• Korea-Australia Rheology Journal
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• v.13 no.3
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• pp.131-139
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• 2001

A coupled approach is proposed for the prediction of sheet profile in sheet casting process, which combines one-dimensional analytical method on planar elongational flow region and three-dimensional numerical method on the other region. The strategy is constructed from the observations that the flow domain of sheet casting process can be separated into two parts based old the flow kinematics. The flow field in the central region of sheet, over which the planar elongational flow dominates, is possibly replaced by one-dimensional analytical solution. Then only a partial flow domain near the edge region of sheet, where the flow kinematics cannot be described by the planar elongational flow itself, requires three-dimensional numerical simulation. Good agreement is observed between the coupled approach developed in this study and the full three-dimensional numerical simulation previously developed and reported by the authors. This coupled approach may have provided flexibility with low costs to accommodate a wide range of die sizes in sheet casting process.

• Advances in Computational Design
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• v.5 no.1
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• pp.55-89
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• 2020

For the first time, an accurate analytical solution, based on coupled three-dimensional (3D) piezoelasticity equations, is presented for free vibration analysis of the angle-ply elastic and piezoelectric flat laminated panels under arbitrary boundary conditions. The present analytical solution is applicable to composite, sandwich and hybrid panels having arbitrary angle-ply lay-up, material properties, and boundary conditions. The modified Hamiltons principle approach has been applied to derive the weak form of governing equations where stresses, displacements, electric potential, and electric displacement field variables are considered as primary variables. Thereafter, multi-term multi-field extended Kantorovich approach (MMEKM) is employed to transform the governing equation into two sets of algebraic-ordinary differential equations (ODEs), one along in-plane (x) and other along the thickness (z) direction, respectively. These ODEs are solved in closed-form manner, which ensures the same order of accuracy for all the variables (stresses, displacements, and electric variables) by satisfying the boundary and continuity equations in exact manners. A robust algorithm is developed for extracting the natural frequencies and mode shapes. The numerical results are reported for various configurations such as elastic panels, sandwich panels and piezoelectric panels under different sets of boundary conditions. The effect of ply-angle and thickness to span ratio (s) on the dynamic behavior of the panels are also investigated. The presented 3D analytical solution will be helpful in the assessment of various 1D theories and numerical methods.

• Earthquakes and Structures
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• v.13 no.2
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• pp.131-136
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• 2017

This paper concerns two new analytical approaches for solving high nonlinear vibration equations. Energy Balance method and Hamiltonian Approach are presented and successfully applied for nonlinear vibration equations. In these approaches, there is no need to use small parameters to solve and only with one iteration, high accurate results are reached. Numerical procedures are also presented to compare the results of analytical and numerical ones. It has been established that, the proposed approaches are in good agreement with numerical solutions.

• Geomechanics and Engineering
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• v.28 no.3
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• pp.225-237
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• 2022

Settlement evaluation is important for shallow tunnels in big cities to estimate the settlement that occurs due to the excavation of twin tunnels. The majority of earlier research on analytical solutions, on the other hand, concentrated on calculating the settlement for a single tunnel. This research introduces a procedure to evaluate the settlement induced by the excavation of twin tunnels (two parallel tunnels). In this study, a series of numerical analysis were performed to validate the analytical solution results. Two geological conditions were considered to derive the settlement depending on each case. The analytical and numerical methods were compared, which involved considering many sections and conducting a parametric study; the results have good agreement. Moreover, a comparison of the 3D flat model and 2D (FEM) with the analytical solution shows that in the fill soil, the maximum settlement values were obtained by the analytical solution. In contrast, the values obtained by the analytical solution in the rock is more conservative than those in the fill. Finally, this method was shown to be appropriate for twin tunnels dug side by side by utilizing finite element analysis 3D and 2D (PLAXIS 3D and PLAXIS 2D) to verify the analytical equations. Eventually, it will be possible to use this approach to predict settlement troughs over twin tunnels.

• Structural Engineering and Mechanics
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• v.5 no.3
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• pp.329-338
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• 1997

In this paper a general analytical approach is proposed to analyse the nonlinear response of elastic cable under complex loads. The effect of temperature change on the cable is also considered. From the vertical equilibrium equations of cable, the general analytical formula of vertical displacement is derived. Based on the vertical displacement formula and on the compatibility condition of the cable, the dimensionless equation with respect to cable tension is established. By means of such analytical procedures, the exact solutions of various cable problems can be obtained quickly. The example given in this paper shows that the new procedure is efficient for practical analysis and can be easily implemented by a general computer program without the superposition problem which there has always been in traditional analytical methods.

• Steel and Composite Structures
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• v.17 no.5
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• pp.721-734
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• 2014

In the current study, we consider a new class of analytical periodic solution for free nonlinear vibration of mechanical systems. Hamiltonian approach is applied to analyze nonlinear problems which occur in dynamics. The proposed method doesn't have the limitations of the classical methods and leads us to a high accurate solution by only one iteration. Two well known examples are studied to show the convenience and effectiveness of this approach. Runge-Kutta's algorithm is also applied and the results of it are compared with the Hamiltonian approach. High accuracy of the proposed approach reveals that the Hamiltonian approach can be very useful for other nonlinear practical problems in engineering.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.684-689
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• 2008

In this study, homogenization method combined with the effective interface model for the characterization of properties of the nanoparticulate composites is developed. In order to characterize particle size effect of nanocomposites, effective interface model has been developed. The application range of analytical micromechanics approach is limited because a simple analytical approach is valid only for simple and uniform geometry of fiber particles. Therefore this study focuses on the analysis of mechanical properties of the effect interface through the continuum homogenization method instead of using analytical micromechanics approach. Using the homogenization method, elastic stiffness properties of the effective interface are numerically evaluated and compared with the analytically obtained micromechanics solutions. The suggested homogenization method is expected to be applied to optimization problems for nanocomposite design.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.5
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• pp.505-508
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• 2006

This paper presents a new analytical approach for designing multiloop PI controllers for disturbance rejection in multivariable processes with time delay. The proposed method is based on IMC-PID design approach. To overcome a sluggish load response by dominant pole in the process, the IMC filter is modified to compensate the dominant pole effect. Based on the modified IMC filter, an analytical tuning rule for multiloop PI controller is driven by extending the generalized IMC-PID method for single input/single output (SISO) systems [1] to multi input/multi output (MIMO) systems. Simulation results show that the proposed method gives a satisfactory load performance as well as servo performance in the multiloop system.

• Earthquakes and Structures
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• v.15 no.6
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• pp.687-699
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• 2018

This paper investigates the pseudo-static analysis of reinforced slopes with geosynthetics under the influence of the uniform surcharge to evaluate the maximum tensile force of reinforcements. The analytical approach has basically been used to develop the new practical procedure to estimate both tensile force and its distribution in the height of the slope. The base of developed relationships has been adapted from the conventional horizontal slice method. The limit equilibrium framework and the assumptions of log-spiral failure surface have directly been used for proposed analytical approach. A new analytical approach considering a single layer of non-cohesion soil and the influence of uniform surcharge has been extracted from the 5n equation and 5n unknown parameters. Results of the proposed method illustrated that the location of the surcharge, amount of internal friction and the seismic coefficient have the remarkable effect on the tensile force of reinforcement and might be 2 times increasing on it. Furthermore, outcomes show that the amount of tensile force has directly until 2 times related to the amount of slope angle and its height range. Likewise, it is observed that the highest value of the tensile force in case of slope degree more than 60-degree is observed on the lower layers. While in case of less degree the highest amount of tensile force has been reported on the middle layers and extremely depended to the seismic coefficient. Hence, it has been shown that the tensile force has increased more than 6 times compared with the static condition. The obtained results of the developed procedure were compared with the outcomes of the previous research. A good agreement has been illustrated between the amount results of developed relationships and outcomes of previous research. Maximum 20 and 25 percent difference have been reported in cases of static and seismic condition respectively.

• Proceedings of the KIEE Conference
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• 2008.07a
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• pp.719-720
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• 2008

This paper deals with analytical approach for rotor loss prediction of permanent magnet synchronous generator(PMSG). The rotor losses of synchronous generator are induced by the magnets. Since stator of our model is skewed, slotting effect can be negligible for our PM wind turbine generator. In order to calculate eddy current, this paper derives analytical solutions by the magnetic vector potential. Finally this paper compared analytical result with eddy current density obtained from finite element(FE) calculations using phase current harmonics analysis.