Search results for: Curved beam

Authors: Akif Kutlu, Merve Ermis, Nihal Eratlı, Mehmet H. Omurtag

Abstract:

The objective of this study is to investigate the forced vibration analysis of a planar curved beam lying on elastic foundation by using the mixed finite element method. The finite element formulation is based on the Timoshenko beam theory. In order to solve the problems in frequency domain, the element matrices of two nodded curvilinear elements are transformed into Laplace space. The results are transformed back to the time domain by the well-known numerical Modified Durbin’s transformation algorithm. First, the presented finite element formulation is verified through the forced vibration analysis of a planar curved Timoshenko beam resting on Winkler foundation and the finite element results are compared with the results available in the literature. Then, the forced vibration analysis of a planar curved beam resting on Winkler-Pasternak foundation is conducted.

Keywords: Curved beam, dynamic analysis, elastic foundation, finite element method.

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Authors: Janis Šliseris, Karlis Rocens

Abstract:

Optimization of rational geometrical and mechanical parameters of panel with curved plywood ribs is considered in this paper. The panel consists of cylindrical plywood ribs manufactured from Finish plywood, upper and bottom plywood flange, stiffness diaphragms. Panel is filled with foam. Minimal ratio of structure self weight and load that could be applied to structure is considered as rationality criteria. Optimization is done, by using classical beam theory without nonlinearities. Optimization of discreet design variables is done by Genetic algorithm.

Keywords: Curved plywood ribs, genetic algorithm, rationalparameters of ribbed panel, structure optimization.

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Authors: Carlos Mendez Galindo, Toshiro Hayashikawa, Javier Gil Belda

Abstract:

This paper investigates the effectiveness of the use of seismic isolation devices on the overall 3D seismic response of curved highway viaducts with an emphasis on expansion joints. Furthermore, an evaluation of the effectiveness of the use of cable restrainers is presented. For this purpose, the bridge seismic performance has been evaluated on four different radii of curvature, considering two cases: restrained and unrestrained curved viaducts. Depending on the radius of curvature, three-dimensional non-linear dynamic analysis shows the vulnerability of curved viaducts to pounding and deck unseating damage. In this study, the efficiency of using LRB supports combined with cable restrainers on curved viaducts is demonstrated, not only by reducing in all cases the possible damage, but also by providing a similar behavior in the viaducts despite of curvature radius.

Keywords: Nonlinear dynamic response, seismic design, seismic isolation, unseating prevention system.

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Abstract:

The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: Curved stretching sheet, finite difference method, MHD, variable thermal conductivity.

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Authors: P. Kamphikul, P. Krachodnok, R. Wongsan

Abstract:

This paper presents the gain improvement of a sector antenna for mobile phone base station by using the new technique to enhance its gain for microstrip antenna (MSA) array without construction enlargement. The curved woodpile Electromagnetic Band Gap (EBG) has been utilized to improve the gain instead. The advantages of this proposed antenna are reducing the length of MSAs array but providing the higher gain and easy fabrication and installation. Moreover, it provides a fan-shaped radiation pattern, wide in the horizontal direction and relatively narrow in the vertical direction, which appropriate for mobile phone base station. The paper also presents the design procedures of a 1x8 MSAs array associated with U-shaped reflector for decreasing their back and side lobes. The fabricated curved woodpile EBG exhibits bandgap characteristics at 2.1 GHz and is utilized for realizing a resonant cavity of MSAs array. This idea has been verified by both the Computer Simulation Technology (CST) software and experimental results. As the results, the fabricated proposed antenna achieves a high gain of 20.3 dB and the half-power beam widths in the E- and H-plane of 36.8 and 8.7 degrees, respectively. Good qualitative agreement between measured and simulated results of the proposed antenna was obtained.

Keywords: Gain Improvement, Microstrip Antenna Array, Electromagnetic Band Gap, Base Station.

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Authors: M. Zahedian, B. Maraghechi, M. H. Rouhani

Abstract:

A nonlinear model of two-beam free-electron laser (FEL) in the absence of slippage is presented. The two beams are assumed to be cold with different energies and the fundamental resonance of the higher energy beam is at the third harmonic of lower energy beam. By using Maxwell-s equations and full Lorentz force equations of motion for the electron beams, coupled differential equations are derived and solved numerically by the fourth order Runge–Kutta method. In this method a considerable growth of third harmonic electromagnetic field in the XUV and X-ray regions is predicted.

Keywords: Free-electron laser, Higher energy beam, Lowerenergy beam, Two-beam

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Authors: S. C. Kattimani

Abstract:

This article deals with the analysis of active constrained layer damping (ACLD) of smart multiferroic or magneto-electro-elastic doubly curved shells. The kinematics of deformations of the multiferroic doubly curved shell is described by a layer-wise shear deformation theory. A three-dimensional finite element model of multiferroic shells has been developed taking into account the electro-elastic and magneto-elastic couplings. A simple velocity feedback control law is employed to incorporate the active damping. Influence of layer stacking sequence and boundary conditions on the response of the multiferroic doubly curved shell has been studied. In addition, for the different orientation of the fibers of the constraining layer, the performance of the ACLD treatment has been studied.

Keywords: Active constrained layer damping, doubly curved shells, magneto-electro-elastic, multiferroic composite, smart structures.

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Authors: Saroj Kumar Sarangi, M. C. Ray

Abstract:

This paper deals with the analysis of active constrained layer damping (ACLD) of doubly curved laminated composite shells using active fiber composite (AFC) materials. The constraining layer of the ACLD treatment has been considered to be made of the AFC materials. A three dimensional energy based finite element model of the smart doubly curved laminated composite shell integrated with a patch of such ACLD treatment has been developed to demonstrate the performance of the patch on enhancing the damping characteristics of the doubly curved laminated composite shells. Particular emphasis has been placed on studying the effect of variation of piezoelectric fiber orientation angle in the constraining AFC layer on the control authority of the ACLD patch.

Keywords: Active constrained layer damping, Active fibercomposites, Finite element modeling, First order shear deformationtheory.

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Authors: Gholamhosein Khosravi, Mohammad Azadi, Hamidreza Ghezavati

Abstract:

In this paper, vibration of a nonlinear composite beam is analyzed and then an active controller is used to control the vibrations of the system. The beam is resting on a Winkler-Pasternak elastic foundation. The composite beam is reinforced by single walled carbon nanotubes. Using the rule of mixture, the material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are determined. The beam is cantilever and the free end of the beam is under follower force. Piezoelectric layers are attached to the both sides of the beam to control vibrations as sensors and actuators. The governing equations of the FG-CNTRC beam are derived based on Euler-Bernoulli beam theory Lagrange- Rayleigh-Ritz method. The simulation results are presented and the effects of some parameters on stability of the beam are analyzed.

Keywords: Carbon nanotubes, vibration control, piezoelectric layers, elastic foundation.

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Authors: Barenten Suciu, Ryoichi Kinoshita

Abstract:

In this paper, an experimental and theoretical study on the bogie pseudo-hunting motion of a reduced-scale model railway vehicle, running on double-curved rails, is presented. Since the actual bogie hunting motion, occurring for real railway vehicles running on straight rails at high travelling speeds, cannot be obtained in laboratory conditions, due to the speed and wavelength limitations, a pseudo- hunting motion was induced by employing double-curved rails. Firstly, the test rig and the experimental procedure are described. Then, a geometrical model of the double-curved rails is presented. Based on such model, the variation of the carriage rotation angle relative to the bogies and the working conditions of the yaw damper are clarified. Vibration spectra recorded during vehicle travelling, on straight and double-curved rails, are presented and interpreted based on a simple vibration model of the railway vehicle. Ride comfort of the vehicle is evaluated according to the ISO 2631 standard, and also by using some particular frequency weightings, which account for the discomfort perceived during the reading and writing activities. Results obtained in this work are useful for the adequate design of the yaw dampers, which are used to attenuate the lateral vibration of the train car bodies.

Keywords: Double-curved rail, octave analysis, lateral vibration, ride comfort, yaw damper, railway vehicle.

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Authors: Ahmed H. El-Masry, Mohamed A. Dabaon, Tarek F. El-Shafiey, Abd El-Hakim A. Khalil

Abstract:

An experimental study was performed to investigate the behavior and strength of proposed technique to connect reinforced concrete (RC) beam to steel or composite columns. This approach can practically be used in several types of building construction. In this technique, the main beam of the frame consists of a transfer part (part of beam; Tr.P) and a common reinforcement concrete beam. The transfer part of the beam is connected to the column, whereas the rest of the beam is connected to the transfer part from each side. Four full-scale beam-column connections were tested under static loading. The test parameters were the length of the transfer part and the column properties. The test results show that using of the transfer part technique leads to modify the deformation capabilities for the RC beam and hence it increases its resistance against failure. Increase in length of the transfer part did not necessarily indicate an enhanced behavior. The test results contribute to the characterization of the connection behavior between RC beam - steel column and can be used to calibrate numerical models for the simulation of this type of connection.

Keywords: Composite column, reinforced concrete beam, Steel Column, Transfer Part.

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Authors: A. Keshavarz

Abstract:

A physical model for guiding the wave in photorefractive media is studied. Propagation of cos-Gaussian beam as the special cases of sinusoidal-Gaussian beams in photorefractive crystal is simulated numerically by the Crank-Nicolson method in one dimension. Results show that the beam profile deforms as the energy transfers from the center to the tails under propagation. This simulation approach is of significant interest for application in optical telecommunication. The results are presented graphically and discussed.

Keywords: Beam propagation, cos-Gaussian beam, Numerical simulation, Photorefractive crystal.

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Authors: Rinna Tanaka, Carlos Mendez Galindo, Toshiro Hayashikawa

Abstract:

The results show that the bridge equipped with seismic isolation bearing system shows a high amount of energy dissipation. The purpose of the present study is to analyze the overall performance of continuous curved highway viaducts with different bearing supports, with an emphasis on the effectiveness of seismic isolation based on lead rubber bearing and hedge reaction force bearing system consisted of friction sliding bearing and rubber bearing. The bridge seismic performance has been evaluated on six different cases with six bearing models. The effects of the different arrangement of bearing on the deck superstructure displacements, the seismic damage at the bottom of the piers, movement track at the pier-s top and the total and strain energies absorbed by the structure are evaluated. In conclusion, the results provide sufficient evidence of the effectiveness on the use of seismic isolation on steel curved highway bridges.

Keywords: Curved highway viaducts, non-linear dynamic response, seismic damage.

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Authors: T. F. Jin, X. C. Yin, P. B. Qian

Abstract:

The present investigation is concerned with sub-impacts taken placed when a rigid hemispherical-head block transversely impacts against a beam at different locations. Dynamic substructure technique for elastic-plastic impact is applied to solve numerically this problem. The time history of impact force and energy exchange between block and beam are obtained. The process of sub-impacts is analyzed from the energy exchange point of view. The results verify the influences of the impact location on impact duration, the first sub-impact and energy exchange between the beam and the block.

Keywords: Beam, sub-impact, substructure, elastic-plasticity.

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Authors: Thanat Rungsirathana, Vorathit Rungsetthaphat, Shogo Azuma, Nobuhiro Harada

Abstract:

This paper presents a 2-D hydrodynamic model of the ablated plasma when irradiating a 50 μm Al solid target with a single pulsed ion beam. The Lagrange method is used to solve the moving fluid for the ablated plasma production and formation mechanism. In the calculations, a 10-ns-single-pulsed of ion beam with a total energy density of 120 J/cm2, is used. The results show that the ablated plasma was formed after 2 ns of ion beam irradiation and it started to expand right after 4-6 ns. In addition, the 2-D model give a better understanding of pulsed ion beam-solid target ablated plasma production and expansion process clearer.

Keywords: Ablated plasma, pulse ion beam, thin foil solid target, two-dimensional model

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Authors: A. Oonsivilai, A. Suthummapiwat, P.Songsiritthigul

Abstract:

In this research, the use of light beam size to design the adjustable mirror bender is presented. The focused beam line characterized by its size towards the synchrotron light beam line is investigated. The COSMOSWorks is used in all simulation components of curvature adjustment system to analyze in finite element method. The results based on simulation covers the use of applied forces during adjustment of the mirror radius are presented.

Keywords: Light beam-line, mirror bender, synchrotron light machine.

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Authors: Amer S. Al-Yahmadi, T.C. Hsia

Abstract:

This paper seeks to develop simple yet practical and efficient control scheme that enables cooperating arms to handle a flexible beam. Specifically the problem studied herein is that of two arms rigidly grasping a flexible beam and such capable of generating forces/moments in such away as to move a flexible beam along a predefined trajectory. The paper develops a sliding mode control law that provides robustness against model imperfection and uncertainty. It also provides an implicit stability proof. Simulation results for two three joint arms moving a flexible beam, are presented to validate the theoretical results.

Keywords: Sliding mode control, cooperative manipulators.

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Authors: G. W. Ni, Y. M. Zhang, D. L. Jiang, J. N. Chen, X. G. Wang

Abstract:

As an economic and safe structure, Bi-steel is widely used in reinforced concrete with less consumption of steel. In this paper, III Bi-steel concrete beam has been analyzed. Through careful observation and theoretical analysis, the new calculating formulae for structural rigidity and crack have been formulated for this Bi-steel concrete beam. And structural rigidity and the crack features have also been theoretically analyzed.

Keywords: Bi-steel, concrete beam, crack, rigidity.

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Authors: P. Chaipanya, R. Keawchai, W. Sombatsanongkhun, S. Jantaramporn

Abstract:

To manage the demand of wireless communication that has been dramatically increased, switched beam antenna in smart antenna system is focused. Implementation of switched beam antennas at mobile terminals such as notebook or mobile handset is a preferable choice to increase the performance of the wireless communication systems. This paper proposes the low complexity switched beam antenna using single element of antenna which is suitable to implement at mobile terminal. Main beam direction is switched by changing the positions of short circuit on the radiating patch. There are four cases of switching that provide four different directions of main beam. Moreover, the performance in terms of Signal to Interference Ratio when utilizing the proposed antenna is compared with the one using omni-directional antenna to confirm the performance improvable.

Keywords: Switched beam, shorted circuit, single element, signal to interference ratio.

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Authors: A. Keshavarz, Z. Roosta

Abstract:

In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: Paraxial group transformation, nonlocal nonlinear media, Cos-Gaussian beam, ABCD law.

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Authors: Masood Abdollahi, Seyed Naser Moghaddas Tafreshi

Abstract:

Expanded polystyrene (EPS) geofoam is a cellular geosynthetic material that can be used to protect lifelines (e.g. pipelines, electricity cables, etc.) below ground. Post and beam system is the most recent configuration of EPS blocks which can be implemented for this purpose. It provides a void space atop lifelines which allows settlement of the loading surface with imposing no pressure on the lifelines system. This paper investigates the efficiency of the configuration of post-beam system subjected to static loading. To evaluate the soil surface settlement, beam deformation and transferred pressure over the beam, laboratory tests using two different densities for EPS blocks are conducted. The effect of geogrid-reinforcing the cover soil on system response is also investigated. The experimental results show favorable performance of EPS post and beam configuration in protecting underground lifelines. 

Keywords: Beam deformation, EPS block, laboratory test, post-beam system, soil surface settlement.

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Authors: Chih-Jer Lin, Chun-Ying Lee, Chiang-Ho Cheng, Geng-Fung Chen

Abstract:

This paper investigates experimental studies on vibration suppression for a cantilever beam using an Electro-Rheological (ER) sandwich shock absorber. ER fluid (ERF) is a class of smart materials that can undergo significant reversible changes immediately in its rheological and mechanical properties under the influence of an applied electric field. Firstly, an ER sandwich beam is fabricated by inserting a starch-based ERF into a hollow composite beam. At the same time, experimental investigations are focused on the frequency response of the ERF sandwich beam. Second, the ERF sandwich beam is attached to a cantilever beam to become as a shock absorber. Finally, a fuzzy semi-active vibration control is designed to suppress the vibration of the cantilever beam via the ERF sandwich shock absorber. To check the consistency of the proposed fuzzy controller, the real-time implementation validated the performance of the controller.

Keywords: Electro-Rheological Fluid, Semi-active vibration control, shock absorber, fuzzy control, Real-time control.

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Authors: I. Turk Cakir, A. Senol, A. T. Tasci, O. Cakir

Abstract:

We study the anomalous WWγ and WWZ couplings by calculating total cross sections of two processes at the LHeC with electron beam energy Ee=140 GeV and the proton beam energy Ep=7 TeV, and at the FCC-ep collider with the polarized electron beam energy Ee=80 GeV and the proton beam energy Ep=50 TeV. At the LHeC with electron beam polarization, we obtain the results for the difference of upper and lower bounds as (0.975, 0.118) and (0.285, 0.009) for the anomalous (Δκγ, λγ) and (Δκz, λz) couplings, respectively. As for FCC-ep collider, these bounds are obtained as (1.101, 0.065) and (0.320, 0.002) at an integrated luminosity of Lint=100 fb^-1.

Keywords: Anomalous Couplings, Future Circular Collider, Large Hadron electron Collider, W-boson and Z-boson.

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Authors: Xing Feng, Yuanbin Li

Abstract:

Oil spills at sea can cause severe marine environmental damage, including bringing huge hazards to living resources and human beings. In situ burning or chemical dispersant methods can be used to handle the oil spills sometimes, but these approaches will bring secondary pollution and fail in some situations. Oil recovery techniques have also been developed to recover oil using oil skimmer equipment installed on ships, while the hydrodynamic process of the oil flowing through the oil skimmer is very complicated and important for evaluating the recovery efficiency. Based on this, a two-dimensional numerical simulation platform for simulating the hydrodynamic process of the oil flowing through the oil skimmer is established based on the Navier-Stokes equations for viscous, incompressible fluid. Finally, the influence of the design of the flow channel in the curved plane oil skimmer on the hydrodynamic process of the oil flowing through the oil skimmer is investigated based on the established simulation platform.

Keywords: Curved plane oil skimmer, flow channel, CFD, VOF.

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Authors: L. Dahmani, M.Kouane

Abstract:

In this paper are illustrated the principal aspects connected with the numerical evaluation of thermal stress induced by high gradient temperature in the concrete beam. The reinforced concrete beam has many advantages over steel beam, such as high resistance to high temperature, high resistance to thermal shock, Better resistance to fatigue and buckling, strong resistance against, fire, explosion, etc. The main drawback of the reinforced concrete beam is its poor resistance to tensile stresses. In order to investigate the thermal induced tensile stresses, a numerical model of a transient thermal analysis is presented for the evaluation of thermo-mechanical response of concrete beam to the high temperature, taking into account the temperature dependence of the thermo physical properties of the concrete like thermal conductivity and specific heat.

Keywords: Cracking, Gradient Temperature, Reinforced Concrete beam, Thermo-mechanical analysis.

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Authors: Mohamed Sanad, Noha Hassan

Abstract:

A multi-beam BTS (Base Transceiver Station) antenna has been developed using dual parabolic cylindrical reflectors. The ±45° polarization feeds are used in spatial diversity MIMO (Multi-Input Multi-Output). They can be replaced by single-port orthogonally polarized feeds. Then, with two sets of beams generated above each other, the ± 45° polarization ports of any conventional transceiver can be connected to two of these beam sets. Thus, with two-port transceivers, the system will be equivalent to 4x4 MIMO, instead of 2x2. Radio Frequency (RF) power combiners/splitters can also be used to combine the multiple beams into a single beam or any arbitrary number of beams/ports. The gain of the combined-beam will be more than 20-24 dBi instead of 17-18 dBi of conventional wide-beam antennas. Furthermore, the gain of the combined beam will be high over the whole beam angle. Moreover, the users will always be close to the peak gain value of the combined beam regardless of their location within the combined beam angle. The frequency bands of all the combined beams are adjusted such that they all have the same frequency band. Different configurations of RF power splitter/combiners can be used to provide any arbitrary number of beams/ports according to the requirements of any existing base station configuration.

Keywords: 5G mobile communications, BTS antennas, MIMO, orthogonally polarized antennas, multi-beam antennas.

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Authors: Khaled Alnefaie

Abstract:

In this study, rotating flexible shaft-disk system having flexible beams is considered as a dynamic system. After neglecting nonlinear terms, torsional vibration of the shaft-disk system and lateral and longitudinal vibration of the flexible beam are still coupled through the motor speed. The system has three natural frequencies; the flexible shaft-disk system torsional natural frequency, the flexible beam lateral and longitudinal natural frequencies. Eigenvalue calculations show that while the shaft speed changes, torsional natural frequency of the shaft-disk system and the beam longitudinal natural frequency are not changing but the beam lateral natural frequency changes. Beam lateral natural frequency stays the same as the nonrotating beam lateral natural frequency ωb until the motor speed ωm is equal to ωb. After then ωb increases and remains equal to the motor speed ωm until the motor speed is equal to the shaft-disk system natural frequency ωT. Then the beam lateral natural frequency ωb becomes equal to the natural frequency ωT and stays same while the motor speed ωm is increased. Modal amplitudes and phase angles of the vibrations are also plotted against the motor speed ωm.

Keywords: Rotor dynamics, beam-shaft coupling, beam vibration, flexible shaft.

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Authors: Xi Pei, Ruifen Cao, Hui Liu, Chufeng Jin, Mengyun Cheng, Huaqing Zheng, Yican Wu, FDS Team

Abstract:

In intensity modulated radiation therapy (IMRT) treatment planning, beam angles are usually preselected on the basis of experience and intuition. Therefore, getting an appropriate beam configuration needs a very long time. Based on the present situation, the paper puts forward beam orientation optimization using ant colony optimization (ACO). We use ant colony optimization to select the beam configurations, after getting the beam configuration using Conjugate Gradient (CG) algorithm to optimize the intensity profiles. Combining with the information of the effect of pencil beam, we can get the global optimal solution accelerating. In order to verify the feasibility of the presented method, a simulated and clinical case was tested, compared with dose-volume histogram and isodose line between target area and organ at risk. The results showed that the effect was improved after optimizing beam configurations. The optimization approach could make treatment planning meet clinical requirements more efficiently, so it had extensive application perspective.

Keywords: intensity modulated radiation therapy, ant colonyoptimization, Conjugate Gradient algorithm

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Authors: P. D. Pastuszak

Abstract:

The present work is devoted to thermographic studies of curved composite panels (unidirectional GFRP) with subsurface defects. Various artificial defects, created by inserting PTFE stripe between individual layers of a laminate during manufacturing stage are studied. The analysis is conducted both with the use finite element method and experiments. To simulate transient heat transfer in 3D model with embedded various defect sizes, the ANSYS package is used. Pulsed Thermography combined with optical excitation source provides good results for flat surfaces. Composite structures are mostly used in complex components, e.g., pipes, corners and stiffeners. Local decrease of mechanical properties in these regions can have significant influence on strength decrease of the entire structure. Application of active procedures of thermography to defect detection and evaluation in this type of elements seems to be more appropriate that other NDT techniques. Nevertheless, there are various uncertainties connected with correct interpretation of acquired data. In this paper, important factors concerning Infrared Thermography measurements of curved surfaces in the form of cylindrical panels are considered. In addition, temperature effects on the surface resulting from complex geometry and embedded and real defect are also presented.

Keywords: Active thermography, finite element analysis, composite, curved structures, defects.

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Authors: Babak H. Mamamqani, Alimohammad Entezarmahdi

Abstract:

There are many researches on parameters affecting seismic behavior of steel moment frames. Great deal of these researches considers cover plate connections with or without haunch and direct beam to column connection for exterior columns. Also there are experimental results for interior connections with equal beam depth on both sides but not much research has been performed on the seismic behavior of joints with unequal beam depth. Based on previous experimental results, a series of companion analyses have been set up considering different beam height and connection detailing configuration to investigate the seismic behavior of the connections. Results of this study indicate that when the differences between beams height on both side increases, use of haunch connection system leads to significant improvement in the seismic response whereas other configurations did not provide satisfying results.

Keywords: Analytical modeling, Haunch connection, Seismic design, Unequal beam depth.

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