Analysis of a typical railway turnout sleeper system using grillage beam analogy

A simplified grillage beam analogy was performed to investigate the behaviour of railway turnout sleeper system with a low value of elastic modulus on different support moduli. This study aimed at determining an optimum modulus of elasticity for an emerging technology for railway turnout application - fibre composites sleeper. The finite element simulation suggests that the changes in modulus of elasticity of sleeper, E_sleeper and the sleeper support modulus, U_s have a significant influence on the behaviour of turnout sleepers. The increase in U_s from 10 to 40 MPa resulted in a 15% reduction in the bending moment while the increase in E_sleeper from 1 GPa to 10 GPa has resulted in almost 75% increase in the bending moment. The shear forces in turnout sleepers is not sensitive to both the changes of the E_sleeper and U_s while the sleeper with low E_sleeper tend to undergo greater settlement into the ballast. An E_sleeper of 4 GPa was found optimal for an alternative fibre composite turnout sleeper provided that the U_s is at least 20 MPa from the consideration of sleeper ballast pressure and maximum vertical deflection. It was established that the turnout sleeper has a maximum bending moment of 19 kN-m and a shear force of 158 kN under service conditions.     

On rotating circular disks with varying material properties

Taking Young’s modulus, thermal expansion coefficient and density to be the functions of the radial coordinate, a closed form solution of rotating circular disks made of functionally graded materials subjected to a constant angular velocity and a uniform temperature change is proposed in this paper. Excellent agreement with the solution from Mathematica 5.0 indicates the correctness of the proposed closed form solution. Distributions of the radial displacement and stresses in the disks are determined with the proposed approach and how material properties, temperature change, geometric size and different material coefficients affect deformations and stresses is investigated.     

On rotating circular disks with varying material properties

Taking Young’s modulus, thermal expansion coefficient and density to be the functions of the radial coordinate, a closed form solution of rotating circular disks made of functionally graded materials subjected to a constant angular velocity and a uniform temperature change is proposed in this paper. Excellent agreement with the solution from Mathematica 5.0 indicates the correctness of the proposed closed form solution. Distributions of the radial displacement and stresses in the disks are determined with the proposed approach and how material properties, temperature change, geometric size and different material coefficients affect deformations and stresses is investigated.     

Reliability analysis and maintenance decision for railway sleepers using track condition information

This paper describes the development of a model which can be used to evaluate the reliability of a sleeper system when the sleeper condition is known. Two cases that are of particular interest to the railway industry are investigated. These are the failure of a sleeper system caused by at least two consecutive failed sleepers and by at least three consecutive failed ones, respectively. A model to optimize sleeper maintenance is proposed, which minimizes the number of sleepers restored during immediate maintenance subject to meeting the requirements of reliable and safe sleeper operation. Finally, an example is given to illustrate the model.     

Nonlinear analysis of thin rectangular plates on Winkler–Pasternak elastic foundations by DSC–HDQ methods

This article introduces a coupled methodology for the numerical solution of geometrically nonlinear static and dynamic problem of thin rectangular plates resting on elastic foundation. Winkler–Pasternak two-parameter foundation model is considered. Dynamic analogues Von Karman equations are used. The governing nonlinear partial differential equations of the plate are discretized in space and time domains using the discrete singular convolution (DSC) and harmonic differential quadrature (HDQ) methods, respectively. Two different realizations of singular kernels such as the regularized Shannon’s kernel (RSK) and Lagrange delta (LD) kernel are selected as singular convolution to illustrate the present DSC algorithm. The analysis provides for both clamped and simply supported plates with immovable inplane boundary conditions at the edges. Various types of dynamic loading, namely a step function, a sinusoidal pulse, an N-wave pulse, and a triangular load are investigated and the results are presented graphically. The effects of Winkler and Pasternak foundation parameters, influence of mass of foundation on the response have been investigated. In addition, the influence of damping on the dynamic analysis has been studied. The accuracy of the proposed DSC–HDQ coupled methodology is demonstrated by the numerical examples.     

Vibrations of a beam-string complex system under a moving force

In this paper, the dynamic response of an Euler-Bernoulli beam and string system traversed by a constant moving force is considered. The force is moving with a constant velocity on the top beam. The complex system is finite, simply supported, parallel one upon the other and continuously coupled by a linear Winkler elastic element. The classical solution of the response of a beam-string system subjected to a force moving with a constant velocity has a form of an infinite series. The main goal of this paper is to show that in the considered case the aperiodic part of the solution can be presented in a closed, analytical form instead of an infinite series. The presented method of finding the solution in a closed, analytical form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations. The dynamic influence lines of complex systems may be used for the analysis the complex models of moving load. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-dimensional vehicle-ballasted track-subgrade interaction: Model construction and numerical analysis

In this work a three-dimensional vehicle-ballasted track-subgrade interaction model is developed, where the vehicle is modeled as a multi-rigid-body system, the track-subgrade interaction is modelled by finite element method (FEM) with the rail modelled as beam elements, the sleeper and the subgrade layers modelled as solid elements, and the vehicle and the track-subgrade system are coupled by unified matrix formulations and solved simultaneously and time-dependently. As the modelling advancement, the versatility for FEM construction of track-subgrade systems has been promoted, where the elemental scale can be arbitrarily chosen without consideration of the node-to-node matching principle as the conventional methods; besides the vehicle and the track-subgrade systems have been coupled effectively by wheel-rail contact models. The applicability of various wheel-rail contact models has been discussed, and to reveal the effectiveness of this model in solving engineering problems such as the soil elasticity unevenness and the contact break of “hanging sleepers”, numerical examples have also been presented with referencable conclusions.     

动态环板元的动刚度矩阵

本文对于环形薄板单元取包含贝塞尔函数的谐振变形作为形状函数,解决了关于特殊函数的复杂积分问题.从而精确推导了环形单元的动刚度矩阵,并用直接刚度法进行了校核.接着,又着重于将封闭形式的动刚度矩阵,按频率平方的升幂式展开,得到了简洁完备的结果,以此作为结构动力特性分析和响应计算的基础.     

Numerical electroseismic modeling: A finite element approach

Electroseismics is a procedure that uses the conversion of electromagnetic to seismic waves in a fluid-saturated porous rock due to the electrokinetic phenomenon. This work presents a collection of continuous and discrete time finite element procedures for electroseismic modeling in poroelastic fluid-saturated media. The model involves the simultaneous solution of Biot’s equations of motion and Maxwell’s equations in a bounded domain, coupled via an electrokinetic coefficient, with appropriate initial conditions and employing absorbing boundary conditions at the artificial boundaries. The 3D case is formulated and analyzed in detail including results on the existence and uniqueness of the solution of the initial boundary value problem. Apriori error estimates for a continuous-time finite element procedure based on parallelepiped elements are derived, with Maxwell’s equations discretized in space using the lowest order mixed finite element spaces of Nédélec, while for Biot’s equations a nonconforming element for each component of the solid displacement vector and the vector part of the Raviart-Thomas-Nédélec of zero order for the fluid displacement vector are employed. A fully implicit discrete-time finite element method is also defined and its stability is demonstrated. The results are also extended to the case of tetrahedral elements. The 2D cases of compressional and vertically polarized shear waves coupled with the transverse magnetic polarization (PSVTM-mode) and horizontally polarized shear waves coupled with the transverse electric polarization (SHTE-mode) are also formulated and the corresponding finite element spaces are defined. The 1D SHTE initial boundary value problem is also formulated and approximately solved using a discrete-time finite element procedure, which was implemented to obtain the numerical examples presented.     

Partial cubes: structures, characterizations, and constructions

Partial cubes are isometric subgraphs of hypercubes. Structures on a graph defined by means of semicubes, and Djokovi?’s and Winkler’s relations play an important role in the theory of partial cubes. These structures are employed in the paper to characterize bipartite graphs and partial cubes of arbitrary dimension. New characterizations are established and new proofs of some known results are given.The operations of Cartesian product and pasting, and expansion and contraction processes are utilized in the paper to construct new partial cubes from old ones. In particular, the isometric and lattice dimensions of finite partial cubes obtained by means of these operations are calculated.     

Unilateral elastic subsoil of Winkler’s type: Semi-coercive beam problem

The mathematical model of a beam on a unilateral elastic subsoil of Winkler’s type and with free ends is considered. Such a problem is non-linear and semi-coercive. The additional assumptions on the beam load ensuring the problem solvability are formulated and the existence, the uniqueness of the solution and the continuous dependence on the data are proved. The cases for which the solutions need not be stable with respect to the small changes of the load are described. The problem is approximated by the finite element method and the relation between the original problem and the family of approximated problems is analyzed. The error estimates are derived in dependence on the smoothness of the solution, the load and the discretization parameter of the partition. This work was supported by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AVOZ 30860518.     

Response of fly ash-reinforced functionally graded rubber composites subjected to mechanical loading

A novel approach to estimate the Young’s modulus of a functionally graded rubber composite (FGRC) from the damping ratio is demonstrated with the examples of unreinforced and fly ash-reinforced materials. FGRC coupons were prepared using the conventional casting technique. The occurrence of gradation in the specimens was attributed to the variable density of particles present in the fly ash, settling at different depths. The technique of free vibrations was used for experimentation. The damping response of the FGRC specimens was studied. The results obtained from the experiments showed that, with growing filler weight fraction, the Young’s modulus of the composite increased. The empirical model developed to predict the magnitude of the modulus turned out to be in good agreement with experimental data.     

Solvability of a dynamic contact problem between a piezoelectric body and a conductive foundation

We consider a mathematical model which describes the dynamic process of contact between a piezoelectric body and an electrically conductive foundation. We model the material’s behavior with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the normal compliance condition and a regularized electrical conductivity condition. We derive a variational formulation for the problem and then, under a smallness assumption on the data, we prove the existence of a unique weak solution to the model. We also investigate the behavior of the solution with respect the electric data on the contact surface and prove a continuous dependence result. Then, we introduce a fully discrete scheme, based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. We treat the contact by using a penalized approach and a version of Newton’s method. We implement this scheme in a numerical code and, in order to verify its accuracy, we present numerical simulations in the study of two-dimensional test problems. These simulations provide a numerical validation of our continuous dependence result and illustrate the effects of the conductivity of the foundation, as well.     

Influence of friction in material characterization in microindentation measurement

A comprehensive computational study is undertaken to identify the influence of friction in material characterization by indentation measurement based on elasto- plastic solids. The impacts of friction on load versus indentation depth curve, and the values of calculated hardness and Young’s modulus in conical and spherical indentations are shown in this paper. The results clearly demonstrate that, for some elasto-plastic materials, the curves of load versus indentation depth obtained either by spherical or conical indenters with different friction coefficients, cannot be distinguished. However, if utilizing the parameter β (see text for details), to quantify the deformation of piling-up or sinking-in, it is easy to find that the influence of friction on piling-up or sinking-in in indentation is significant. Therefore, the material parameters which are related to the projected area will also have a large error caused by the influence of friction. The maximum differences on hardness and Young’s modulus can reach 14.59% and 6.78%, respectively, for some elastic materials shown in this paper. These results do not agree with those from researchers who stated that the instrumented indentation experiments are not significantly affected by friction.     

Non-linear analysis of the consolidation of an elastic saturated soil with incompressible fluid and variable permeability by FEM

Research interest in the mechanical behaviour of soils is growing as a result of an increasing number of geomechanical problems involving consolidation effects. The main aim of this paper is to validate and to solve a model for consolidation of an elastic saturated soil with incompressible fluid and variable permeability. Firstly, we prove the existence and uniqueness of the solution of the variational problem corresponding to an initial and boundary value problem (IBVP): a special case of the Biot’s ‘consolidation of clay’ model (where the applied forces depend on time). Secondly, we prove the convergence of the method using a technique based on the proof of solution’s existence. Finally, we then solved this constitutive model by the finite element method (FEM) employing repeated fixed point techniques in order to obtain the results for displacement and pore water pressure. The pore fluid is considered incompressible. The results of the numerical experiments are compared with analytical solutions and, in cases where such solutions do not exist, with experimental data. Therefore, the model can be used for quantitative predictions of consolidation behaviour of soils with permeability dependent on the settlement.     

Methods of analysing ropes. The extension–torsion method

Two new approaches are used for calculating the stress–strain state of a rope and its stiffnesses. The first approach relies on the theory of fibrous composites and Saint-Venant's solution for a cylinder with helical anisotropy. The second approach is based on the solution by the finite element method of the three-dimensional problem of elasticity theory for a solid inhomogeneous cylinder formed by a finite number of elastic fibres arranged in helical lines and connected by a weak filler (in the sense that its Young's modulus is several orders of magnitude less than the Young's modulus of the fibre). The behaviour of the stiffness when the modulus of elasticity of the filler tends to zero is analysed, and the results of the limiting transition are discussed. The numerical results obtained are compared with calculations by other well-known applied theories.     

Nonlinear resonances of a semi-infinite cable on a nonlinear elastic foundation

The Multiple Time Scale (MTS) method is applied to the study of nonlinear resonances of a semi-infinite cable resting on a nonlinear elastic foundation, subject to a constant uniformly distributed load and to a linear viscous damping force. The zero order solution provides the static displacement, which is governed by a nonlinear equation which has been solved in closed form. The first order solution provides the linear resonances, which are seen to be functions of the nonlinearity parameter and of the static displacement at the finite boundary only. Although the first-order governing equation is linear, it has non constant coefficients and cannot be solved in closed form, so that a numerical solution is considered; the eigenfrequencies obtained in this way are also compared with the approximate eigenvalues obtained by the WKB method. At the second order of the MTS expansion, we see that the solution is independent of the intermediate time scale; some additional terms are present, including a time-independent shift of the average position of the oscillations. Finally, the nonlinear frequency–amplitude response curves, which are investigated in detail and which represent the main result of this work, are obtained from the solvability condition at the third order.     

Radical cube zero weakly symmetric algebras and support varieties

One of our main results is a classification of all the weakly symmetric radical cube zero finite dimensional algebras over an algebraically closed field having a theory of support via the Hochschild cohomology ring satisfying Dade’s Lemma. In the process we give a characterization of when a finite dimensional Koszul algebra has such a theory of support in terms of the graded centre of the Koszul dual.     

Application of Nelder-Mead simplex method for unconfined seepage problems

In unconfined seepage problems, the phreatic line resulted from mesh deforming methods is rarely a smooth and continuous curve. The main problem is at the meeting point of the phreatic line with the down stream face of the dam where the phreatic line must be tangent to the seepage face according to the fluid continuity principle. In this paper a mesh deforming finite element method based on Nelder-Mead simplex optimization is presented to solve this problem. The phreatic line is approximated by a 4th degree polynomial and Nelder-Mead simplex method is used to calculate the polynomial’s coefficients minimizing an error function which is introduced based on the conditions on the phreatic line. Tangentiality of the phreatic line to the seepage face is introduced in the solution by a constraint in optimization procedure. The results of the presented method are verified by the results of the nonlinear finite element and other mesh deforming methods.     

Finite element based nonlinear dynamic response of elastically supported piezoelectric functionally graded beam subjected to moving load in thermal environment with random system properties

The second order statistics in terms of mean and standard deviation (SD) of normalized nonlinear transverse dynamic central deflection (NTDCD) response of un-damped elastically supported functionally graded materials (FGMs) beam with surface-bonded piezoelectric layers under the action of moving load are investigated in this paper. The random system properties such as Young's modulus, Poisson's ratio, density, thermal expansion coefficients, piezoelectric materials, volume fraction exponent and external loading are modeled as uncorrelated random variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics combined with Newton–Raphson technique through Newmark's time integrating scheme using finite element method (FEM). The non-uniform temperature distribution with temperature dependent material properties is taken into consideration for consideration of thermal loading. The one parameter Pasternak elastic foundation with Winkler cubic nonlinearity is considered as an elastic foundation. The stochastic based second order perturbation technique (SOPT) and direct Monte Carlo simulation (MCS) are adopted for the solution of nonlinear dynamic governing equation. The influences of volume fraction exponents, temperature increments, moving loads and velocity, nonlinearity, slenderness ratios, foundation parameters and external loadings with random system properties on the NTDCD are examined. The capability of present stochastic model in predicting the NTDCD statistics are compared by studying their convergence with the existing results those available in the literature.