• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.192-199
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• 1997

The purpose of this paper is to get a powerful tool for response analysis of a spherical dome subjected to dynamic excitation based on mathematically analytical method, i. e., the Galerkin procedure in modal analysis, with sufficient accuracy and practicality. At first, this paper provides an approximate solution of eigen modes, which has sufficient accuracy and praticallity for response analysis in symmetric and antisymmetric state. In the second stage of this paper, response analysis of a dome subjected to horizontal earthquakes is executed as the application of these approximate modes. Many important response characteristics may manifest themselves through parametric survey of material and geometric properties.

• Bulletin of the Korean Chemical Society
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• v.12 no.1
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• pp.39-47
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• 1991

A cluster made of $N_A,\;N_B\;and\;N_C$ atoms in the x, y and z directions respectively, is treated with Huckel method. We obtain the approximate expressions for the eigenvalues and eigenvectors of f.c.c., b.c.c. and h.c.p. clusters in closed forms. The maximum and minimum values of the band so obtained converge to those derived from the Bloch sum in the limit of infinite extension. For a small cluster (of $9{\times}9{\times}5$ atoms, for instance), LDOS from the analytical (approximate) solution manifests better agreement at the surface, than inside the bulk.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.24 no.1
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• pp.9-15
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• 2012

An effectiveness model has been developed from the approximate analytical solution of a rotary desiccant wheel. The resulting equations clearly show that the maximum air temperature and humidity differences are two independent driving forces commonly acting in the heat and mass transfer processes. Comparison with the numerical model from the preceeding study revealed that the effectiveness model could make realistic predictions roughly with 10% uncertainty. The model may be useful for the rough design and analysis of desiccant evaporative cooling systems.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.1967-1973
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• 1994

The free vibration of a thin plate with three different boundary conditions is discussed in this paper. A semi-analytical approach to the plate problems has been exploited using computer algebra system(CAS). The approximate solutions are assumed as algebraic polynomials that satisfy the appropriate boundary conditions. In order to solve problems, Galerkin method is used, which is known as an ineffective tool for practical engineering problems, being involved with a large number of multiple integration and differentiation. All the admissible functions used in this paper are generated automatically by CAS otherwise a tedious algebraic manipulations should be done by hand. One, six and fifteen-term solutions in terms of frequency parameters are presented and compared with exact solutions. Even using one-term solution, the comparison with existing data shows good agreement and accuracy of the present method.

• Structural Engineering and Mechanics
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• v.26 no.2
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• pp.151-162
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• 2007

Rigorous analytical solutions are obtained for the plane stress problem of a rectangular plate subjected to non-linearly distributed bending loads on two opposite edges. They are then used in a Galerkin type solution to obtain the corresponding convergent buckling loads. It is shown that the critical bending moment depends significantly on the actual edge load distribution and further the number of nodal lines of the buckled configuration can also be different from that corresponding to a linear antisymmetric distribution of the bending stresses. Results are tabulated for future use while judging approximate numerical solutions.

• Structural Engineering and Mechanics
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• v.51 no.2
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• pp.349-360
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• 2014

In this study, three approximate analytical methods have been proposed to prepare an accurate analytical solution for nonlinear oscillators with fractional potential. The basic idea of the approaches and their applications to nonlinear discontinuous equations have been completely presented and discussed. Some patterns are also presented to show the accuracy of the methods. Comparisons between Energy Balance Method (EBM), Variational Iteration Method (VIM) and Hamiltonian Approach (HA) shows that the proposed approaches are very close together and could be easily extend to conservative nonlinear vibrations.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.8
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• pp.945-956
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• 1999

This work reports a set of approximate analytical solutions describing the initial transient process of close-contact melting between a rectangular parallelepiped solid and a flat plate on which either constant temperature or constant heat flux is imposed. Not only relative motion of the solid block tangential to the heating plate, but also the density difference between the solid and liquid phase is incorporated in the model. The thin film approximation reduces the force balance between the solid weight and liquid pressure, and the energy balance at the melting front into a simultaneous ordinary differential equation system. The normalized model equations admit compactly expressed analytical solutions which include the already approved two-dimensional solutions as a subset. In particular, the normalized liquid film thickness is independent of all pertinent parameters, thereby facilitating to define the transition period of close-contact melting. A unique behavior of the solid descending velocity due to the density difference is also resolved by the present solution. A new geometric function which alone represents the three-dimensional effect is introduced, and its properties are clarified. One of the representative results is that heat transfer is at least enhanced at the expense of the increase in friction as the cross-sectional shape deviates from the square under the same contact area.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.1
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• pp.172-178
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• 1990

To predict the qualitative performance characteristics of Stirling Engines, an analytical approach to the Ideal Adiabatic Model set up by Urieli et al. has been treated. First, volume variations of both the expansion and the compression cylinders are approximated to piecewise linear function of the crank angle, which make it possible to specify the mass flow direction of each cylinder a priori to solve a set of basic equation. In consequences, an engine cycle can be considered as a combination of 4-type fundamental process. For each process, pressure is obtained as a solution of the algebraic equation. Application of the cyclic steady condition to the whole cycle completes the analysis. Further investigations result in analytical expressions for cyclic heat and work in terms of dependent variables determined from the pressure. The results are expected useful in establishing the preliminary design conditions of Stirling Engines.

• Composites Research
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• v.17 no.2
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• pp.9-14
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• 2004

In this study, analytical investigations on the flexural behavior of FRP reinforced concrete slab were discussed. In the derivation of analytic solution, the FRP reinforced concrete slab was modeled as a structural orthotropic plate. To determine the flexural rigidities of an orthotropic plate model, the elastic equivalence method was employed. In the finite element analysis, the approximate method to determine the rigidity matrix of orthotropic plate element was also suggested using the elastic equivalence method. The results obtained by the analytical solution and the finite element analysis were compared with that of experiment.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.409-420
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• 2019

In this article, we discussed semi-analytical approximated methods for solving mixed Volterra-Fredholm integro-differential equations, namely: Adomian decomposition method and modified Adomian decomposition method. Moreover, we prove the uniqueness results and convergence of the techniques. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.