreement between the simulation results and the scaled experimental outcome when compared with the measured data from other sources is found to be satisfactory. In the framework of the physical scaled model, the filtering effect due to the vehicle bogie base is also examined.

Interactions between blades and abradable coatings: A numerical approach considering geometrical nonlinearity

Blades in modern aero engines are designed to be larger and geometrically more complex; this enhances the nonlinear effects on the blade vibrations caused by blade-coating interactions arising from the tighter blade-casing clearance. This paper proposes a numerical strategy to capture the interacting behaviors between blades and abradable coatings. The geometrical nonlinearities of the blades are considered in the numerical strategy. The blades are modeled using co-rotational finite elements based on the Euler-Bernoulli beam theory. The abradable coatings are modeled using rod elements, and the casing surfaces are smoothed using b-spline surfaces. Incremental iterative processes based on the Newton-Raphson method are employed to solve the nonlinear dynamic equations and determine the contact configurations. Experimental observations are utilized to assess and verify the numerical method. Based on the proposed method, critical parameters that affect the nonlinear behaviors of blade-casing interactions are identified. The numerical process and results can form the basis for further rubbing analysis in which the geometrical nonlinearities of blade models are considered.

Numerical Analysis on the Seismic Performance of Plane Irregular Structure Based on ABAQUS

Rod element and shell element were used in finite element software ABAQUS to establish dynamic elastic-plastic analysis model of the structure, the seismic performance of an irregular plane complex overrun structure numerical simulation, the structure was calculated under different input level and displacement response of the acceleration response, and analyses the force of the wear layer column and the floor of the open hole stress level. The results were compared with the shaking table test to verify the accuracy of the numerical simulation results. The results of numerical calculation were basically consistent with the experimental results, and the finite element model basically reflected the response of the structure under the simulated earthquake.

Boundary rod elements for modeling the railway at the bridge crossing under the action of the speed railway load

New rod boundary elements on an elastic foundation (finite elements of large length, when approximating the displacements by a set of linear and trigonometric functions) are proposed for calculating the path oscillations outside the bridge and on the bridge, combined with a double-track beam bridge connected through a layer with a high-speed rolling stock movement. The selection of interlayer material is related to the dynamics of the bridge. To build the methodology, the articles published earlier by the author are used: a step-by-step procedure for solving the problems of unsteady dynamics of structures and the method of “nodal accelerations” to take into account the action on the structures of a moving inertial load.

Stress-strain state prediction for statically indeterminate system with accounting for malfunctioning of rod elements production

The use of pre-tension as a regulating mechanism in structures that are statically indeterminate rod systems usually implies the absence of initial forces and stresses. It is necessary to take into account its initial stresses from probabilistic positions and adjust the pre-tension parameters accordingly. The laws of distribution of deviations of rod elements or shipment-sized sets of details from nominal sizes and shapes are usually known. The technique of determination of reliable enough value of initial effort in the certain connection of interest of the statically indeterminate system (SIS) because of deviations of rod elements or shipment-sized sets of details from their nominal sizes and forms is presented. Thus, deviations of both rod elements and dispatch brands from the nominal sizes and forms are known to be random variables with symmetric laws of distribution. The task is solved in linear statement with result of research giving the opportunity to determine the value of initial effort using just one static design calculation.

Інженерна методика розрахунку елементів із комбінованої клеєної деревини

Extensive world experience in the implementation of building structures made of timber, in particular glued timber, for various purposes confirms the feasibility of their use. This is facilitated by the fact that glued timber effectively accumulates the positive properties of timber as a structural material level the shortcomings of solid timber. One of the types of constructions of glued timber are constructions of combined glued timber. Taking into account the structure and features of elements of combined glued timber of rectangular cross section, for a detailed analysis of the stress-strain state, a method is proposed, which consists in applying to standard formulas for calculating the reduced cross-sectional characteristics: reduced area, reduced moment of inertia, reduced moment of resistance. To calculation, the elements of combined glued timber of rectangular cross section according to the second limit state (serviceability), it is proposed to use the reduced modulus of elasticity of the section to the boards of the outer layers. To analyze the proposed method, a number of numerical studies of beams of combined and glued timber of the same strength class using analytical calculation methods and using the finite element method in the software package LIRA-CAD, using three-dimensional and flat finite elements. Numerical studies show that the results of calculations of beams of combined glued and glued timber of the same strength class differ within 20% in the direction of increasing the values of deflections and normal stresses in the elements of combined glued timber. Finite element calculations in the software package LIRA-CAD beams of combined and glued timber of the same strength class modeled volumetric and flat showed almost complete coincidence of results with a discrepancy of up to 2%, which suggests the need to significantly simplify the modeling, set elements from glued timber with flat finite elements. It is confirmed that the analytical calculation of beams of combined glued timber is recommended to be carried out according to the proposed method. The proposed technique allows to take into account the thickness and mechanical characteristics for the strength class of each board of which the glued cross section of the element, which significantly expands the range of use of combined glued timber. The high level of coincidence (within 5%) of the proposed analytical method with determination of the given cross-sectional characteristics with the results obtained by the finite element method for different cross-sections and spans of beams is confirmed, which allows to assert the expediency of its application in engineering calculations. In addition, the modeling of structures made of combined glued timber is possible with rod elements with the provision of the reduced modulus of elasticity according to the proposed method, which greatly simplifies the calculation of complex rod systems.

Effects of the roughness height in turbulent boundary layers over rod- and cuboid-roughened walls

Direct numerical simulations (DNSs) of spatially developing turbulent boundary layers (TBLs) over two-dimensional (2D) rod-roughened walls and three-dimensional (3D) cuboid-roughened walls are conducted to investigate the effects of the roughness height on the flow characteristics in the outer layer. The rod elements are periodically aligned along the downstream direction with a pitch of px/θin = 12, and the cuboid elements are periodically staggered with a pitch of px/θin = 12 and pz/θin = 3, where px and pz are correspondingly the streamwise and spanwise pitches of the roughness and θin is the momentum thickness at the inlet. The first surface roughness is placed 80θin downstream from the inlet, leading to a step change from a smooth to rough surface. The rod and cuboid roughness height (k) is varied in the range of 0.1 ≤ k/θin ≤ 1.8 (13 ≤ δ/k ≤ 285), respectively (δ is the boundary layer thickness), and the Reynolds number based on the momentum thickness (θ) is varied in the range of Reθ = 300 ~ 1400. For each case, the self-preservation form of the velocity-defect and the turbulent Reynolds stresses is achieved along the downstream direction. As the roughness height increases, the roughness function (ΔU+) extracted from the mean velocity profiles increases, although the velocity-defect profiles for the rough-wall cases show good agreement with the profile from the smooth-wall case. The magnitude of the Reynolds stresses in the outer layer increases with an increase of k/δ. The outer layer similarity between the flows over the rough and smooth-walls is found when δ/k ≥ 250 and 100 for the 2D rod and 3D cuboid, respectively. The continuous increase of the Reynolds stresses in the outer layer with an increase of k/δ is explained by a large population of very long structures over the rough-wall flows. Because the characteristic width of the structures increases continuously with an increase of k/δ for the rod and cuboid roughness, a wide width of the structures leads to frequent spanwise merging between adjacent structures. The active spanwise merging events with an increase of k/δ increase the streamwise coherence of the structures with the appearance of significant meandering.

A new type of peridynamics: Element-based peridynamics

The general peridynamic theories are constructed using the interactions of particles in a horizon. The interactions of particles can be connected by using spring, rod and beam, etc. Element-based peridynamics (EBPD) is proposed in the present study, in which the interactions of particles are expressed by using elements in a horizon, and the basic element concepts in the continuum mechanics are reserved exactly. The force density of EBPD is described using 2-node rod elements for one-dimensional (1D) problems, 3-node triangle elements for two-dimensional (2D) problems and 4-node tetrahedron elements for three-dimensional (3D) problems. The EBPD equations are derived from the principle of the minimum potential energy. The treatments of surface effects, boundary conditions, failure criterion and solving process of the EBPD are provided in detail. The examples of the 1D singular bar, 2D stationary crack near-tip solution, 2D plate crack propagation and 3D cubic demonstrate the effectivity of the proposed EBPD. The proposed EBPD model is used for elasticity, and defined new nonlocal stress and strain expressions. In addition, no restriction of Poisson’s ratio and no zero energy modes are included in EBPD. Furthermore, EBPD has the potential to study the nonuniform discretization, varying horizons, plasticity, thermodynamic and anisotropic material. It is also convenient to couple with FEM to reduce the computational burden.

Mathematical Packages Application in The Process of Energy-Saving Technology Development of Metal Structures with Rod Elements Production

Mathematical Packages Application in The Process of Energy-Saving Technology Development of Metal Structures with Rod Elements Production