• 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.

• Smart Structures and Systems
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• v.13 no.4
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• pp.587-614
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• 2014

In recent years the interest in online monitoring of lightweight structures with ultrasonic guided waves is steadily growing. Especially the aircraft industry is a driving force in the development of structural health monitoring (SHM) systems. In order to optimally design SHM systems powerful and efficient numerical simulation tools to predict the behaviour of ultrasonic elastic waves in thin-walled structures are required. It has been shown that in real industrial applications, such as airplane wings or fuselages, conventional linear and quadratic pure displacement finite elements commonly used to model ultrasonic elastic waves quickly reach their limits. The required mesh density, to obtain good quality solutions, results in enormous computational costs when solving the wave propagation problem in the time domain. To resolve this problem different possibilities are available. Analytical methods and higher order finite element method approaches (HO-FEM), like p-FEM, spectral elements, spectral analysis and isogeometric analysis, are among them. Although analytical approaches offer fast and accurate results, they are limited to rather simple geometries. On the other hand, the application of higher order finite element schemes is a computationally demanding task. The drawbacks of both methods can be circumvented if regions of complex geometry are modelled using a HO-FEM approach while the response of the remaining structure is computed utilizing an analytical approach. The objective of the paper is to present an efficient method to couple different HO-FEM schemes with an analytical description of an undisturbed region. Using this hybrid formulation the numerical effort can be drastically reduced. The functionality of the proposed scheme is demonstrated by studying the propagation of ultrasonic guided waves in plates, excited by a piezoelectric patch actuator. The actuator is modelled utilizing higher order coupled field finite elements, whereas the homogenous, isotropic plate is described analytically. The results of this "semi-analytical" approach highlight the opportunities to reduce the numerical effort if closed-form solutions are partially available.

• International Journal of Aeronautical and Space Sciences
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• v.4 no.2
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• pp.17-25
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• 2003

Simple methods are developed to predict temperatures of a satellite box during launch stage. The box is mounted on outer surface of satellite and directly exposed to space thermal environment for the time period from fairing jettison to separation. These simple methods are to solve a 1st order ordinary differential equation (ODE) which is simplified from the governing equation after applying several assumptions. The existence of analytical solution for the 1st order ODE is determined depending on treatment of time-dependent molecular heating term. Even for the case that the analytical solution is not available due to the time dependent term, the 1st order ODE can be solved by relatively simple numerical techniques. The temperature difference between two different approaches (analytical and numerical solutions) is relatively small (Jess than $1^{\circ}C$ along the time line) when they are applied to STSAT-I launch scenario. The present methods can be generally used as tools to quickly check whether a satellite box is safe against space environment during the launch stage for the case that the detailed thermal analysis is not available.

• International Journal of Ocean System Engineering
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• v.2 no.2
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• pp.116-138
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• 2012

As in the other fields of mechanics, analytical methods represent an important analysis tool in marine hydrodynamics. The analytical approach is interesting for different reasons : it gives reference results for numerical codes verification, it gives physical insight into some complicated problems, it can be used as a simplified predesign tool, etc. This approach is of course limited to some simplified geometries (cylinders, spheres, ...), and only the case of one or more cylinders, truncated or not, will be considered here. Presented methods are basically eigenfunction expansions whose complexity depends on the boundary conditions. The hydrodynamic boundary value problem (BVP) is formulated within the usual assumptions of potential flow and is additionally simplified by the perturbation method. By using this approach, the highly nonlinear problem decomposes into its linear part and the higher order (second, third, ...) corrections. Also, periodicity is assumed so that the time dependence can be factorized i.e. the frequency domain formulation is adopted. As far as free surface flows are concerned, only cases without or with small forward speed are sufficiently simple to be solved semi-analytically. The problem of the floating body advancing in waves with arbitrary forward speed is far more complicated. These remarks are also valid for the general numerical methods where the case of arbitrary forward speed, even linearized, is still too difficult from numerical point of view, and "it is fair to say that there exists at present no general practical numerical method for the wave resistance problem" [9], and even less for the general seakeeping problem. We note also that, in the case of bluff bodies like cylinders, the assumptions of the potential flow are justified only if the forward speed is less than the product of wave amplitude with wave frequency.

• Journal of the Korean Wood Science and Technology
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• v.36 no.3
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• pp.24-29
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• 2008

Numerical analysis model was used to analyse the behaviors of multiple bolted connections. Axial-bending element was supposed as basic model, and the effects of frame members and steel fasteners were classified for the behavior analysis. In the condition only two bolts were used, the traditional analytical methods, which show somewhat accuracy, have some advantages more than numerical analysis that need many time consuming, However, more many bolts were used in practical field condition. Also, it is impossible to analyse the behaviors of various bolts layouts and arrangements conditions by traditional analytical methods. Therefore, there is only numerical analysis method for the accurate behavioranalysis on the practical bolted connection condition. Therefore, numerical analysis method was applied on the various multiple bolted connections. On the result exactness and the reflection of connection condition, numerical analysis method showed the superiority more than widely used traditional empirical analysis methods as yield model.

• 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 nano research
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• v.16 no.6
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• pp.549-564
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• 2024

This paper aims to analyze the dynamic response of thermoelectric carbon nanotube-reinforced composite (CNTRC) beams under moving harmonic load resting on Pasternak elastic foundation. The governing equations of thermoelectric CNTRC beam are obtained based on the Karama shear deformation beam theory. The beams are resting on the Pasternak foundation. Previous articles have not performed the moving load mode with the analytical method. The exact solution for the transverse and axial dynamic response is presented using the Laplace transform. A comparison of previous studies has been published, where a good agreement is observed. Finally, some examples were used to analyze, such as excitation frequency, voltage, temperature, spring constant factors, the volume fraction of Carbon nanotubes (CNTs), the velocity of a moving harmonic load, and their influence on axial and transverse dynamic and maximum deflections. The advantages of the proposed method compared to other numerical methods are zero reduction of the error percentage that exists in numerical methods.

• International Journal of Highway Engineering
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• v.18 no.3
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• pp.21-32
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• 2016

PURPOSES : In this paper, the analytical solutions suggested to simulate the behavior of rheological fluids were rigorously re-derived and investigated for fixed conditions to evaluate the applicability for the solutions on a mini-cone slump test of cement paste. The selected solutions with proper boundary conditions can be used as reference solutions to evaluate the performance of numerical simulation approaches, such as the discrete element method. METHODS : The slump, height, and spread radius for the given boundary and yield stress conditions that are determined by five different analytical solutions are compared. RESULTS : The analytical solution based on fluid mechanics for pure shear flow shows similar results to that for intermediate flow at low yield stresses. The fluid mechanics-based analytical solution resulted in a very similar trend to the geometry-based analytical solution. However, it showed a higher slump at high yield stress and lower slump at low yield stress ranges than the geometry-based analytical model. The analytical solution based on the mini-cone geometry was not significantly affected by the yield criteria, such as von Mises and Tresca. CONCLUSIONS : Even though differences among the analytical solutions in terms of slump and spread radius existed, the difference can be considered insignificant when the solutions were used as reference to evaluate the appropriateness of numerical approaches, such as the discrete element method.

• Wind and Structures
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• v.18 no.2
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• pp.103-116
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• 2014

Aeroelasticity is the main source of instability in structures which are subjected to aerodynamic forces. One of the major reasons of instability is the coupling of bending and torsional vibration of the flexible bodies, which is known as flutter. The presented investigation aims to study the aeroelastic stability of composite blades of wind turbine. Geometry, layup, and loading of the turbine blades made of laminated composites were calculated and evaluated. To study the flutter phenomenon of the blades, two numerical and analytical methods were selected. The finite element method (FEM), and JAR-23 standard were used to perform the numerical studies. In the analytical method, two degree freedom flutter and Lagrange's equations were employed to study the flutter phenomena analytically and estimate the flutter speed.

• International Journal of Railway
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• v.3 no.1
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• pp.14-18
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• 2010

This paper describes design and characteristic analysis of long primary type linear synchronous motor (LSM) for high speed train system. LSM is designed using loading distribution method and magnetic equivalent circuit. For characteristic analysis of LSM, analytical and numerical methods are applied. Analytical method for solving the magnetic field distribution of the analytic model is based on the Maxwell’s equations. Using the characteristic equation and magnetic equivalent circuit, we analyze the effect of variation of parameters, and then we validate the result by comparing with numerical method by finite element method (FEM). We compare the analytical method with numerical method for analyzing the effect by variable parameters. This result will be useful of design and forecast of performance without FEM.