Spatial Finite Element Research Articles

Nonlinear seismic assessment of isolated high-speed railway bridge subjected to near-fault earthquake scenarios

An iterative framework is introduced in this present study to detect seismic isolation precursors of the shortcut calculation method for the isolated benchmark high-speed railway RC bridge. The spatial finite element (FE) analysis model of a benchmark isolated high-speed railway reinforced concrete (RC) bridge system under high-speed railway vehicles is set up based on the equivalent linear method. The vehicle with two bogies is assumed to be represented by a 3 D discrete rigid multi-body system with 23 degrees of freedoms (DOFs). The present study compares the nonlinear seismic response of a high-speed railway bridge with and without isolation bearings. Numerical results demonstrate that the isolation system with the optimal parameters can simultaneously reduce the deck displacement and the internal force of the isolated railway bridge under near-fault (NF) ground motions with various peak accelerations and peak velocity ratios, to ensure the adequate isolation efficiency of isolated structures. Specifically, the study shows that the seismic response of the seismically isolated bridge (IB) and the running safety indexes of the train are primarily dominated by the contents around the fundamental frequency of the train-bridge system subjected to the earthquakes.

Consideration of the Torsional Stiffness in Hollow-Core Slabs’ Design

The paper discusses the principles of precast concrete hollow-core slabs taking into account their spatial work. It is shown that consideration of spatial work makes it possible to determine the forces in individual floor slabs significantly more precise. The fact that strain redistribution between precast floor slabs depends on slabs’ bending and torsional stiffness is shown. The research has been mostly devoted to determination of the bending stiffness with regard to formation of cracks and the change in torsional stiffness, especially considering the presence of normal cracks, which is still unstudied. This paper presents the technique for determining the torsional stiffness of hollow-core slabs with normal cracks. In order to determine the components included in the resolving system of equations, it is proposed to use an approximation method based on the processing of numerical data using spatial finite elements.

Modal analysis of thin parabolic shells

The modal analysis of parabolic shells of revolution is based on using the finite-element model of inhomogeneous shell. The shells can have complex-shaped midsurface, geometrical features throughout the thickness, or multilayer structure. To develop the finite-element shell model we approximate a thin shell by one spatial finite element throughout the thickness. The structural elements of an inhomogeneous shell require the finite element to be universal: it should be eccentrically arranged relative to the mid-surfaces of the casing, it should be possible to vary the thickness of the lateral edges of the finite element and ets. The universal finite element is based on an isoparametric spatial finite element with polylinear shape functions for coordinates and displacements. Additional variable parameters are introduced to enhance the capabilities of the modified finite element. Two hypotheses are used to describe the features of the stress–strain state of a thin inhomogeneous shell. The static hypothesis assumes that the compressive stresses in the fibers throughout the thickness are constant. The nonclassical kinematic hypothesis of deformed straight line is used: a straight segment along the thickness remains straight though stretched or shortened during deformation. This segment is not necessarily normal to the mid-surface of the shell.The stress–strain state of a shell and its structural elements is determined using the geometrically nonlinear equations of the three-dimensional theory of thermoelasticity. A linear elastic continuous medium with large displacements and small strains is used as a model whose properties correspond to the generalized Duhamel–Neumann law. To derive the governing finite-element equations for displacements the moment finite-element scheme is used. The moment finite-element scheme approximations of displacements and strains guarantee a correct description of the rigid-body displacements of finite elements, which enhances the convergence and accuracy of solutions on coarse meshes.The natural vibrations of parabolic shells with various heights have been investigated. The convergence of solutions has been studied and compared with the results obtained by other authors.During operation, realistic shell structures often undergo various changes in the temperature field. This can significantly affect their dynamic characteristics. Extension of this work to modal analysis of parabolic shells considering heating is currently being pursued.

ANALYSIS OF THE DIFFERENCES OF THE RESULTS OF CALCULATIONS OF THE STABILITY COEFFICIENT OF THE LANDSLIDE SLOPE

Purpose . Improving the accuracy of determining the stability of landslide slopes in some cases requires the use of several methods to find the coefficient of stability. Therefore, it is necessary to analyze the discrepancy between the results of the calculation of the coefficient of stability of landslide slopes. Methodology. The solution to the problem of finite element slope modeling in the LIRA-SAPR 2016 software package is based on the creation of a spatial finite element model. With its help, the nonlinear problem of geomechanics was solved with the introduction of special finite elements, which simulates the work of the soil. As a reference, the coefficient of stability was calculated by the round-cylindrical sliding surface method. Landslide slope in the software package «OTKOS» was created and calculated. Results. The results of the calculation of the finite element model of the landslide slope in the LIRA-SAPR 2016 software package were obtained. The value of the coefficient of stability of the landslide-hazardous section of the slope in the «OTKOS» was obtained using eight methods. The calculation results in the «OTKOS» are compared with the coefficient of stability determined by the method of a circular-cylindrical sliding surface. Originality. The results of the calculation of the coefficients of stability in the «OTKOS» allowed us to divide the curves of the sliding surface into two groups: that which do not belong to circular-cylindrical, and that which satisfy the results of finite element modeling. Practical value. After a series of calculations and after analyzing the results, it turned out that not all methods equally solve the problem of the stability of landslide slopes. This is due to the different limitations of each of the methods, so as a criterion for the adequacy of the results obtained, it is necessary to analyze the magnitude of the discrepancy between the obtained values of the coefficient of stability.

Dynamic response of long-span continuous curved box girder bridge under seismic excitation

Form function matrix is created by introducing high order displacement interpolation function in the node. Based on the virtual work principle and dynamic finite element theory, the spatial element stiffness matrix, mass matrix and earthquake mass matrix of a thin-walled box girder having 9 freedom degrees at each node are deduced. The D’Alembert vibration equation is also established. Newmark-β method is used through MATLAB to solve the seismic response of a long-span continuous curved box girder bridge under El-centro seismic waves. Meanwhile the spatial finite element model of the whole bridge is established by ANSYS. The results indicate that the dynamic responses of pier columns exhibit spatiality. The dynamic response of a bridge structure under 2D coupling horizontal seismic excitation is much bigger than that under 1D horizontal seismic excitation. The critical angle of seismic waves is 50° for radial displacement response. Theoretical calculation results are in agreement with the finite element analysis results. The deduced element matrix not only can be used to calculate the seismic response of long-span curved beam bridge structures but also can provide significant references for the structures in vibration response caused by moving traffic.

STRESS-STRAIN STATE ASSESSMENT OF THE BOGIE FRAME OF DPKR-2 DIESEL TRAIN UNDER ACTION OF DESIGN AND OPERATIONAL LOADS

Purpose. The article is aimed to ensure the operation safety, increase in the strength and durability of the most loaded supporting elements of rolling stock – bogies, in particular the bogies of the DPKr-2 diesel train. Methodology. In order to assess the design strength of the bogie prototype, a spatial solid-state 3D model was constructed. Using the software package implementing the finite element method, the most loaded nodes of the bogie frame are determined based on the Palmgren–Miner–Mises theory. During the finite element modeling, the peculiarities of the design work in operation, the action of static loads and the corresponding dynamic additives are taken into account. The results of calculation were used to develop the layout diagram of the strain gauges on the bogie frame during the running strength tests. According to their results, the fatigue strength of the bogie frame prototype under the action of operating loads was estimated and a conclusion was made about the need to strengthen its design. The design management of the PJSC «Kryukov Railway Car Building Works» proposed the variant of enhancing the bogie frame prototype. Findings. Based on the results of theoretical and experimental studies, the prototype design of the DPKr-2 diesel train was modernized, which made it possible to reduce stresses in the most loaded nodes and significantly increase its durability. Strength calculations and running strength tests of diesel trains with modernized bogies were carried out. Originality. For the first time, a spatial finite element model of the new generation diesel train was constructed and the strength calculation was carried out under the action of design loads. The constructed model made it possible to choose the variant of modernizing the frame prototype that satisfies the fatigue strength conditions. The conducted experimental studies have shown the efficiency of modernization, in particular the increase in strength and durability of the design. Practical value. The complex of design and experimental work on the assessment of the stress-strain state of the bogie frame of the DPKr-2 diesel train under the action of design and operating loads allowed creating a design that satisfies both the operational requirements and the requirements of strength and durability. The developed design of the bogie frame makes it possible to increase the operation safety and can be used in the next generation diesel trains.

Fully discrete finite element approximation of unsteady flows of implicitly constituted incompressible fluids

Abstract Implicit constitutive theory provides a very general framework for fluid flow models, including both Newtonian and generalized Newtonian fluids, where the Cauchy stress tensor and the rate of strain tensor are assumed to be related by an implicit relation associated with a maximal monotone graph. For incompressible unsteady flows of such fluids, subject to a homogeneous Dirichlet boundary condition on a Lipschitz polytopal domain $\varOmega \subset \mathbb{R}^d$, $d \in \{2,3\}$, we investigate a fully discrete approximation scheme, using a spatial mixed finite element approximation on general shape-regular simplicial meshes combined with backward Euler time-stepping. We consider the case when the velocity field belongs to the space of solenoidal functions contained in $\textrm{L}^\infty (0,T;\textrm{L}^2(\varOmega )^d)\cap \textrm{L}^q(0,T;\textrm{W}^{1,q}_0(\varOmega )^d)$ with $q\in \left (2d/(d+2), \infty \right )$, which is the maximal range of $q$ with respect to existence of weak solutions. In order to facilitate passage to the limit with the discretization parameters for the sub-range $q \in \left (2d/(d+2), (3d+2)/(d+2) \right )$, we introduce a regularization of the momentum equation by means of a penalty term, and first show convergence of a subsequence of approximate solutions to a weak solution of the regularized problem; we then pass to the limit with the regularization parameter. This is achieved by the use of a solenoidal parabolic Lipschitz truncation method, a local Minty-type monotonicity result, and various weak compactness techniques. For $q \geq (3d+2)/(d+2)$ convergence of a subsequence of approximate solutions to a weak solution can be shown directly, without the regularization term.

НАПРЯЖЕННО-ДЕФОРМИРОВАННОЕ СОСТОЯНИЕ КОНСТРУКЦИЙ КАРКАСА ПРИ ВАРЬИРОВАНИИ СНЕГОВОЙ НАГРУЗКИ

The multi-variant loading of the large-span unique steel covering of the stadium under snow load is considered. The spatial finite element model is developed using LIRA software. The analysis of the existing schemes application of snow loading is carried out according to the codes. Four snow load cases on the stadium's covering are assumed for analysis. The analysis of the stress-strain state of the stadium structures, the selection and verification of sections of the steel covering are performed. The results show that it is necessary to simulate behaviour of a structure under all possible load cases.

Mechanical performance study and parametric analysis of three-tower four-span suspension bridges with steel truss girders

This paper aims to study the mechanical performance of three-tower four-span suspension bridges with steel truss girders, including the static and dynamic characteristics of the bridge system, and more importantly, the influence of structural parameters including the side-main span ratio, sag-to-span ratio and the girder stiffness on key mechanical indices. For this purpose, the Oujiang River North Estuary Bridge which is a three-tower four-span suspension bridge with two main spans of 800m under construction in China is taken as an example in this study. This will be the first three-tower suspension bridge with steel truss girders in the world. The mechanical performance study and parametric analysis are conducted based on a validated three-dimensional spatial truss finite element model established for the Oujiang River North Estuary Bridge using MIDAS Civil. It is found that a relatively small side-main span ratio seems to be quite appropriate from the perspective of mechanical performance. And decreasing the sag-to-span ratio is an effective way to reduce the horizontal force subjected to the midtower and improve the antiskid safety of the main cable, while the vertical stiffness of the bridge will be reduced. However, the girder stiffness is shown to be of minimal significance on the mechanical performance. The findings from this paper can be used for design of three-tower suspension bridges with steel truss girders.

Nonuniform stress state of a hoisting shaft lining as a result of disturbance of the ground freezing technology

The paper deal with the defining stress state of a hoisting shaft lining, lying in the sandy loam, when performing and disturbing the ground freezing technology. The relevance of the performed research lies in the fact that at nonuniform freezing or defrosting, nonuniform stress state is formed, which causes a significant over-stresses of the lining. To research the nonuniform stress state, a spatial finite element model of a hoisting shaft was developed, in which the case of nonuniform ground freezing was simulated. The calculation by the finite-element technique was carried out on the basis of the computational professional complex Structure CAD for Windows. In the course of the analysis, the values of stress state for linings made of reinforced-concrete blocks, B30 concrete, gray and modified cast-iron tubbings. A comparison of the components of stress state for sandy loam at a temperature of -2 °C (freezing), nonuniform freezing and at a temperature of + 8 °C (defrosting) was carried out. It was found that for the proposed geotechnical conditions in the form of soft, water-saturated sandy loam, it is recommended to use a lining made of gray and modified cast-iron tubbings.

Strong and Weak Convergence Rates of a Spatial Approximation for Stochastic Partial Differential Equation with One-sided Lipschitz Coefficient

Strong and weak approximation errors of a spatial finite element method are analyzed for the stochastic partial differential equations (SPDEs) with one-sided Lipschitz coefficients, including the s...

Analysis of non-stationary reaction of elastic shell to impulse load

An effective numerical method for studying non-stationary vibrations of thin elastic shells is proposed. The method is based on the finite element model of a thin elastic inhomogeneous shell and the reduced model created on its basis for the dynamics problems.The finite-element shell model is based on the relations of the three-dimensional theory of thermo-elasticity and is developed with the use a tensor calculus apparatus, a geometrically nonlinear formulation of the problem in increments and the application of the moment finite-element scheme. To develop the finite-element shell model we approximate a thin shell by one spatial finite element throughout the thickness which is an efficient approach. The structural elements of an inhomogeneous shell require the finite element to be universal: it should be eccentrically arranged relative to the mid-surfaces of the casing (of the shell’s sections without stepwise-variable thickness), it should be possible to vary the thickness of the lateral edges of the finite element; the lateral edges of the neighboring finite elements should be in continuous contact; and it should be possible to model sharp bends and the multilayer structure of the shell. The universal finite element is based on an isoparametric spatial finite element with polylinear shape functions for coordinates and displacements. Additional variable parameters are introduced to enhance the capabilities of the modified finite element. Two hypotheses are used to describe the features of the stress–strain state of a thin inhomogeneous shell. The first static hypothesis assumes that the compressive stresses in the fibers throughout the thickness are constant. The next is the nonclassical kinematic hypothesis of deformed straight line: though stretched or shortened during deformation, a straight segment along the thickness remains straight. This segment is not necessarily normal to the mid-surface of the shell.The method for studying non-stationary vibrations of the shells under the action of short-term loads is based on the application of reduced models. The use of the basic nodes method allowed us to develop a simple and effective algorithm for solving this problem. We have transformed a system of coupled differential equations describing the motion of a shell to independent ones. The solution of obtained Cauchy problems is easily found by the well-developed Runge-Kutta numerical method.The possibility of applying the developed method to assess the effect of short-term load on the behavior of a thin-walled structure is shown on the test problems. Convergence of solutions is investigated and a comparison with theoretical data and results obtained with the help of the SCAD software is made.

A novel high-order approximate scheme for two-dimensional time-fractional diffusion equations with variable coefficient

Based on the spatial quasi-Wilson nonconforming finite element method and temporal L2−1σ formula, a fully-discrete approximate scheme is proposed for a two-dimensional time-fractional diffusion equations with variable coefficient on anisotropic meshes. In order to demonstrate the stable analysis and error estimates, several lemmas are provided, which focus on high accuracy about projection and superclose estimate between the interpolation and projection. Unconditionally stable analysis are derived in L2-norm and broken H1-norm. Moreover, convergence result of accuracy O(h2+τ2) and superclose property of accuracy O(h2+τ2) are deduced by combining interpolation with projection, where h andτ are the step sizes in space and time, respectively. And then, the global superconvergence is presented by employing interpolation postprocessing operator. Finally, numerical results are provided to demonstrate the validity of the theoretical analysis.

Variational-based locking-free energy–momentum schemes of higher-order for thermo-viscoelastic fiber-reinforced continua

Locking-free finite elements and energy–momentum time integration schemes are two of the best-known algorithmic improvements of finite element methods. Both are developed since the middle of the eighties of the last century, but usually independently from each other. Therefore, a smart interface between both algorithms is rarely a development goal of the researcher. In this paper, we present such a smart interface, namely the Hu–Washizuprocedure applied to the principle of virtual power. By using of the resulting mixed variational principle, we avoid locking in a spatial finite element discretization of non-isothermal inelastic fiber-reinforced materials, and obtain a family of corresponding higher-order accurate energy–momentum schemes. Thereby, we consider volumetric locking in the matrix material and line locking in the fibers. We show that this reduction of locking in the energy–momentum schemes leads to an increase of the maximum time step size, such that the efficiency of the time integration is improved in the sense that less CPU time is required. This could be shown by using an automatic time step size control with the iteration number of the applied Newton–Raphson scheme as target function. As numerical examples, we consider slender fiber-reinforced structures as a turbine rotor and a lightweight beam consisting of fiber-reinforced trusses. Here, we simulate different combinations of mechanical and thermal Dirichlet and Neumann boundary conditions.

Effects of Wind Barrier Porosity on the Coupled Vibration of a Train-Bridge System in a Crosswind

This paper investigates the effect of wind barrier porosity on the dynamic performance of a railway bridge and the safety of the trains using it. Dynamic analyses were performed on a long-span cabled-stayed bridge in China. The bridge was modeled with spatial finite elements and each vehicle was modeled with a multi-rigid-body system. The wind excitations on the bridge and train were numerically simulated using the aerodynamic coefficients measured by wind tunnel tests. Simulations were conducted of trains passing over the bridge in a crosswind for different wind barrier porosities. The results show that the wind barrier porosity has a great influence on the aerodynamic performance of the bridge and the trains, and the maximum vertical displacement of the bridge increases as the wind barrier porosity increases from 10 to 40%. The effect of porosity on the dynamic responses of the windward train is greater than the effect on the leeward train. When the wind barrier porosity increases from 20 to 40%, derailment factors and offload factors increase significantly for the windward train.

Mechanical Behavior Analysis of Long-span Steel Truss Arch Bridge Based on Static Load Test

In order to inspect mechanical behavior analysis of long-span steel truss arch bridge, the spatial finite element model was established to analyze the mechanical behavior of the structure under static load and mobile load. Static load test of three span continuous steel truss arch bridge was carried out. The strains, deflection and the tension of the slings were measured. Comparison of testing data with the theoretical values obtained from finite element analysis was carried out. The results showed that the strength and stiffness of the bridge met the design requirements, and the static load test results were basically consistent with the theoretical analysis, which verified the mechanical characteristics of the bridge.

Longitudinal Seismic Response of Continuously Welded Track on Railway Arch Bridges

The seismic response of continuously welded track on bridges is seeing increased interest. Taking the railway deck arch bridge as an example, a track–bridge spatial coupling finite element model was established, and the effects of arch rib temperature difference and bridge span layout on rail seismic force were analyzed. The results show that the peak rail seismic force is larger than the maximum expansion force, and thus track constraints should be taken into consideration in railway arch bridge seismic design. The area enclosed by the hysteresis curve of track resistance increases gradually with an increase in dynamic displacement, and under seismic loading the track constraints can be considered to be in a relatively stable state of energy dissipation. The rail seismic forces under different waves varied greatly, so a wave whose spectrum characteristics fit the bridge site well should be used. The beam temperature difference can affect the structural seismic response, but this effect can be ignored when only considering the maximum rail seismic force. With the application of a series of three continuous beams on the arch and the reasonable arrangement of fixed bearings and speed locks, the track longitudinal stress deformation during an earthquake outperforms that of supported beams.

Impact of nonlinearity on bolt forces in multi-bolted joints: A case of the assembly stage

This article concerns modeling, computation and analysis of multi-bolted joints in the assembly stage. The physical joint model is introduced as the assembly of the following three basic subsystems: a set of fasteners (bolts), a flexible joined flange and a contact layer between it and a rigid support. The finite element method (FEM) is used for modeling. Bolts are replaced by the bolt models of the spider type. The joined flange is modeled with spatial finite elements. As a model of the contact layer, the Winkler contact layer model is adopted. The truth of the theorem has been tested, according to which nonlinear characteristics of the contact layer may have an insignificant impact on computational final values of bolt preloads in the case of sequential tightening of the joint. The results of the calculations for the selected multi-bolted joint are given and compared with the experimental results. Conclusions of paramount importance to the engineering practice are comprised.

An Interactive Solution for Lateral-Torsional Buckling of the Mono-Symmetric Beam-Columns with Discrete Lateral Bracings

The beam-column members are widely used in civil structures. These members are subjected simultaneously to the axial load and the bending moment. In this paper, the buckling strength and the bracing stiffness requirement of the mono-symmetric beam-columns with discrete lateral bracing have been investigated. For this purpose, a numerical method based on the finite element analysis is developed to calculate the buckling load-set of the mono-symmetric beam-columns. This proposed method is capable to consider the initial geometric imperfection. The proposed method is compared with the results of experimental and numerical studies obtained by previous researchers and the spatial finite element analysis, which it shows good agreement. Also, by using the matrix form of the energy equation, a closed form solution of the bracing stiffness requirement is suggested for an arbitrary number of bracing points. The P-M interaction curve and formula are presented for mono-symmetric beam-columns. The results show that the peak point of the curve occurs at the P = Pey and M = Peyy0, where Pey is Euler's buckling load. Finally, a parametric study is done to investigate the effects of the eccentricity and degree of mono-symmetry on the buckling strength and bracing stiffness requirement.

Large-eddy simulations of the vortex-induced vibration of a low mass ratio two-degree-of-freedom circular cylinder at subcritical Reynolds numbers

The vortex induced vibration phenomenon of a low mass ratio (m*=2.6) two-degree-of-freedom circular cylinder at subcritical Reynolds numbers (Re=3900, 5300, 11,000) has been investigated by means of large-eddy simulations. A low-dissipative spatial and time discretisation finite element schemes have been implemented and combined with the Wall-Adapting Local-Eddy viscosity (WALE) subgrid-scale model to solve the filtered incompressible flow equations. Several values of the reduced velocity in the range 3 ⩽ U* ⩽ 12 have been considered. The numerical results are extensively compared with available experimental and numerical data. Particular interest has been placed in the region of maximum cross-flow amplitudes, the super-upper branch, where previous high-fidelity numerical simulations have underestimated the peak amplitudes compared with experimental results. The transition between the super-upper and lower branches is also shown and described. The numerical simulations successfully reproduce the three-branch response maximum oscillation amplitudes and associated vortex formation modes. The 2T vortex formation mode, i.e. two triplets of vortices per oscillation period, has been observed to occur in the super-upper branch, for the three different values of the Reynolds number investigated. These results contradict the claim made in previous works [27] that the vortex formation mode in the super-upper branch is Reynolds number dependent. Beats are observed to appear prior the transition from the super-upper to the lower branch. It is argued that they may be related with the coherence and strength of the third vortex shed at the shoulder of the cylinder each half-cycle, which is finally suppressed in the transition to the lower branch.