Rod Elements Research Articles

Mathematical modelling and development of a computational algorithm for the study of thermo-stressed state of a heat-resistant alloy

The problem of increasing the thermal stability of structural elements made of heat-resistant metals and alloys operating in a complex force and thermal field is one of the key priorities of modern high technology research. The most important case is the study of the thermal stability of structural elements in real conditions of heat fluxes with varying intensity, with a complex configuration of heat-insulated local surfaces and internal point heat sources. Many basic load-bearing structural elements operating in a large thermal field (elements of gas turbine and jet engines, etc.), are made of heat-resistant alloys. The physical feature of such alloys is that the coefficient of thermal expansion and the modulus of elasticity of the material strictly depends on the temperature distribution field, that is, the coefficients are a function of temperature. The purpose of this study is to simulate a thermo-stressed state in rod elements of a structure based on the law of conservation of energy, in the presence of a heat flux applied on the lateral surface, which varies along the coordinate in a linear manner. To solve the outlined problem, a potential energy minimisation method is used in combination of a quadratic finite element with three nodes. As a result, from the condition of the minimum of the functional defining the potential energy, a resolving system of linear algebraic equations is obtained. All possible natural boundary conditions are taken into account. In this system, all integrals used are calculated analytically. Moreover, the law of conservation of energy is fulfilled for each of the equations of the resulting system. As a result, the values of displacement, deformation and stresses were calculated, as well as the values of elastic temperature and thermoelastic components of deformations and stresses for a specific example.

The inverse non-stationary problem of identification of defects in an elastic rod

Non-stationary inverse problems of deformed solid mechanics are among the most underexplored due to, inter alia, increasing dimension of non-stationary problems per unit as compared with stationary and static problems, as well as necessity to consider the initial conditions. In the context of the continuing progress of the aviation and aerospace industries, the question arises about technical condition monitoring of aircraft for the purposes of their safe operation. A large proportion of an aircraft structure consists of beam and rod elements exposed to various man-made and natural effects which cause defects inaccessible for visual inspection and required to be identified well in advance. It is well known that defects (such as cracks, cavities, rigid and elastic inclusions) are concentrators of stresses and largely cause processes, which lead to the destruction of elastic bodies. Therefore, the problem of identification of such defects and their parameters, i.e. the problem of identification, represents a great practical interest. Mathematically, the problem of identification represents a non-linear inverse problem. The development of methods of solving such problems is currently a live fundamental research issue.

Seismic behavior of the main girder of a bridge with viscoelastic dampers

Introduction. The seismic stability of bearing structures is one of the main objectives of design and construction of structures in earthquake areas. The co-authors have analyzed the effect of a damper, located at the intersection of structural elements, on the seismic response of the main girder of a steel-concrete bridge exposed to the seismic impact. The purpose of this study is to select optimal values of viscous and elastic elements to ensure the seismic resistance of the bridge.
 Materials and methods. The finite element method was used to simulate the geometric characteristics of the bridge. The model of the bridge has rod elements to simulate girders and viscous elastic elements to simulate dampers. In the study, different values of elastic and viscous characteristics of the damper were used in pairs. The nonlinear problem statement helped to analyze the bridge structure using the direct dynamic method.
 Results. As a result, we obtained a graphic chart describing the relationship between horizontal displacements and the time for each pair of values of elastic and viscous characteristics of the damper for Maxwell and Kelvin – Voigt models. The effect of changes in the values of stiffness and damping parameters on the values of the period and eigenfrequencies of this superstructure was also investigated.
 Conclusions. The co-authors chose the damper parameters to minimize seismic displacements of the bridge girder and optimally suppress the dynamic interaction between the bridge elements. Viscoelastic elements of the Kelvin – Voigt type provide more regular values of horizontal displacements of the girder when the direction of the seismic effect changes. We also recommend to select the pair of values equal to 20 000 kN/m, 800 kN s/m, and to use the Kelvin – Voigt model in the design of a viscoelastic damper.

Five-mode quasilinear model of nonlinear dynamics of extended system

Distributed systems are widely used in practice. These are cosmic ligaments in the near-Earth space with a length of tens of kilometers. They approximate reinforced concrete piles in the soil when calculating the stress-strain state and assessing the technical condition; pipelines both in air and in liquid, underwater towed systems. Known underwater airlift systems of great length for the extraction of minerals (nodules) from the ocean floor with a length of 5-10 km. To solve the problems of the dynamics of such systems in various environments, the well-known mathematical models are not quite correct from the point of view of taking into account the variety of wave processes. It determines the need to build refined wave models. A new quasilinear mathematical model, which describes the nonlinear four-mode dynamics of the distributed system in the spatially inhomogeneous field of mass and surface forces, has been obtained. It is described by a nonlinear system of twelve first-order partial differential equations. For it, the principles of ultimate and hyperbolicity are fulfilled. Together with the boundary and initial conditions, it can be used to describe dynamics and statics of geometrically and physically nonlinear rod elements, piles in the ground, crane equipment ropes, mine lifts, aerial cableways, towed systems in liquid and gas flow, etc. For two-mode spatial reduction of the model, the theorem about correctness of Cauchy problem has been considered. As a result of the calculations, the earlier assumptions about the movement of the cable along its initial configuration were changed as the length of the cable changed. It has been found out that this assumption is only true for the initial transition participant. It is also established that at a given tachogram in the configuration of the towed line, there is a point of inflection, which shifts from top to bottom when lifting it. It can be a factor in the looping, contributing to the breakage of the cable system during towing.

Simplified Beam Element Model of Badminton Batting Process Based on Motion Differential Equation

Badminton is not only a traditional sport in China, but also an advantage sport in China. It has good entertainment, appreciation, and exercise, as well as a very broad mass base in China. Badminton racket as the key equipment of badminton, its production and design has a very critical impact on the development of the sport; the current existing research lacks the analysis of badminton batting moment. In order to more intuitively and clearly understand the force and displacement relationship of the racket net at the moment of badminton hitting, this study is based on the differential equation of motion, combined with the finite element analysis method to build a simplified beam element model. In order to verify the reliability of the model, the displacement of the beam element and the rod element of the badminton racket under the same load is constructed. Through the research results, it can be seen that the beam element model is more reliable for the numerical calculation of badminton batting moment. The in-depth analysis of badminton batting process has a certain reference significance for the production and design of badminton racket.

Microstrip rectangular patch antenna using coplanar parasitic rod elements with substrate integrated feeding line technique

Microstrip antenna technology is fast growing technology in present days there are broadly used in mobile communication and satellite communication. The microstrip antennas are very low cost and low profile and ease fabrication. However, the bandwidth utilization is the drawback for this system. Now proposed methodology can be reduced that drawback and provide efficient bandwidth utilization factor in proposed method design a microstrip rectangular patch antenna using co-planar parasitic rod elements with substrate intergrading feeding line technique. This proposed method, microstrip rectangular patch antenna is designed for the enhancement of bandwidth, Improvement in front to back ratio, reduction in losses and high-quality factor and power handling capability. The proposed method enhances the bandwidth ratio from 4% to 18% it shows that the proposed method gives the best results compared to the existing approach. The simulation and 3D plot results can be obtained from Ansoft HFSS (High-frequency structure simulator) Software.

DESIGNING ANNULAR ELASTIC VALVE THAT CONTROLS AIR EXHAUST FROM WORKING CHAMBER OF PNEUMATIC IMPACT MACHINE

The paper considers one of the promising shut-off and control elements of the air distribution system of pneumatic impact machines - an annular elastic valve (CUV). This element allows you to reduce the energy consumption of pneumatic devices. Unfavorable combinations of factors that hinder the movement of the valve necessary for sealing the working chamber are considered. The paper presents a method for calculating the elastic valve that controls the release of energy from the return chamber of the pneumatic impact machine, which allows determining the main geometric dimensions of the valve device at the design stage, which provides a stable self-oscillating cycle of the pneumatic impact machine with the specified energy characteristics. The developed technique was used in the modernization of the air distribution system of the ring impact machine (KUM), designed for immersion of rod elements in the ground. Tests of the resulting sample in production conditions confirmed the increase in energy performance compared to previously produced machines of a similar type.

Simulation of the forming of tufted multilayer composite preforms

Tufting of preforms increases the resistance of the laminated composites to delamination. Draping of the preforms is clearly modified by the presence of tufting threads. A simulation approach for the forming of tufted textile reinforcement stacks is proposed. It determines the state of the tufted preforms after forming and in particular the possible wrinkles. The layers of textile reinforcements are modeled by stress resultant shells. Tufting threads are modeled by rod chains that can slide with friction relative to the textile reinforcements. The geometry of these rod elements is enhanced by a description of Hermite and the bending of the threads is taken into account through the position of neighboring elements. The approach accurately simulates the forming of tufted preforms and in particular the wrinkles that are observed in the forming experiments.

An approach to design of large-sized deployable hoop space antenna reflector

Amongst the large-sized transformable space antennas, the most attention is currently paid to developing of antennas with hoop-shaped reflectors. The developers are faced with the necessity of looking for optimal design concepts. This paper shows the various concepts of building of the reflectors of the cable-rod scheme, containing a circular load-bearing framework (load-bearing rim) with a deployment drive set on it and the reflecting surface shape-generating structure, assembled into a single construction by the cable and rod elements. The difference between the proposed design concepts of the reflectors is the various structures of the controllable unfolding mechanisms. In the first alternative of the reflector structure, the unfolding process is supported by the cable, which restrains relative displacements of the tips of the initially compressed springs. The second alternative supposes the cable not to be the restraining element, but an active unit of the unfolding mechanism. This paper also describes various alternatives for connection between tension tie cables and the load-bearing rim. It is shown that the alternative of connection of the tension tie cables to the middles of the load-bearing rim edges allows to perform stress analysis of the structure elements and to obtain required characteristics of the spring drive. The numerical calculations for optimal angular position of the deployment drive pulleys holder relative to the sections of the load-bearing rim for the second alternative of the reflector design, which provides the most force effect on shape-generating structure of the reflector, when the knitted mesh fabric is being pulled, are under consideration in this article. The calculations are confirmed by experimental investigations.

Estimation of deformations of steel constructions of cranes based on photogrammetry

The paper considers the results of the application of photogrammetry to assess the deformations of rod and plate elements of the steel constructions of hoisting machines, the analysis of the main problems arising in their processing and the proposed solutions to ensure the necessary accuracy. The authors, based on their own research and practical experiences application in the use of photogrammetry, carried out accuracy rating the magnitude of deformations. Based on a brief review of normative documents, proposals for rationing the permissible values of measurement errors are given. The paper also considers the problems that may arise in the assessment of the deformed state of design status and proposes approaches to solving these problems. One of the problems solved in the study was to assess the magnitude of the deformation of the rear belt of support of blocks of equalizing polyspast, resulting from an emergency situation during the operation of the crane KPL-16-30. In addition to assessing the overall deformed state of the entire element, the deformation in some sections of the structure was assessed. The application of some approaches to estimating the deformation of rod structure elements based on modeling the shape of the a curved axis of a beam or rod. Also considered the experience of deflection measurement the deflection of the 0.5 t electric hoists guide in the laboratory of hoisting machines. The authors shared their inspecting of the wagon tippler No. 2 examination. In addition to the assessment of transverse deformations, the task was to check the possible torsion of the metal structure of the moving part. In the process of work some problems were also revealed, the solution of which will make it possible to provide the necessary accuracy of measurements. When evaluating the approximation accuracy, the authors propose to use several approaches.

Numerical calculation of the natural vibration frequencies of thermo-elastic rods taking into account the effect of the temperature gradient

Elastic rod elements are considered, the axial line of which in the natural state is a flat curve and remains a flat curve after loading. The following assumptions are used: the normal cross-sections, which are flat before deformation, remain flat and normal to the deformed thermo-elastic axial line after deformation; the temperature field is stationary and non-uniform. Nonlinear equations of motion of the rod are obtained, taking into account the rotational inertia of cross-section and the extensibility of the axial line.

Mathematical modeling of power loads in the construction of a parallelogram lift

The question of determining the power loads in the elements of the supporting structure of a parallelogram hoist is considered. The design diagram of the lift supporting structure and the mathematical model describing the dependence of the power geometric characteristics of the structure are presented. To simplify the design scheme, not a volumetric, but a flat supporting structure was considered. Equilibrium equations were compiled for each element of the design scheme. The dependence of the angle of inclination of the element of the hydraulic cylinder rod on the angle of lifting of the supporting structure is obtained and the nature of the dependence is shown. The system of equations was solved in matrix form for the given values of the angle of the hydraulic cylinder rod position.

Absolute Nodal Coordinate Formulation-Based Decoupled-Stranded Model for Flexible Cables With Large Deformation

Abstract The existing flexible cable dynamics model, established using the absolute nodal coordinate formulation (ANCF), suffers from the issue of strain coupling. It also does not consider the nonlinear mechanical properties inside the flexible cable and consequently provides an inaccurate description of the strain and the constitutive properties. In this study, the axial strain of the flexible cable was redescribed by constructing an equivalent rod element in order to decouple the axial strain and bending strain. Subsequently, a strain-decoupled ANCF cable element was derived. Then, by analyzing the geometry of the stranded flexible cable as well as the relative sliding and friction between the wires in the cable, the axial stiffness and bending stiffness calculation formulae were obtained and the decoupled-stranded model was established. This study, therefore, achieved an improvement upon the traditional model in describing the strain and constitutive properties. The simulation results show that the decoupled model eliminates the strain coupling effect compared with the traditional model and has the advantages of fast convergence and high accuracy. The stiffness characteristics analysis shows that the bending stiffness of the cable changes during the bending process due to the relative motion and friction between the wires. Finally, the comparative analysis shows that the accuracy of the decoupled-stranded model is very close to that of the detailed model and performs much better than the other ANCF models, and the complexity of the decoupled-stranded model is far lower than that of the detailed model.

Forced vibrations of size-dependent rods subjected to: impulse, step, and ramp excitations

Forced longitudinal vibration response of nonlocal strain gradient (NLSG) rods is scrutinized and compared with nonlocal (NL), strain gradient (SG), and classical (CL) rods. In this respect, size-dependent kinematics and extended Hamilton’s principle are utilized to derive governing equations of motion. For the first time, forced longitudinal vibratory behavior of non-classical and classical rods is presented including three different types of non-harmonic forcing functions: unit impulse, unit step, and unit ramp. Forcing terms are functions of both temporal and spatial domains. Nonlocal strain gradient and nonlocal rod models take into account the Laplacian of the external forcing term as well. This implies that in models including nonlocal effects (NL, NLSG-h, s, n), forcing term is reduced by the order of its Laplacian with respect to spatial variables. Effect of non-classical parameters over time-domain response of the system is analyzed in details. Results are compared with benchmark for the sake of evaluation. This implies the necessity of adopting proper values of non-classical theory and corresponding parameters through analysis of forced oscillations of small-scaled size-dependent rods. Such external excitations are modeled using spatial Dirac delta function as a concentrated force applying at the critical point of mode shape function. Findings of this research reveal the underlying impact of non-classical theorems along with corresponding non-classical parameters over the prediction of the response of size-dependent rod elements for wide range of applications such as in musical instruments, navigating equipment, gyroscopes, control of robotics, sensors and actuators, resonators, energy harvesters, and vibration control systems.

On the simultaneous use of simple geometrically exact shear-rigid rod and shell finite elements

This work addresses simultaneous use of geometrically exact shear-rigid rod and shell finite elements and describes both models within the same framework. Parameterization of the rotation field is performed by Rodrigues rotation vector, which makes the incremental updating of the rotational variables remarkably simple. For the rod element, cubic Hermitian interpolation for the displacements together with quadratic Lagrange interpolation for the incremental torsion angle were employed, while, for the triangular shell element, a complete quadratic Lagrange interpolation was used. The internal incremental torsion angle resulting from the displacement field within the shell element is then made compatible with the boundary incremental torsion angle of the shell element by an internal Lagrange multiplier. The compatibility between contiguous shell elements as well rod elements is mastered in the standard way by simply connecting nodes. This technique is an important contribution of the work, whose performance is illustrated by several numerical examples.

Microstrip rectangular patch antenna using coplanar parasitic rod elements with substrate integrated feeding line technique

Microstrip antenna technology is fast growing technology in present days there are broadly used in mobile communication and satellite communication. The microstrip antennas are very low cost and low profile and ease fabrication. However, the bandwidth utilization is the drawback for this system. Now proposed methodology can be reduced that drawback and provide efficient bandwidth utilization factor in proposed method design a microstrip rectangular patch antenna using co-planar parasitic rod elements with substrate intergrading feeding line technique. This proposed method, microstrip rectangular patch antenna is designed for the enhancement of bandwidth, Improvement in front to back ratio, reduction in losses and high-quality factor and power handling capability. The proposed method enhances the bandwidth ratio from 4% to 18% it shows that the proposed method gives the best results compared to the existing approach. The simulation and 3D plot results can be obtained from Ansoft HFSS (High-frequency structure simulator) Software.

Plastic stiffness matrix of a plane rod macroelement for discrete-analytical strength computation

The paper considers a discrete-analytical solution of the plane strength problem, with the rod system being under elastic-plastic loading, and the rod performance is considered fundamentally important for the study. Simplifications are proposed in determining the plastic stiffness matrix of the rod element using the integral function of the law of the section state. A mathematical model has been developed to determine the tangential stiffness of a cross-section of the rod of a variable form at a time step, during elastic-plastic camputation. The results of a physically nonlinear calculation of the planar system with the articulation of a large number of rod macro-elements are presented.

Theoretical foundations of the diagram method for calculating rod elements made of reinforced concrete

At the present stage of development, the diagram method for calculating rod elements made of reinforced concrete has a number of disadvantages, which is due to the lack of a single holistic theory. The paper attempts to propose its foundations. For this purpose, the most General structure of the theory has been developed, and a three-level computational model has been proposed, hierarchically built on the principle of the computational scheme discretization: level 1 - “element” - the rod design model, built according to the well-known rules of construction mechanics; level 2 – “cross” – enhanced non-linear (discrete) deformation model, adopted by BC 63.13330 with some significant author’s clarification; level 3 – material – the standard samples’ analysis model of concrete and rerod subject to the axial compressive action or tensile static short-term load or under static short-time load, pure shear (to describe proposed Jenny more deformation curve of concrete). A detailed algorithm for the relationship of models at all three levels is described.

Деформационный расчет и устойчивость стержневых элементов стальных конструкций с несимметричным сечением

To develop practical recommendations for calculating the stability of rod elements of steel structures with an asymmetric cross-section, which is formed as a result of uneven corrosion damage, strengthening or reduction of the cross-section, there is proposed a numerical and analytical solution of the deformation problem, taking into account physical and geometric (according to the spatially deformed scheme) nonlinearities. It allows reducing the calculation time by several orders of magnitude as compared to the existing numerical solutions. The analytical solution of the deformation problem of elastic rods compressed-bent in two planes is based on the qualitative proximity of bending forms of deformation under central compression, namely, sinusoids with corresponding forms obtained by non-deformational calculation, on a square parabola. The latter was replaced by a sinusoid, which allowed obtaining a general solution. The manifestations of physical nonlinearity are compensated by additional loading of the elastic rod with a fictitious force with biaxial eccentricities, which is assessed using the «section» algorithm in the most loaded section, taking into account its spatial displacements. As a result, there was obtained a system of numerical-analytical equilibrium equations in dimensionless parameters, the solutions of which, as the load increases, allow assessing the coefficient of loss of spatial stability.

Совершенствование обратного численно-аналитического метода расчета ЛСТК на устойчивость при внецентренном сжатии

The paper proposes an improved reverse numerical-analytical method for calculating thin-walled cold-formed rod elements for stability, taking into account the loss of local stability and the section shape. The presented approach makes it possible to automate and speed up the process of analytical calculation, which enables quickly obtaining the coefficients of loss of overall stability of rods of the LSTW structures. As a result, a complex and time-consuming calculation process is reduced to using a single formula in combination with the tabular data.