Infinite Element Model Research Articles

A frequency-domain formulation for predicting ground-borne vibration induced by underground train on curved track

The vibration caused by underground trains running on a curved track often has a greater impact on residents, buildings, or sensitive instruments than that of a straight track. A formulation including two frequency-domain models for simulating the generation and propagation of train-induced vibrations is presented in this study. Based on an analytical model of a curved track subjected to moving forces, an approach to determine the wheel–rail contact forces and excitation forces acting on the roadbed from the measured dynamic response of the rails is developed. Frequency-domain excitation forces are applied to a periodic finite element–infinite element model to predict ground-borne vibration. In this model, the tunnel structure and soils in the near field are modelled as finite elements, whereas infinite elements are used to simulate wave propagation in the far-field soils. An experiment to measure the vibrations on the rail and ground surface during train passages in the Beijing metro was conducted to validate the proposed formulation. It is shown that high computational efficiency and accuracy in this formulation can be expected in the prediction of ground-borne vibration in a curved tunnel–soil system.

Study on the Method for Measuring Stress on Rock Mass Excavation Surface under Extremely High Stress Conditions

In view of the limitations of several existing stress measurement methods under extremely high stress conditions ( stress − strength ratio σ / R c > 0.5 ), this paper proposes a slot relief method based on partial deformation recovery to measure rock mass surface stress under extremely high stress conditions and justifies its viability with the help of an infinite element model. This method is then used to measure and study a research tunnel in West China’s Jinping II Hydropower Station, where the maximum stress measured reached 80 MPa. In the process of measurement, this method needs neither complete borehole core nor ultrahigh pressure equipment. On the contrary, the test equipment is easy to carry and operate on, suitable for rock mass surface stress measurement under extremely high stress conditions, and able to provide in situ stress measurements for cavern rockburst prevention and slope management.

Experimental Determination and Modeling of Drying Process of Woody Biomass

Birch is a kind of readily available woody biomass resource, which can be used to crush and manufacture fuel particles and animal bedding. One of the important aspects during the production system is the drying of biomass prior to storage or processing. Moisture migration in wood is a particularly important factor in determining the drying process. The objectives of this study are to investigate the drying characteristics of Birch and develop a model to simulate moisture diffusion in Birch during the drying process. Experiments were conducted in a controlled environment chamber. Different temperatures and relative humidity were set to simulate the different drying conditions. The mechanism of moisture movement in Birch samples during the drying process was represented by a diffusion model according to Fick’s second law. A computer program in Matlab software was developed to simulate the infinite element model. Moisture diffusivity of Birch was determined by minimising the sum of squares of the residuals between experimental results and numerically predicted data. Results showed that the moisture diffusion coefficients of Birch ranged from 1.2×10−7m2/hr to 9.6×10−7m2/hr with temperature varying from 20°C to 60°C. And the trend of diffusion coefficient versus temperature was in accordance with the Arrhenius equation.

A Dual-Coil Method for Electromagnetic Attraction Forming of Sheet Metals

Electromagnetic forming is a novel technology in which a coil is used to generate a pulsed Lorentz force for shaping sheet metal pieces. However, the Lorentz force between the coil and the sheet metal is generally repulsive due to the Lenz’s Law, which limits the practical application of this technology. To break this bottleneck, a dual-coil method is proposed to generate attractive Lorentz force, which is then used to form sheet metals. The theoretical principle of this method is presented, and an infinite element model is established to simulate the forming effect. The simulation results show that an A1060-O plate with a diameter of 140 mm and thickness of 1 mm can be attractively shaped under this method. The maximum axial displacement of the plate reaches 2.74 mm. Unfortunately, a dent exists in this situation. Further analysis indicates that this dent can be eliminated by increasing the inner and outer diameters of the coils. Further, it is found that when the capacitance value of the long pulse-width discharge circuit is set to 5.6 mF and the initial discharge voltage is set to 10.690 kV, the sheet metal attains the best shape.

Dynamic response of soft soils in high-speed rail foundation: in situ measurements and time domain finite element method model

The dynamic response of soil to vibrations induced by moving trains has been widely studied using in situ measurements. However, few in situ tests have been conducted to measure the resulting vibration of foundation soils, especially for the foundation of high-speed rail (HSR) in a soft area. In this study, a number of field experiments were conducted on Shanghai–Hangzhou HSR in a suburb of Shanghai, China. The testing instruments were installed in foundation soils just beneath the HSR track to measure the vibration induced by trains moving at different speeds. Test results show the frequencies of foundation soil vibration are characterized by the train speed and geometrical features of the trains and slab track. In the frequency domain, the dominant frequency bands for vertical acceleration, velocity, and displacement of foundation soil decrease successively. In the time domain, the magnitudes of vibration levels at different locations in a soil foundation decrease gradually with increasing distance from the track. Furthermore, higher train speed can result in higher vibration level. Based on the field conditions, a three-dimensional dynamic finite–infinite element model is developed in the time domain. It shows the model is capable of capturing the primary characteristics of train-induced vibration in the field.

Analysis of the Vibration Mitigation Characteristics of the Ballasted Ladder Track with Elastic Elements

Despite the fact railways are seen as an environmentally friendly and sustainable form of transport, however, the train-induced vibration has been seen as a negative environmental consequence. The ballasted ladder track is one type of ballasted track with longitudinal sleepers. The elastic elements can not only protect the track structure but also control the vibration. To investigate the vibration mitigation effects of ballasted ladder track with elastic elements, a finite element - infinite element (FE-IFE) model was built considering the elastic elements of under-sleeper pads (USPs) and under-ballast mats (UBMs). This model was validated by a laboratory test. Then, the moving train load was obtained based on the multi-body dynamics (MBD)-finite elements method (FEM) analysis. The vibration mitigation effects of the ballasted ladder track with different types of elastic elements were calculated compared with the ballasted tracks without elastic elements. The results indicate that: (1) the ballasted ladder track has the advantage of vibration reduction at low frequencies, with a maximum vibration attenuation of 25.2 dB and an averaged vibration attenuation of 19.0 dB between 5 and 20 Hz through the ballast. (2) The ballasted ladder track with USPs or UBMs can provide better vibration attenuation between 30 and 100 Hz, but it induces a vibration amplification between 5 and 30 Hz. (3) The ballasted ladder track with elastic elements in different cases can provide different vibration mitigation effects. The ballasted ladder track with both USPs and UBMs can provide the best mitigation effect with an average vibration mitigation of approximately 15 dB and a maximum vibration mitigation of 30 dB between 30 and 100 Hz.

Numerical study of isolation in the backfill zone of foundation pit method to reduce railway generated vibration in high‐rise buildings

SummaryThe conventional methods to reduce building vibration include isolation of vibration sources, isolation of buildings, and setting trenches in the propagation path. However, it is evidenced that these methods are not feasible for high‐rise buildings in crowded urban areas. This paper proposes a new method to reduce vibration for high‐rise buildings by using the existing construction backfill zone, the isolation in the backfill zone of foundation pit (IBF). Numerical analyses were first carried out to obtain a realistic excitation time history, and a finite element–infinite element model was developed and calibrated using test data from an actual building site. The contributions of the basement sidewalls and foundation slabs to floor vibration and the influence of infill material properties are investigated. Lastly, a composite isolation layer was suggested to provide both sufficient restraining effects to the building foundation and satisfactory vibration isolation. The analyses confirmed that the proposed IBF method reduces ground‐borne vibration in high‐rise buildings by up to 66% when railway is on the ground.

Dynamic shakedown limits for flexible pavement with cross-anisotropic materials

Shakedown solution is widely used to analyse the elastic-plastic behaviours of structures in pavement design. Previous studies only concerned the shakedown theorem under traffic loads for an isotropic material, although the material is usually anisotropic. This paper firstly proposed a numerical analysis for anisotropic materials under moving traffic load, based on Melan’s lower-bound shakedown theory. An anisotropic Finite Element–Infinite Element (FE–IE) model is used to calculate the dynamic stresses in the anisotropic material subjected to moving traffic loads with different speeds. Then, the shakedown limits for an anisotropic half-space and a two-layered pavement system are determined, respectively. It is found that the Rayleigh wave speed of the soil has a significant effect on the shakedown limits. For a cross-anisotropic half-space, the shakedown limits mainly depend on the stiffness ratio of the two layers and the Poisson’s ratio only has a small effect, although both of them significantly affect the Rayleigh wave speed. Furthermore, the shakedown limit increases with increasing cohesion ratio until it reaches a maximum value, and it gets rid of the control of shakedown condition when the moving speed exceeds the Rayleigh wave speed. For a two-layered anisotropic system, the results are similar to those in an isotropic system. Failure tends to occur on the top of the second layer instead of the first layer when the speed of moving load or the anisotropic Young’s modulus ratio increases, together with the decrease of shakedown limit.

Seismic Response Analysis of Reservoir Water-Gravity Dam-Foundation System

The Scaled boundary finite element method and finite-infinite element method are used to model the system of reservoir water – gravity Dam - infinite foundation. The effect of the reservoir water and the infinite foundation on the seismic response of the dam system is analyzed. In the paper, taking the Koyna gravity dam as the research object, the dynamic water pressure on the upstream face of the dam is calculated by SBFEM. The finite-infinite element method is used to model the infinite foundation. Finally, the time history of seismic displacement and the response of the dam under different elastic modulus are evaluated. By comparing the displacement response of the infinite element model of different elastic modulus, the conclusion is drawn that the response of the dam is increased with the increase of the elastic modulus of the foundation. In addition, the calculated results are compared with those of the model with no-mass foundation. It shows that the results of the model considering the radiation damping of the foundation are less than that of the model with no mass foundation.

Investigation of rail noise and bridge noise using a combined 3D dynamic model and 2.5D acoustic model

Bridge noise and rail noise are two major sources of an elevated rail transit bridge in the low and medium frequency range (20–1000Hz). However, in most of the existing literature, the noise radiated from the bridge and rail was investigated separately or using a simplified source model. In this study, an accurate method is proposed to simulate both the rail noise and bridge noise simultaneously. First, the dynamic responses of the rail and multi-span bridge are obtained using a three-dimensional (3D) vehicle-track-bridge interaction analysis model. Then, the two-dimensional (2D) infinite element model is used to calculate 3D modal acoustic transfer vectors of the rail and bridge based on the wavenumber transformation, in order to overcome the singularity and non-uniqueness of the conventional boundary element method and reduce the computation cost. Third, a field test is conducted, and the accuracy of the proposed simulation procedure is verified. Finally, the contribution of the rail and bridge noise to the total noise level is investigated in the whole space near the bridge. Generally the bridge noise occupies a higher contribution in the space beneath the girder due to the shielding effect of the bridge shape on the rail noise, while the rail noise is dominant in the upper space above the bridge. It is found the presence of the vehicle bodies has considerable effect on the rail noise but little influence on the bridge noise. The slope of the roughness level spectrum has significant influence on the dominant field of bridge noise and rail noise. For the excitation of the assumed ISO roughness level used in this study, the difference between the rail noise and bridge noise is only about 3dB at field points 15–30m away from the track center, which indicates both the bridge and rail noise should be included in the noise prediction for an elevated rail transit bridge.

A Semi-Analytical Approach to Predict Ground Vibration by Identification of Soil Properties and Train-Transit Loads

Train-induced ground vibration problems have become an important subject, as the number of the high speed railroad construction projects rapidly increases worldwide. Various numerical approaches have been proposed and used for the prediction of the train-induced ground vibration. However, the estimation performance has not been satisfactory due to the difficulty in modeling the train-transit loads on railroad structures and the structure-soil interaction system, which are essential for the accurate prediction of ground vibration. In this study, a new semi-analytical method was proposed for the prediction of ground vibration and the evaluation of environmental vibration levels with simple measurements of the ground vibration on the surface. The proposed method does not need any analytical model for inputting the train load. Instead, it identifies the effective train loads acting on the railroad track structure based on the measured ground responses at several locations and the numerical model of the structure-soil interaction system through the identification of the properties of the soil layers. Then, the effective train load is utilized as an input to the structure-soil interaction problem to predict the ground vibrations and the environmental vibration levels of the structures. A finite and infinite element model was utilized to solve the wave propagation problem in the soil medium in the frequency domain. Field validations were carried out at a site where Korea high-speed trains run over an elevated bridge structure. The predicted ground accelerations were found to be in good agreement with the measured data.

Discrete modelling of vertical track–soil coupling for vehicle–track dynamics

This paper presents a coupled lumped mass model (CLM model) for the vertical dynamic coupling of railway track through the soil. The well-known Winkler model and its extensions are analysed and fitted on the result obtained numerically with a finite–infinite element model in order to validate the approach in a preliminary step. A mass–spring–damper system with frequency independent parameters is then proposed for the interaction between the foundations, representing the contact area of the track with the soil. The frequency range of track–soil coupling is typically under 100 Hz. Analytical expressions are derived for calibrating the system model with homogeneous and layered half-spaces. Numerical examples are derived, with emphasis on soil stiffness and layering. The dynamic analysis of a track on various foundation models is compared with a complete track–soil model, showing that the proposed CLM model captures the dynamic interaction of the track with the soil and is reliable to predict the vertical track deflection and the reaction forces acting on the soil surface.

Three dimensional infinite element model to study thermal disturbances in human peripheral region due to tumor

Three dimensional infinite element model to study thermal disturbances in human peripheral region due to tumor

A Two Dimensional Infinite Element Model to Study Temperature Distribution in Human Dermal Regions due to Tumors

In this study, a two dimensional infinite element model has been developed to study thermal effect in human dermal regions due to tumors. This model incorporates the effect of blood mass flow rate, metabolic heat generation and thermal conductivity of the tissues.The dermal region is divided into three natural layers, namely, epidermis, dermis and subdermal tissues. A uniformly perfused tumor is assumed to be present in the dermis. The domain is assumed to be finite along the depth and infinite along the breadth. The whole dermis region involving tumor is modelled with the help of triangular finite elements to incorporate the geometry of the region. These elements are surrounded by infinite domain elements along the breadth. Appropriate boundary conditions has been incorporated. A computer program has been developed to obtain the numerical results.

A parallel finite–infinite element model for two-dimensional soil–structure interaction problems

A parallel soil–structure interaction (SSI) model is presented for applications on distributed computer systems. Substructring method is applied to the SSI system and a coupled finite–infinite element based parallel computer program is developed. In the SSI system, infinite elements are used to represent the soil which extends to infinity. In this case, a large finite element mesh is required to define the near field for reliable predictions. The resulting large-scale problems are solved on distributed computer systems in this study. The domain is represented by separated substructures and an interface. The number of substructures are determined by the available processors in the parallel platform. To avoid the formation of large interface equations, smaller interface equations are distributed to processors while substructure contributions are performed. This saves a lot of memory storage and computational effort. Direct solution techniques are used for the solution of interface and substructure equation systems. The program is investigated through some example problems. The example problems exposed the need for solving large-scale problems in order to reach better results. The results of the example problems demonstrated the benefits of the parallel SSI algorithm.

Wave localization on a submerged cylindrical shell with rib aperiodicity.

The results of a numerical study of vibration localization due to stiffener variability in a framed shell are reported. An axisymmetric finite element (FE)-infinite element model is used to obtain predictions in good general agreement with previously reported experimental results. Over the frequency band of this study, up to three times the ring frequency, two structural resonances dominate the vibratory response of the shell for high circumferential orders (n > 10). Localization is shown to be linked to the sensitivity of the local resonance frequencies of the system to specific geometrical parameters. Specifically, rib thickness variations strongly affect the first pass band, while rib spacing variations strongly affect the second pass band.

Numerical Simulation of Contaminant Transport in One‐Dimensional Infinite Media

Abstract: In this paper, seawater or contaminant intrusion into fresh groundwater in lowland areas is treated as a mass transfer problem in infinite media. For numerical simulation of such problem, a transient infinite element model has been presented to simulate the mass transfer process in infinite media. The main merit of using the present transient finite and infinite element coupled model is that the numerical analysis of contaminant transport problems in infinite media can be carried out using microcomputers. The comparison of the present numerical results with the previous analytical results indicates the accuracy, efficiency and effectiveness of the present infinite element.

A dynamic infinite element for three‐dimensional infinite‐domain wave problems

AbstractA three‐dimensional dynamic infinite element which satisfies the following requirements: (1) displacement compatibility on the interface between finite and infinite elements; (2) definition of the wave propagation and amplitude attenuation behaviours in the infinite element using wave propagation functions; (3) convergence of the generalized integrals related to mass and stiffness matrices of the infinite element: and (4) displacement continuity along the common boundary of neighbouring infinite elements in the case of simulating multiple material layers or multiple wave numbers within the foundation, is presented in this paper. Since P‐waves, S‐waves and R‐waves in the foundation can be simulated Simultaneously in the present infinite element, the seismic response of an arch‐dam‐foundation system, especially a thin double‐curvature arch‐dam‐foundation system where the boundary element loses its competitive capacity with the finite element, can be economically calculated by coupling this infinite element with conventional finite elements. The good accuracy obtained using the present infinite element and finite element coupling model to simulate foundation wave problems has been proven by comparing the current numerical results with previous analytical results.

3‐D infinite boundary elements and simulation of monolithic dam foundations

AbstractBased on the asymptotic behaviour of the fundamental solution for 3‐D elasticity problems, this paper presents an infinite boundary element model (IBEM) and its interpolation form. By using the analytical solution for half‐space under a vertical loading, excellent accuracy of this model has been verified. As an engineering application, the infinite foundation of a monolithic gravity dam was modelled by IBEM and the dam itself by normal BEM, and the displacement and stress distributions of the dam were analysed. It was concluded that large structure and foundation problems can be solved by this coupling system with the advantage of having fewer degrees of freedom and less data preparations. The results also clearly show the great improvement of the 3‐D model for critical stresses of the dam over the 2‐D plane model for narrow canyons having a width‐height ratio less than 2·4. Thus, a more economical cross‐section for dams can be achieved by 3‐D analysis.

Diffraction of waves by semi‐infinite breakwater using finite and infinite elements

AbstractA finite and infinite element model is derived to predict wave patterns around a semi‐infinite breakwater in water of constant depth. Both circular and square meshes of elements are used. The wave theory used is that of Berkhoff. The appropriate boundary conditions for finite and infinite boundaries are described. The singularity in the velocity at the breakwater tip is modelled effectively using the technique of Henshell and Shaw originally developed in elasticity. The results agree well with the analytical solution. In addition the problem of waves incident upon a semi‐infinite breakwater and parabolic shoal, where both diffraction and refraction are present, is solved. There is no analytical solution for this case. The combination of finite and infinite elements is found to be an effective and accurate technique for such problems.