Search results for: Equivalent stiffness

Authors: T. Hirata, G. H. Yokoyama, L. H. M. Duque

Abstract:

The posteroanterior manipulation technique is usually include in the procedure of the lumbar spine to evaluate the intervertebral motion according to mechanical resistance. The mechanical device with visual feedback was proposed that allows one to analysis the lumbar segments mobility “in vivo" facilitating for the therapist to take its treatment evolution. The measuring system uses load cell and displacement sensor to estimate spine stiffness. In this work, the device was tested by 2 therapists, female, applying posteroanterior force techniques to 5 volunteers, female, with frequency of approximately 1.2-1.8 Hz. A test-retest procedure was used for 2 periods of day. The visual feedback results small variation of forces and cycle time during 6 cycles rhythmic application. The stiffness values showed good agreement between test-retest procedures when used same order of maximum forces.

Keywords: Biomechanics, lumber spine stiffness, intervertebral manipulation device, visual feedback

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová, Vladimír Habán

Abstract:

A mathematical model of the additional effects of the liquid in the hydrodynamic gap is presented in the paper. An incompressible viscous fluid is considered. Based on computational modeling are determined the matrices of mass, stiffness and damping. The mathematical model is experimentally verified.

Keywords: Computational modeling, mathematical model, hydrodynamic gap, matrices of mass, stiffness and damping.

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Authors: J. H. Kim, J. H. Kwon, J. S. Park, K. J. Lim

Abstract:

This paper has been investigated a technique that predicts the performance of a bar-type unimorph piezoelectric vibration actuator depending on the frequency. This paper has been proposed an equivalent circuit that can be easily analyzed for the bar-type unimorph piezoelectric vibration actuator. In the dynamic analysis, rigidity and resonance frequency, which are important mechanical elements, were derived using the basic beam theory. In the equivalent circuit analysis, the displacement and bandwidth of the piezoelectric vibration actuator depending on the frequency were predicted. Also, for the reliability of the derived equations, the predicted performance depending on the shape change was compared with the result of a finite element analysis program.

Keywords: Actuator, performance, piezoelectric, unimorph.Actuator, performance, piezoelectric, unimorph.

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Authors: Anas M. Fares

Abstract:

The configuration of shear walls in plan of building will affect the seismic design of structure. The position of these walls will change the stiffness of each floor in the structure, the diaphragm center of mass displacement, and the drift of floor. Structural engineers preferred to distribute the walls in buildings to make the center of mass almost close enough to the center of rigidity, but to make this condition satisfied, they have many choices: construct the walls on the perimeter, or use intermediate walls, or use walls as core. In this paper and by using ETABS, each case is studied and compared to other cases according to three parameters: lateral stiffness, diaphragm displacement, and drift. It is found that the core walls are the best choice for the position of the walls in the buildings to resist earthquake loads.

Keywords: Lateral loads, lateral displacement, reinforced concrete, shear wall, seismic, ASCE7-16 code, ACI code, stiffness, drift.

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Authors: Anas M. Fares

Abstract:

The using of finite element programs in analyzing and designing buildings are becoming very popular, but there are many engineers still using the tributary area method (TAM) in designing the structural members such as columns. This study is an attempt to investigate the accuracy of the TAM results with different load condition (gravity and lateral load), different floors numbers, and different columns stiffness's. To conduct this study, linear elastic analysis in ETABS program is used. The results from finite element method are compared to those obtained from TAM. According to the analysis of the data obtained, it can be seen that there is significance difference between the real load carried by columns and the load which is calculated by using the TAM. Thus, using 3-D models are the best choice to calculate the real load effected on columns and design these columns according to this load.

Keywords: Tributary area method, finite element method, ETABS, lateral load, axial loads, reinforced concrete, stiffness, multi-floor buildings.

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Authors: Haider AlAbadi, Joe Petrolito, Nelson Lam, Emad Gad

Abstract:

In areas of low to moderate seismicity many building contents and equipment are not positively fixed to the floor or tied to adjacent walls. Under seismic induced horizontal vibration, such contents and equipment can suffer from damage by either overturning or impact associated with rocking. This paper focuses on the estimation of shock on typical contents and equipment due to rocking. A simplified analytical model is outlined that can be used to estimate the maximum acceleration on a rocking object given its basic geometric and mechanical properties. The developed model was validated against experimental results. The experimental results revealed that the maximum shock acceleration can be underestimated if the static stiffness of the materials at the interface between the rocking object and floor is used rather than the dynamic stiffness. Excellent agreement between the model and experimental results was found when the dynamic stiffness for the interface material was used, which was found to be generally much higher than corresponding static stiffness under different investigated boundary conditions of the cushion. The proposed model can be a beneficial tool in performing a rapid assessment of shock sensitive components considered for possible seismic rectification. 

Keywords: Impact, shock, earthquakes, rocking, building contents, overturning.

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Authors: G. H. Majzoob, B. Sharifi Hamadani

Abstract:

Mapping between local and global coordinates is an important issue in finite element method, as all calculations are performed in local coordinates. The concern arises when subparametric are used, in which the shape functions of the field variable and the geometry of the element are not the same. This is particularly the case for C* elements in which the extra degrees of freedoms added to the nodes make the elements sub-parametric. In the present work, transformation matrix for C1* (an 8-noded hexahedron element with 12 degrees of freedom at each node) is obtained using equivalent C0 elements (with the same number of degrees of freedom). The convergence rate of 8-noded C1* element is nearly equal to its equivalent C0 element, while it consumes less CPU time with respect to the C0 element. The existence of derivative degrees of freedom at the nodes of C1* element along with excellent convergence makes it superior compared with it equivalent C0 element.

Keywords: Mapping, Finite element method, C* elements, Convergence, C0 elements.

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Authors: Nicolò Vaiana, Giorgio Serino

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In this paper, a one-dimensional (1d) Parallel Elasto- Plastic Model (PEPM), able to simulate the uniaxial dynamic behavior of seismic isolators having a continuously decreasing tangent stiffness with increasing displacement, is presented. The parallel modeling concept is applied to discretize the continuously decreasing tangent stiffness function, thus allowing to simulate the dynamic behavior of seismic isolation bearings by putting linear elastic and nonlinear elastic-perfectly plastic elements in parallel. The mathematical model has been validated by comparing the experimental force-displacement hysteresis loops, obtained testing a helical wire rope isolator and a recycled rubber-fiber reinforced bearing, with those predicted numerically. Good agreement between the simulated and experimental results shows that the proposed model can be an effective numerical tool to predict the forcedisplacement relationship of seismic isolators within relatively large displacements. Compared to the widely used Bouc-Wen model, the proposed one allows to avoid the numerical solution of a first order ordinary nonlinear differential equation for each time step of a nonlinear time history analysis, thus reducing the computation effort, and requires the evaluation of only three model parameters from experimental tests, namely the initial tangent stiffness, the asymptotic tangent stiffness, and a parameter defining the transition from the initial to the asymptotic tangent stiffness.

Keywords: Base isolation, earthquake engineering, parallel elasto-plastic model, seismic isolators, softening hysteresis loops.

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Authors: M. Ghareh, L. Sepahi

Abstract:

Temperature rise in a transformer depends on variety of parameters such as ambient temperature, output current and type of the core. Considering these parameters, temperature rise estimation is still complicated procedure. In this paper, we present a new model based on simple electrical equivalent circuit. This method avoids the complication associated to accurate estimation and is in very good agreement with practice.

Keywords: Thermal modeling, temperature rise, equivalent thermal circuit.

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Authors: M. Salih Taci, N. Tayebi, I. Bozkır

Abstract:

In this paper, the equivalent circuit of the ideal single-phase power transformer with its appropriate voltage current measurement was presented. The calculated values of the voltages and currents of the different connections single phase normal transformer and the results of the simulation process are compared. As it can be seen, the calculated results are the same as the simulated results. This paper includes eight possible different transformer connections. Depending on the desired voltage level, step-down and step-up application transformer is considered. Modelling and analysis of a system consisting of an equivalent source, transformer (primary and secondary), and loads are performed to investigate the combinations. The obtained values are simulated in PSpice environment and then how the currents, voltages and phase angle are distributed between them is explained based on calculation.

Keywords: Transformer, simulation, equivalent model, parallel series combinations.

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Authors: Zhaohao Wang, Lan Shu

Abstract:

In this paper, we generalize some propositions in [C.Z. Wang, D.G. Chen, A short note on some properties of rough groups, Comput. Math. Appl. 59(2010)431-436.] and we give some equivalent conditions for rough subgroups. The notion of minimal upper rough subgroups is introduced and a equivalent characterization is given, which implies the rough version of Lagranges Theorem.

Keywords: Lower approximations, Upper approximations, Rough sets, Rough groups, Lagrange

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Authors: Md Rashadul Islam, Mesbah U. Ahmed, Rafiqul A. Tarefder

Abstract:

This study evaluates the back calculation of stiffness of a pavement section on Interstate 40 (I-40)in New Mexico through numerical analysis. Falling Weight Deflectometer (FWD) test has been conducted on a section on I-40. Layer stiffness of the pavement has been backcalculated by a backcalculation software, ELMOD, using the FWD test data. Commercial finite element software, ABAQUS, has been used to develop the Finite Element Model (FEM) of this pavement section. Geometry and layer thickness are collected from field coring. Input parameters i.e. stiffnesses of different layers of the pavement are used as the backcalculated ones. Resulting surface deflections at different radial distances from the FEM analysis are compared with field FWD deflection values. It shows close agreement between the FEM and FWD outputs. Therefore, the FWD test method can be considered to be a reliable test procedure for evaluating the in situ stiffness of pavement material.

Keywords: Falling weight deflectometer test, Finite element model, Flexible pavement, moduli, surface deflection.

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Authors: Xie Kefeng, Zhang He

Abstract:

For the stability and control demand of offshore small floating platform, a 2-HUS/U parallel mechanism was presented as offshore platform. Inverse kinematics was obtained by institutional constraint equation, and the dynamic model of offshore 2-HUS/U parallel platform was derived based on rigid body’s Lagrangian method. The equivalent moment of inertia, damping and driving force/torque variation of offshore 2-HUS/U parallel platform were analyzed. A numerical example shows that, for parallel platform of given motion, system’s equivalent inertia changes 1.25 times maximally. During the movement of platform, they change dramatically with the system configuration and have coupling characteristics. The maximum equivalent drive torque is 800 N. At the same time, the curve of platform’s driving force/torque is smooth and has good sine features. The control system needs to be adjusted according to kinetic equation during stability and control and it provides a basis for the optimization of control system.

Keywords: 2-HUS/U platform, Dynamics, Lagrange, Parallel platform.

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Authors: Ridha Salhi, Mondher Labidi, Fethi Choubani

Abstract:

Metamaterials have attracted much attention in recent years because of their electromagnetic exquisite proprieties. We will present, in this paper, the modeling of three metamaterial structures by equivalent circuit model. We begin by modeling the SRR (Split Ring Resonator), then we model the HIS (High Impedance Surfaces), and finally, we present the model of the CPW (Coplanar Wave Guide). In order to validate models, we compare the results obtained by an equivalent circuit models with numerical simulation.

Keywords: Metamaterials, SRR, HIS, CPW, IDC.

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Authors: S. W. Lo, S.-H. Lu, Y. H. Guo, L.-C. Hsu

Abstract:

In this paper a novel design of aerostatic thrust bearing is proposed and is analyzed numerically. The capillary restrictor and bearing disk are made of elastomer like silicone and PU. The viscoelasticity of elastomer helps the capillary expand for more air flux and at the same time, allows conicity of the bearing surface to form when the air pressure is enhanced. Therefore the bearing has the better ability of passive compensation. In the present example, as compared with the typical model, the new designs can nearly double the load capability and offer four times static stiffness.

Keywords: Aerostatic, bearing, elastomer, static stiffness.

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Authors: Himanshu V. Gajjar, Anish H. Gandhi, Tanvir A Jafri, Harit K. Raval

Abstract:

Bendability is constrained by maximum top roller load imparting capacity of the machine. Maximum load is encountered during the edge pre-bending stage of roller bending. Capacity of 3-roller plate bending machine is specified by maximum thickness and minimum shell diameter combinations that can be pre-bend for given plate material of maximum width. Commercially available plate width or width of the plate that can be accommodated on machine decides the maximum rolling width. Original equipment manufacturers (OEM) provide the machine capacity chart based on reference material considering perfectly plastic material model. Reported work shows the bendability analysis of heavy duty 3-roller plate bending machine. The input variables for the industry are plate thickness, shell diameter and material property parameters, as it is fixed by the design. Analytical models of equivalent thickness, equivalent width and maximum width based on power law material model were derived to study the bendability. Equation of maximum width provides bendability for designed configuration i.e. material property, shell diameter and thickness combinations within the machine limitations. Equivalent thicknesses based on perfectly plastic and power law material model were compared for four different materials grades of C-Mn steel in order to predict the bend-ability. Effect of top roller offset on the bendability at maximum top roller load imparting capacity is reported.

Keywords: 3-Roller bending, Bendability, Equivalent thickness, Equivalent width, Maximum width.

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Authors: Dong Wook Lee

Abstract:

This paper presents a method to analyze the stiffness of the expansion joint with structural support using a hybrid method combining computational and analytical methods. Many expansion joints found in tubes and ducts of mechanical structures are designed to absorb thermal expansion mismatch between their structural members and deal with misalignments introduced from the assembly/manufacturing processes. One of the important design perspectives is the system’s vibrational characteristics. We calculate the stiffness as a characterization parameter for structural joint systems using a combined Finite Element Analysis (FEA) and an analytical method. We apply the methods to two sample applications: external configurations of aircraft engines and nuclear power plant structures.

Keywords: Expansion joint, expansion joint stiffness, Finite Element Analysis, FEA, nuclear power plants, aircraft engine external configurations.

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Authors: M. Collins, B. O’Regan, T. Cosgrove

Abstract:

To determine the potential of a low cost Irish engineered timber product to replace high cost solid timber for use in bending active structures such as gridshells a single Irish engineered timber product in the form of orientated strand board (OSB) was selected. A comparative study of OSB and solid timber was carried out to determine the optimum properties that make a material suitable for use in gridshells. Three parameters were identified to be relevant in the selection of a material for gridshells. These three parameters are the strength to stiffness ratio, the flexural stiffness of commercially available sections, and the variability of material and section properties. It is shown that when comparing OSB against solid timber, OSB is a more suitable material for use in gridshells that are at the smaller end of the scale and that have tight radii of curvature. Typically, for solid timber materials, stiffness is used as an indicator for strength and engineered timber is no different. Thus, low flexural stiffness would mean low flexural strength. However, when it comes to bending active gridshells, OSB offers a significant advantage. By the addition of multiple layers, an increased section size is created, thus endowing the structure with higher stiffness and higher strength from initial low stiffness and low strength materials while still maintaining tight radii of curvature. This allows OSB to compete with solid timber on large scale gridshells. Additionally, a preliminary sustainability study using a set of sustainability indicators was carried out to determine the relative sustainability of building a large-scale gridshell in Ireland with a primary focus on economic viability but a mention is also given to social and environmental aspects. For this, the Savill garden gridshell in the UK was used as the functional unit with the sustainability of the structural roof skeleton constructed from UK larch solid timber being compared with the same structure using Irish OSB. Albeit that the advantages of using commercially available OSB in a bending active gridshell are marginal and limited to specific gridshell applications, further study into an optimised engineered timber product is merited.

Keywords: Bending active gridshells, High end timber structures, Low cost material, Sustainability.

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová

Abstract:

The article presents two mathematical models of the interaction between a rotating shaft and an incompressible fluid. The mathematical model includes both the journal bearings and the axially traversed hydrodynamic sealing gaps of hydraulic machines. A method is shown for the identification of additional effects of the fluid acting on the rotor of the machine, both for a linear and a nonlinear model. The interaction is expressed by matrices of mass, stiffness and damping.

Keywords: CFD modeling, hydrodynamic gap, matrices of mass, stiffness and damping, nonlinear mathematical model.

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Authors: Parvinder S. Sandhu, Iqbaldeep Kaur, Amit Verma, Inderpreet Kaur, Birinderjit S. Kalyan

Abstract:

This work is a proposed model of CMOS for which the algorithm has been created and then the performance evaluation of this proposition has been done. In this context, another commonly used model called ZSTT (Zero Switching Time Transient) model is chosen to compare all the vital features and the results for the Proposed Equivalent CMOS are promising. In the end, the excerpts of the created algorithm are also included

Keywords: Dual Capacitor Model, ZSTT, CMOS, SPICEMacro-Model.

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Authors: Anas M. Fares, A. Touqan

Abstract:

A common approach in resisting lateral forces is the use of reinforced concrete shear walls in buildings. These walls represent the main elements to resist the lateral forces due to their large strength and stiffness. However, such walls may contain many openings due to functional requirements, and this may largely affect the overall lateral stiffness of them. It is thus of prime importance to quantify the effect of openings on the dynamic performance of the shear walls. SAP2000 structural analysis program is used as a main source after verifying the results. This study is made by using linear elastic analysis. The results are compared to ASCE7-16 code empirical equations for estimating the fundamental period of shear wall structures. Finally, statistical regression is used to fit an equation for estimating the increase in the fundamental period of shear-walled regular structures due to windows openings in the walls.

Keywords: Concrete, earthquake-resistant design, finite element, fundamental period, lateral stiffness, linear analysis, modal analysis, rayleigh, SAP2000, shear wall, ASCE7-16.

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Authors: Ming-Chu Yin, Ping-An Du

Abstract:

The shielding ability of a shielding cavity with an aperture will be greatly degraded at resonance frequencies, and the resonance modes and frequencies are affected by aperture resonances and aperture-cavity coupling, which are closely related with aperture sizes. The equivalent circuit method and numerical method of Transmission Line Matrix (TLM) are used to analyze the effects of aperture resonances and aperture-cavity coupling on the electromagnetic resonances of a cavity with an aperture in this paper. Both analytical and numerical results show that the resonance modes of a shielding cavity with an aperture consist of cavity resonance modes and aperture resonance modes, and the resonance frequencies will shift with the change of the aperture sizes because of the aperture resonances and aperture-cavity coupling. Variation rules of electromagnetic resonances with aperture sizes for a cavity with an aperture are given, which will be useful for design of shielding cavities.

Keywords: Aperture-cavity coupling, equivalent circuit method, resonances, shielding equipment.

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Authors: V. Polenta, S. D. Garvey, D. Chronopoulos, A. C. Long, H. P. Morvan

Abstract:

A parametric study on circular thin-walled pipes subjected to pure bending is performed. Both straight and curved pipes are considered. Ratio D/t, initial pipe curvature and internal pressure are the parameters varying in the analyses. The study is mainly FEA-based. It is found that negative curvatures (opposite to bending moment) considerably increase stiffness and buckling limit of the pipe when no internal pressure is acting and, similarly, positive curvatures decrease the stiffness and buckling limit. For internal pressurised pipes the effects of initial pipe curvature are less relevant. Results show that this phenomenon is in relationship with the cross-section deformation due to bending moment, which undergoes relevant ovalisation for no pressurised pipes and little ovalisation for pressurised pipes.

Keywords: Buckling, curved pipes, internal pressure, ovalisation, pure bending, thin-walled pipes.

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Authors: Alexander Winkler, Jozef Suchý

Abstract:

This paper investigates simple implicit force control algorithms realizable with industrial robots. A lot of approaches already published are difficult to implement in commercial robot controllers, because the access to the robot joint torques is necessary or the complete dynamic model of the manipulator is used. In the past we already deal with explicit force control of a position controlled robot. Well known schemes of implicit force control are stiffness control, damping control and impedance control. Using such algorithms the contact force cannot be set directly. It is further the result of controller impedance, environment impedance and the commanded robot motion/position. The relationships of these properties are worked out in this paper in detail for the chosen implicit approaches. They have been adapted to be implementable on a position controlled robot. The behaviors of stiffness control and damping control are verified by practical experiments. For this purpose a suitable test bed was configured. Using the full mechanical impedance within the controller structure will not be practical in the case when the robot is in physical contact with the environment. This fact will be verified by simulation.

Keywords: Damping control, impedance control, robot force control, stability, stiffness control.

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Authors: Gemma A. Gruyal

Abstract:

Plants can contain a wide variety of substances with antioxidative properties which are associated with important health benefits. These positive health effects are of great importance at a time when the environment is laden with many toxic substances. Five selected herbal plants namely, Mimosa pudica, Phyllanthus niruri, Ceiba pentandra, Eleusine polydactyla and Trema amboinensi, were chosen for the experiment to investigate their total phenolics content and antioxidant activities using ABTS radical cation decolorization power, and ferric reducing antioxidant power. The total phenolic content of each herbal plants ranges from 0.84 to 42.59 mg gallic acid equivalent/g. The antioxidant activity in the ABTS radical cation decolorization power varies from 0.005 to 0.362 mg trolox equivalent/g and the FRAP ranges from 0.30 to 28.42 mg gallic acid equivalent/g. Among the five medicinal plants, Mimosa pudica has been an excellent performer in terms of the 3 parameters measured; it is followed by Phyllanthus niruri. The 5 herbal plants do not have equivalent antioxidant power. The relative high values for M. pudica and P. niruri supports the medicinal value of both plants. The total phenolics, ABTS and FRAP correlate strongly with one another.

Keywords: ABTS, FRAP, leaf extracts, phenol.

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Authors: Ayman M. Othman, Hassan Y. Ahmed

Abstract:

This paper discusses the effect of using blast furnace iron slag as a part of fine aggregate on the mechanical performance of hot mix asphalt (HMA). The mechanical performance was evaluated based on various mechanical properties that include; Marshall/stiffness, indirect tensile strength and unconfined compressive strength. The effect of iron slag content on the mechanical properties of the mixtures was also investigated. Four HMA with various iron slag contents, namely; 0%, 5%, 10% and 15% by weight of total mixture were studied. Laboratory testing has revealed an enhancement in the compressive strength of HMA when iron slag was used. Within the tested range of iron slag content, a considerable increase in the compressive strength of the mixtures was observed with the increase of slag content. No significant improvement on Marshall/stiffness and indirect tensile strength of the mixtures was observed when slag was used. Even so, blast furnace iron slag can still be used in asphalt paving for environmental advantages.

Keywords: Blast furnace iron slag, HMA, Marshall/stiffness, indirect tensile strength, compressive strength.

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Authors: Muhammad E. Rahman, Trevor Orr

Abstract:

This paper presents the use of three-dimensional finite elements coupled with infinite elements to investigate the ground vibrations at the surface in terms of the peak particle velocity (PPV) due to construction of the first bore of the Dublin Port Tunnel. This situation is analysed using a commercially available general-purpose finite element package ABAQUS. A series of parametric studies is carried out to examine the sensitivity of the predicted vibrations to variations in the various input parameters required by finite element method, including the stiffness and the damping of ground. The results of this study show that stiffness has a more significant effect on the PPV rather than the damping of the ground.

Keywords: Finite Elements, PPV, Tunnelling, Vibration

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Authors: P. Nagendra, S. Halder nee Dey, S. Paul, T. Datta

Abstract:

This paper presents a methodology to assess the voltage stability status combined with optimal power flow technique using an instantaneous two-bus equivalent model of power system incorporating static var compensator (SVC) and thyristor controlled series compensator (TCSC) controllers. There by, a generalized global voltage stability indicator being developed has been applied to a robust practical Indian Eastern Grid 203-bus system. Simulation results have proved that the proposed methodology is promising to assess voltage stability of any power system at any operating point in global scenario. Voltage stability augmentation with the application of SVC at the weakest bus and TCSC at critical line connected to the weakest bus is compared with the system having no compensation. In the proposed network equivalent model the generators have been modeled more accurately considering economic criteria.

Keywords: Equivalent two-bus model, global voltage security indicator, optimal power flow, SVC, TCSC.

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Authors: Kaman M. O., Celik N.

Abstract:

In this study, stress distributions on dental implants made of functionally graded biomaterials (FGBM) are investigated numerically. The implant body is considered to be subjected to axial compression loads. Numerical problem is assumed to be 2D, and ANSYS commercial software is used for the analysis. The cross section of the implant thread varies as varying the height (H) and the width (t) of the thread. According to thread dimensions of implant and material properties of FGBM, equivalent stress distribution on the implant is determined and presented with contour plots along with the maximum equivalent stress values. As a result, with increasing material gradient parameter (n), the equivalent stress decreases, but the minimum stress distribution increases. Maximum stress values decrease with decreasing implant radius (r). Maximum von Mises stresses increases with decreasing H when t is constant. On the other hand, the stress values are not affected by variation of t in the case of H = constant.

Keywords: Functionally graded biomaterials, dental implant finite element method.

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Authors: Emin Z. Mahmud

Abstract:

This paper presents the observations from a series of shaking-table tests done on a 1:1 scaled confined masonry wall model, with opening for a door – specimens CMDuS (confined masonry wall with opening for a door before strengthening) and CMDS (confined masonry wall with opening for a door after strengthening). Frequency and stiffness changes before and after GFRP (Glass Fiber Reinforced Plastic) wall strengthening are analyzed. Definition of dynamic properties of the models was the first step of the experimental testing, which enabled acquiring important information about the achieved stiffness (natural frequencies) of the model. The natural frequency was defined in the Y direction of the model by applying resonant frequency search tests. It is important to mention that both specimens CMDuS and CMDS are subjected to the same effects. The tests are realized in the laboratory of the Institute of Earthquake Engineering and Engineering Seismology (IZIIS), Skopje. The specimens were examined separately on the shaking table, with uniaxial, in-plane excitation. After testing, samples were strengthened with GFRP and re-tested. The initial frequency of the undamaged model CMDuS is 13.55 Hz, while at the end of the testing, the frequency decreased to 6.38 Hz. This emphasizes the reduction of the initial stiffness of the model due to damage, especially in the masonry and tie-beam to tie-column connection. After strengthening of the damaged wall, the natural frequency increases to 10.89 Hz. This highlights the beneficial effect of the strengthening. After completion of dynamic testing at CMDS, the natural frequency is reduced to 6.66 Hz.

Keywords: Behavior of masonry structures, Eurocode, fundamental frequency, masonry, shaking table test, strengthening.

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