This study was carried out on the background of Sutong Bridge project based on fracture mechanics, aiming at analyzing the growth mechanism of fatigue cracks of a bridge under the load of vehicles. Stress intensity factor (SIF) can be calculated by various methods. Three steel plates with different kinds of cracks were taken as the samples in this study. With the combination of finite element analysis software ABAQUS and the J integral method, SIF values of the samples were calculated. After that, the extended finite element method in the simulation of fatigue crack growth was introduced, and the simulation of crack growth paths under different external loads was analyzed. At last, we took a partial model from the Sutong Bridge and supposed its two dangerous parts already had fine cracks; then simulative vehicle load was added onto the U-rib to predict crack growth paths using the extended finite element method.
The formulation of a plate finite element with so called ‘physical’ shape functions is revisited. The derivation of the ‘physical’ shape functions is based on Hencky-Bollé theory of moderately thick plates. The considered finite element was assessed in the past, and the tests showed that the solution convergence was achieved in a wide range of thickness to in-plane dimensions ratios. In this paper a holistic correctness assessment is presented, which covers three criteria: the ellipticity, the consistency and the inf-sup conditions. Fulfilment of these criteria assures the existence of a unique solution, and a stable and optimal convergence to the correct solution. The algorithms of the numerical tests for each test case are presented and the tests are performed for the considered formulation. In result it is concluded that the finite element formulation passes every test and therefore is a good choice for modeling plate structural elements regardless of their thickness.
Magnetic properties of silicon iron electrical steel are determined by using standardized measurement setups and distinct excitation parameters. Characteristic values for magnetic loss and magnetization are used to select the most appropriate material for its application. This approach is not sufficient, because of the complex material behavior inside electrical machines, which can result in possible discrepancies between estimated and actual machine behavior. The materials’ anisotropy can be one of the problems why simulation and measurement are not in good accordance.With the help of a rotational single sheet tester, the magnetic material can be tested under application relevant field distribution. Thereby, additional effects of hysteresis and anisotropy can be characterized for detailed modelling and simulation.
Underground mining extraction causes the displacement and changes of stress fields in the surrounding rock mass. The determination of the changes is extremely important when the mining activity takes place in the proximity of post-flotation tailing ponds, which may affect the stability of the tailing dams. The deterministic modeling based on principles of continuum mechanics with the use of numerical methods, e.g. finite element method (FEM) should be used in all problems of predicting rock mass displacements and changes of stress field, particularly in cases of complex geology and complex mining methods. The accuracy of FEM solutions depends mainly on the quality of geomechanical parameters of the geological strata. The parameters, e.g. young modulus of elasticity, may require verification through a comparison with measured surface deformations using geodetic methods. This paper presents application of FEM in predicting effects of underground mining on the surface displacements in the area of the KGHM safety pillar of the tailing pond of the OUOW Żelazny Most. The area has been affected by room and pillar mining with roof bending in the years 2008-2016 and will be further exposed to room-and-pillar extraction with hydraulic filling in the years 2017–2019.
This paper deals with the modelling of traction linear induction motors (LIMs) for public transportation. The magnetic end effect inherent to these motors causes an asymmetry of their phase impedances. Thus, if the LIM is supplied from the three-phase symmetrical voltage, its phase currents become asymmetric. This effect must be taken into consideration when simulating the LIMs’ performance. Otherwise, when the motor phase currents are assumed to be symmetric in the simulation, the simulation results are in error. This paper investigates the LIM performance, considering the end-effect induced asymmetry of the phase currents, and presents a comparative study of the LIM performance characteristics in both the voltage and the current mode.
The accurate prediction of iron losses has become a prominent problem in electromagnetic machine design. The basis of all iron loss models is found in the spatial field-locus of the magnetic flux density (B) and magnetic field (H). In this paper the behavior of the measured BH-field-loci is considered in FEM simulation. For this purpose, a vector hysteresis model is parameterized based on the global measurements, which then can be used to reproduce the measurement system and obtain more detailed insights on the device and its local field distribution. The IEM has designed a rotary loss tester for electrical steel, which can apply arbitrary BH-field-loci occurring during electrical machine operation. Despite its simplicity, the proposed pragmatic analytical model for vector hysteresis provides very promising results.
By simulating the actual working conditions of a cable, the temperature variation rule of different measuring points under different load currents was analyzed. On this basis, a three-dimensional finite element model (FEM) was established, and the difference and influence factors between the simulation temperature and the experimental measured value were discussed, then the influence of thermal conductivity on the operating temperature of the conductor layer was studied. Finally, combined with the steady-state thermal conductivity model and the experimental measured data, the relation between thermal conductivity and load current was obtained.
The paper presents a new geotechnical solution indicating a possibility of effective building structures protection. The presented solutions enable minimization of negative effects of underground mining operations. Results of numerical modelling have been presented for an example of design of preventive ditches reducing the influence of mining operations on the ground surface. To minimize the mining damage or to reduce its reach it is reasonable to look for technical solutions, which would enable effective protection of building structures. So far authors concentrated primarily on the development of building structure protection methods to minimize the damage caused by the underground mining. The application of geotechnical methods, which could protect building structures against the mining damage, was not considered so far in scientific papers. It should be noticed that relatively few publications are directly related to those issues and there are no practical examples of effective geotechnical protection. This paper presents a geotechnical solution indicating a possibility of effective protection of building structures. The presented solutions enable minimization of negative effects of underground mining operations. Results of numerical modelling have been presented for an example of design of preventive ditches reducing the influence of mining operations on the ground surface. The calculations were carried out in the Abaqus software, based on the finite element method.
In this study, free and forced vibration responses of carbon nanotube reinforced uniform and tapered composite beams are investigated. The governing differential equations of motion of a carbon nanotube (CNT) reinforced uniform and tapered composite beams are presented in finite element formulation. The validity of the developed formulation is demonstrated by comparing the natural frequencies evaluated using present FEM with those of available in literature. Various parametric studies are also performed to investigate the effect of aspect ratio, percentage of CNT content, ply orientation, and boundary conditions on natural frequencies and mode shapes of a CNT reinforced composite beam. It was observed that the addition of carbon nanotube in fiber reinforced polymer composite (FRP) beam enhances the stiffness of the structure which consequently increases the natural frequencies and alters the mode shapes.
The present paper reports the results of theoretical and experimental studies of the process of die forging a bimetallic door handle intended for the production of a helicopter. The aim of the studies was to develop and implement a technology for die forging of a product with a specific mass similar to that of magnesium alloys which will have, however higher corrosion resistance. Numerical modelling and industrial tests were carried out based on the previously forging processes for an AZ31 alloy door handle. The material for the tests was a bimetallic bar produced by the explosive welding method, in which the core was of alloy AZ31, and the cladding layer was made of 1050A grade aluminium. The studies were conducted for two variants: Variant I – the forging process was mapped by numerical modelling and industrial tests for the die shape and parameters used in the forging of the AZ31 alloy door handle, Variant II – the tool shape was optimized and process parameters were selected so as to obtain a finished product characterized by a continuous Al layer. From the theoretical studies and experimental tests carried out it has been found that the application of the Variant I does not assure that a finished door handle characterized by a continuous cladding layer will be produced. Within this study, a novel method of bimetallic door handle die forging (Variant II) has been developed, which limits the amount of the flash formed and assures the integrity of the cladding layer.
The paper presents a numerical model of the novel design of the axial magnetic bearing with six cylindrical poles. The motivation behind this idea was to eliminate vibrations in rotating machinery due to the axial load. Common conception of such a bearing provides a single component of the electromagnetic force, which is not enough to reduce transverse and lateral vibrations of the armature. The proposed design allows for avoiding wobbling of the disc with the use of a few axial force components that are able to actively compensate the axial load and stabilise the disc in a balanced position. Before a real device is manufactured, a virtual prototype should be prepared. The accurate numerical model will provide essential knowledge about the performance of the axial magnetic bearing.
The present paper addresses the analysis of structural vibration transmission in the presence of structural joints. The problem is tackled from a numerical point of view, analyzing some scenarios by using finite element models. The numerical results obtained making use of this process are then compared with those evaluated using the EN 12354 standard vibration reduction index concept. It is shown that, even for the simplest cases, the behavior of a structural joint is complex and evidences the frequency dependence. Comparison with results obtained by empirical formulas reveals that those of the standards cannot accurately reproduce the expected behavior, and thus indicate that alternative complementary calculation procedures are required. A simple methodology to estimate the difference between numerical and standard predictions is here proposed allowing the calculation of an adaptation term that makes both approaches converge. This term was found to be solution-dependent, and thus should be evaluated for each structure.
Experimental design and computational model for predicting debonding initiation and propagation are of interest of scientists and engineers. The design and model are expected to explain the phenomenon for a wide range of loading rates. In this work, a method to measure and quantify debonding strength at various loading rates is proposed. The method is experimentally verified using data obtained from a static test and a pulse-type dynamic test. The proposed method involves the cohesive zone model, which can uniquely be characterized with a few parameters. Since those parameters are difficult to be measured directly, indirect inference is deployed where the parameters are inferred by minimizing discrepancy of mechanical response of a numerical model and that of the experiments. The main finding suggests that the design is easy to be used for the debonding characterization and the numerical model can accurately predict the debonding for the both loading cases. The cohesive strength of the stress-wave case is significantly higher than that of the static case; meanwhile, the cohesive energy is twice larger.
This paper presents a numerical investigation of the effects of lamination orientation on the fracture behaviour of rectangular steel wires for civil engineering applications using finite element (FE) analysis. The presence of mid-thickness across-the-width lamination changes the cup and cone fracture shape exhibited by the lamination-free wire to a V-shaped fracture with an opening at the bottom/pointed end of the V-shape at the mid-thickness across-the-width lamination location. The presence of mid-width across-the-thickness lamination changes the cup and cone fracture shape of the lamination-free wire without an opening to a cup and cone fracture shape with an opening at the lamination location. The FE fracture behaviour prediction approach adopted in this work provides an understanding of the effects of lamination orientation on the fracture behaviour of wires for civil engineering applications which cannot be understood through experimental investigations because it is impossible to machine laminations in different orientations into wire specimens.
This research presents a method for the simulation of the magneto-mechanical system dynamics taking motion and eddy currents into account. The major contribution of this work leans on the coupling the field-motion problem considering windings as the current forced massive conductors, modelling of the rotor motion composed of two conductive materials and the torque calculation employing the special optimal predictor combined with the modified Maxwell stress tensor method. The 3D model of the device is analysed by the time stepping finite element method. Mechanical motion of the rotor is determined by solving the second order motion equation. Both magnetic and mechanical equations are coupled in the iterative solving process. Presented method is verified by solving the TEAM Workshop Problem 30.
Percutaneous RF ablation is one of alternative treatment for non-surgical liver tumors. Ablative changes in hepatic tissue can be successfully estimated using the finite element method. The authors created a 3D model of a multi-tine applicator immersed in liver tissue, and then determined the optimal values of voltage applied to such an RF electrode, which do not exceed the therapeutic temperature range valid during thermal ablation procedure. Importantly, the simulations were carried out for the RF electric probes with 2 to 5 evenly spaced arms. Additionally, the thermal damage of hepatic tissue for multi-armed applicators working at pre-defined limit values of voltages was established based on the Arrhenius model.
In this paper a scaling approach for the solution of 2D FE models of electric machines is proposed. This allows a geometrical and stator and rotor resistance scaling as well as a rewinding of a squirrel cage induction machine enabling an efficient numerical optimization. The 2D FEM solutions of a reference machine are calculated by a model based hybrid numeric induction machine simulation approach. In contrast to already known scaling procedures for synchronous machines the FEM solutions of the induction machine are scaled in the stator-current-rotor-frequency-plane and then transformed to the torque- speed-map. This gives the possibility to use a new time scaling factor that is necessary to keep a constant field distribution. The scaling procedure is validated by the finite element method and used in a numerical optimization process for the sizing of an electric vehicle traction drive considering the gear ratio. The results show that the scaling procedure is very accurate, computational very efficient and suitable for the use in machine design optimization.
The present paper is devoted to the discussion and review of the non-destructive testing methods mainly based on vibration and wave propagation. In the first part, the experimental methods of actuating and analyzing the signal (vibration) are discussed. The piezoelectric elements, fiber optic sensors and Laser Scanning Doppler Vibrometer (SLDV) method are described. Effective detecting of the flaws needs very accurate theoretical models. Thus, the numerical methods, e.g. finite element, spectral element method and numerical models of the flaws in isotropic and composite materials are presented. Moreover, the detection of the damage in structures, which are subjected to cyclic or static loads, is based on the analyzing of the change in natural frequency of the whole structure, the change of internal impedance of the material and the change in guided waves propagating through the investigated structure. All these cases are characterized in detail. At the end of this paper, several applications of the structural health monitoring systems in machine design and operation are presented.
Based on the example of the pilot area in Kiev the influence of the increased static load on the superstructure of the stress-strain state of the slope was studied. The efficiency of the proposed methodology when considering the work of "home-slope-retaining structure" depending on natural and anthropogenic factors was demonstrated.
Some materials-related microstructural problems calculated using the phase-field method are presented. It is well known that the phase field method requires mesh resolution of a diffuse interface. This makes the use of mesh adaptivity essential especially for fast evolving interfaces and other transient problems. Complex problems in 3D are also computationally challenging so that parallel computations are considered necessary. In this paper, a parallel adaptive finite element scheme is proposed. The scheme keeps the level of node and edge for 2D and level of node and face for 3D instead of the complete history of refinements to facilitate derefinement. The information is local and exchange of information is minimized and also less memory is used. The parallel adaptive algorithms that run on distributed memory machines are implemented in the numerical simulation of dendritic growth and capillary-driven flows.
Numerical methods are mostly used to predict the acoustic pressure inside duct systems. In this paper, the development of a numerical method based on the convected Helmholtz equation to compute the acoustic pressure inside an axisymmetric duct is presented. A validation of the proposed method was done by a comparison with the analytical formulation for simple cases of hard wall and lined ducts. The effect of the flow on the acoustic pressure inside these ducts was then evaluated by computing this field with different Mach numbers.
A numerical method is developed for estimating the acoustic power of any baffled planar structure, which is vibrating with arbitrary surface velocity profile. It is well known that this parameter may be calculated with good accuracy using near field data, in terms of an impedance matrix, which is generated by the discretization of the vibrating surface into a number of elementary radiators. Thus, the sound pressure field on the structure surface can be determined by a combination of the matrix and the volume velocity vector. Then, the sound power can be estimated through integration of the acoustic intensity over a closed surface. On the other hand, few works exist in which the calculation is done in the far field from near field data by the use of radiation matrices, possibly because the numerical integration becomes complicated and expensive due to large variations of directivity of the source. In this work a different approach is used, based in the so-called Propagating Matrix, which is useful for calculating the sound pressure of an arbitrary number of points into free space, and it can be employed to estimate the sound power by integrating over a finite number of pressure points over a hemispherical surface surrounding the vibrating structure. Through numerical analysis, the advantages/disadvantages of the current method are investigated, when compared with numerical methods based on near field data. A flexible rectangular baffled panel is considered, where the normal velocity profile is previously calculated using a commercial finite element software. However, the method can easily be extended to any arbitrary shape. Good results are obtained in the low frequency range showing high computational performance of the method. Moreover, strategies are proposed to improve the performance of the method in terms of both computational cost and speed.
The rigid finite element method (RFEM) has been used mainly for modelling systems with beam-like links. This paper deals with modelling of a single set of electrodes consisting of an upper beam with electrodes, which are shells with complicated shapes, and an anvil beam. Discretisation of the whole system, both the beams and the electrodes, is carried out by means of the rigid finite element method. The results of calculations concerned with free vibrations of the plates are compared with those obtained from a commercial package of the finite element method (FEM), while forced vibrations of the set of electrodes are compared with those obtained by means of the hybrid finite element method (HFEM) and experimental measurements obtained on a special test stand.
The paper presents a model of a rapping system of an electrostatic precipitator. The rapping system consists of a set of collecting electrodes hanging on a suspension bar and braced together in a brushing bar. The suspension and brushing bars are modeled using the rigid finite element method, while the collecting plates are modeled using the hybrid method. The method combines the rigid finite element method with the classical finite element method. As a result, the mass matrix is diagonal. Some results of numerical simulations concerning free vibrations of the collecting plates and the influence of the number of elements, into which the plate is divided, on the vibrations of the rapping system are presented.