• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.649-664
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• 2015

In this study, the authors present an analytical approach to find the axisymmetric buckling load of two joined isotropic conical shells under axial compression. The problem of two joined conical shells may be considered as the generalized form of joined cylindrical and conical shells with constant or stepped thicknesses. Thickness of each cone is constant; however it may be different from the thickness of the other cone. The boundary conditions are assumed to be simply supported with rigid rings. The governing equations for the conical shells are obtained and solved with an analytical approach. A simple closed-form expression is obtained for the buckling load of two joined truncated conical shells. Results are compared and validated with the numerical results of finite element method. The variation of buckling load with changes in the thickness and semi-vertex angles of the two cones is studied. Finally, application of the results in practical design and range of engineering validity are investigated.

• Structural Engineering and Mechanics
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• v.68 no.1
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• pp.103-119
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• 2018

In the present research, an attempt is made to obtain a semi analytical solution for both nonlinear natural frequency and forced vibration of embedded functionally graded double layered nanoplates with all edges simply supported based on nonlocal strain gradient elasticity theory. The interaction of van der Waals forces between adjacent layers is included. For modeling surrounding elastic medium, the nonlinear Winkler-Pasternak foundation model is employed. The governing partial differential equations have been derived based on the Mindlin plate theory utilizing the von Karman strain-displacement relations. Subsequently, using the Galerkin method, the governing equations sets are reduced to nonlinear ordinary differential equations. The semi analytical solution of the nonlinear natural frequencies using the homotopy analysis method and the exact solution of the nonlinear forced vibration through the Harmonic Balance method are then established. The results show that the length scale parameters give nonlinearity of the hardening type in frequency response curve and the increase in material length scale parameter causes to increase in maximum response amplitude, whereas the increase in nonlocal parameter causes to decrease in maximum response amplitude. Increasing the material length scale parameter increases the width of unstable region in the frequency response curve.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.6 s.46
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• pp.53-58
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• 2005

Semi-analytical methodology to examine the dynamic responses of a bridge is developed via the joint probability density function. The evolution of joint probability density function is evaluated by the semi-analytical procedure developed. The joint probability function of the bridge responses can be obtained by solving the path-integral solution of the Fokker-Planet equation corresponding to the stochastic differential equations of the system. The response characteristics are observed from the joint probability density function and the boundary of the envelope of the probability density function can provide the maxima ol the bridge responses.

• Structural Engineering and Mechanics
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• v.14 no.1
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• pp.99-118
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• 2002

The scaled-boundary finite element method is a novel semi-analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. The method works by weakening the governing differential equations in one coordinate direction through the introduction of shape functions, then solving the weakened equations analytically in the other (radial) coordinate direction. These coordinate directions are defined by the geometry of the domain and a scaling centre. This paper presents a general development of the scaled boundary finite-element method for two-dimensional problems where two boundaries of the solution domain are similar. Unlike three-dimensional and axisymmetric problems of the same type, the use of logarithmic solutions of the weakened differential equations is found to be necessary. The accuracy and efficiency of the procedure is demonstrated through two examples. The first of these examples uses the standard finite element method to provide a comparable solution, while the second combines both solution techniques in a single analysis. One significant application of the new technique is the generation of transition super-elements requiring few degrees of freedom that can connect two regions of vastly different levels of discretisation.

• Journal of Soil and Groundwater Environment
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• v.13 no.6
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• pp.50-61
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• 2008

In this study, new integrated particle tracking algorithm was developed to reduce the inherent problem of Eulerian- Lagrangian method, or adverse effect of particle tracking error on mass balance error. The new integrated particle tracking algorithm includes numerical method, semi-analytical method, and analytical method which consider both temporal and spatial changes of velocity field during time step. Detail of mathematical derivations is well illustrated and four examples are made to verify through the comparison of the new integrated particle tracking with analytical solution or Runge-Kutta method. Additionally, It was shown that the there is better superiority of the new integrated particle tracking algorithm over other existing particle tracking method such as Lu's method.

• Journal of IKEEE
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• v.15 no.1
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• pp.64-69
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• 2011

In this paper, a semi-analytical approach is proposed for decode-and-forward(DF) relay systems over rayleigh fading channels. At first, we derive the general form of the averaged bit error rate(BER) based on error-events at relay nodes in which a selection scheme is not used. It is confirmed that an erroneous detection and transmission at relay nodes can cause the degradation of the received signal-to-noise ratio (SNR) and the averaged BER performance. Furthermore, the proposed method can be extended to selective-DF(SDF) relay schemes so that it is verified to be another general solution for DF relay systems. Also, proposed semi-analytical expressions have been verified by comparing with simulations.

• Structural Engineering and Mechanics
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• v.73 no.4
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• pp.407-426
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• 2020

In this present paper, a semi-analytical mesh-free method is employed for the three-dimensional free vibration analysis of a bi-directional functionally graded piezoelectric circular structure. The dependent variables have been expanded by Fourier series with respect to the circumferential direction and have been discretized through radial and axial directions based on the mesh-free shape function. The current approach has a distinct advantage. The nonlinear Green-Lagrange strain is employed as the relationship between strain and displacement fields to observe thermal impacts in stiffness matrices. Nevertheless, high order terms have been neglected at the final steps of equations driving. The material properties are assumed to vary continuously in both radial and axial directions simultaneously in accordance with a power law distribution. The convergence and validation studies are conducted by comparing our proposed solution with available published results to investigate the accuracy and efficiency of our approach. After the validation study, a parametric study is undertaken to investigate the temperature effects, different types of polarization, mechanical and electric boundary conditions and geometry parameters of structures on the natural frequencies of functionally graded piezoelectric circular structures.

• Steel and Composite Structures
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• v.44 no.3
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• pp.371-388
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• 2022

The present study tackles the problem of forced vibration of imperfect axially functionally graded shell structure with truncated conical geometry. The linear and nonlinear large-deflection of the structure are considered in the mathematical formulation using von-Kármán models. Modified coupled stress method and principle of minimum virtual work are employed in the modeling to obtain the final governing equations. In addition, formulations of classical elasticity theory are also presented. Different functions, including the linear, convex, and exponential cross-section shapes, are considered in the grading material modeling along the thickness direction. The grading properties of the material are a direct result of the porosity change in the thickness direction. Vibration responses of the structure are calculated using the semi-analytical method of a couple of homotopy perturbation methods (HPM) and the generalized differential quadrature method (GDQM). Contradicting effects of small-scale, porosity, and volume fraction parameters on the nonlinear amplitude, frequency ratio, dynamic deflection, resonance frequency, and natural frequency are observed for shell structure under various boundary conditions.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.165-177
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• 2013

In this paper, we apply Homotopy perturbation transform method (HPTM) for solving singular fourth order parabolic partial differential equations with variable coefficients. This method is the combination of the Laplace transform method and Homotopy perturbation method. The nonlinear terms can be easily handled by the use of He's polynomials. The aim of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in other semi-analytical methods such as Homotopy perturbation method (HPM), Variational iteration method (VIM) and Adomain Decomposition method (ADM). The proposed scheme finds the solutions without any discretization or restrictive assumptions and avoids the round-off errors. The comparison shows a precise agreement between the results and introduces this method as an applicable one which it needs fewer computations and is much easier and more convenient than others, so it can be widely used in engineering too.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.11
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• pp.1133-1143
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• 2009

Vibro-acoustic characteristics of a simplified disk-brake rotor containing a narrow radial slot are studied using a semi-analytical procedure. First, modal sound radiations for flexural and radial modes of a generic annular disk having identical key dimension and slot(with free boundaries) are defined using pre-developed analytical solutions based on the modal vibrations from finite element model. The analytical solutions are validated by fully computational methods. Second, sound radiation from a simplified brake rotor simulated using sound radiation solution of the generic disk based on the rotor eigensolutions computed using a finite element code. Predictions by the semi-analytical method matched well numerical calculations using finite element and boundary element method. Finally, sound radiation and vibration characteristics for the example rotor due to a harmonic excitation fixed to the rotor or rotating around the rotor are also obtained.