• Structural Engineering and Mechanics
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• v.27 no.6
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• pp.713-739
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• 2007

Nowadays computers can perform symbolic computations in addition to mere number crunching operations for which they were originally designed. Symbolic computation opens up exciting possibilities in Structural Mechanics and engineering. Classical areas have been increasingly neglected due to the advent of computers as well as general purpose finite element software. But now, classical analysis has reemerged as an attractive computer option due to the capabilities of symbolic computation. The repetitive cycles of simultaneous - equation sets required by the finite element technique can be eliminated by solving a single set in symbolic form, thus generating a truly closed-form solution. This consequently saves in data preparation, storage and execution time. The power of Symbolic computation is demonstrated by six examples by applying symbolic computation 1) to solve coupled shear wall 2) to generate beam element matrices 3) to find the natural frequency of a shear frame using transfer matrix method 4) to find the stresses of a plate subjected to in-plane loading using Levy's approach 5) to draw the influence surface for deflection of an isotropic plate simply supported on all sides 6) to get dynamic equilibrium equations from Lagrange equation. This paper also presents yet another computationally efficient and accurate numerical method which is based on the concept of derivative of a function expressed as a weighted linear sum of the function values at all the mesh points. Again this method is applied to solve the problems of 1) coupled shear wall 2) lateral buckling of thin-walled beams due to moment gradient 3) buckling of a column and 4) static and buckling analysis of circular plates of uniform or non-uniform thickness. The numerical results obtained are compared with those available in existing literature in order to verify their accuracy.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.4C
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• pp.413-423
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• 2003

The CMA algorithmis most widely investigated blind algorithm and the most widely used one in practice. But, since nonlinear CM cost function have not closed form solution about the optimum weight. There have been difficultiesto analyze the CMA equalizer's theoretical performance. Recently, Zeng presents the notable theoretical resultabout the MSE of CM-minimizing estimators for the FIR linear channel in the presence of AWGN. Through this method, It wouldbe possible to campare the theoretical performance between CMA and Wiener equalizer in terms of MSE. In this paper, based on Zeng's method, we first calculate the theoretical MSE bound of CMA equalizer in partial response channel which is widely used in HDD, digital VCR such as high-density digital recording.playback systems. We confirmedthis result withthe computer simulation. Except this, we also performedthe theoretical and simulation analysis about the modified CMA equalizer, which was proposed to improve the performance of CMA equalizer in partial response channel. Finally, we compare and evaluate the performance analysis results between CMA and Modified CMA equalizer.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.2 no.4
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• pp.208-222
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• 1990

The nonlinear hydrodynamic pressure force and moment on hinged wavemakers of variable-draft are presented. A closed-form solution (correct to second-order) for the nonlinear wavemaker boundary value problem has been obtained by employing the Stokes perturbation expansion scheme. The physical significance of the second-order contributions to the hydrodynamic pressure moment are examined in detail. Design curves are presented which demonstrate both the magnitude of the second-order nonlinearities and the effects of the variable-draft hinge height. The second-order contributions to the total hydrodynamic force and moment consist of a time-dependent and a steady part. The sum of the first and second-order pressure force and moment show a significant increase over those predicted by linear wavemaker theory. The second-order effects are shown to vary with both relative water depth and wave amplitude. The second-order dynamic effects are relatively more important for hinged wavemakers with shallower drafts.

• Geomechanics and Engineering
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• v.31 no.1
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• pp.99-112
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• 2022

The present study examines the natural frequencies (NFs) of perfect/imperfect functionally graded sandwich beams (P/IP-FGSBs), which are composed of a porous core constructed of functionally graded materials (FGMs) and a homogenous isotropic metal and ceramic face sheets resting on elastic foundations. To accomplish this, the material properties of the FGSBs are assumed to vary continuously along the thickness direction as a function of the volume fraction of constituents expressed by the modified rule of the mixture, which includes porosity volume fraction represented using four distinct types of porosity distribution models. Additionally, to characterize the reaction of the two-parameter elastic foundation to the Perfect/Imperfect (P/IP) FGSBs, the medium is assumed to be linear, homogeneous, and isotropic, and it is described using the Winkler-Pasternak model. Furthermore, the kinematic relationship of the P/IP-FGSBs resting on the Winkler-Pasternak elastic foundations (WPEFs) is described using trigonometric shear deformation theory (TrSDT), and the equations of motion are constructed using Hamilton's principle. A closed-form solution is developed for the free vibration analysis of P/IP-FGSBs resting on the WPEFs under four distinct boundary conditions (BCs). To validate the new formulation, extensive comparisons with existing data are made. A detailed investigation is carried out for the effects of the foundation coefficients, mode numbers (MNs), porosity volume fraction, power-law index, span to depth ratio, porosity distribution patterns (PDPs), skin core skin thickness ratios (SCSTR), and BCs on the values of the NFs of the P/IP-FGSBs.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.36 no.4
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• pp.255-262
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• 2018

In order to determine the three-dimensional position in photogrammetry, a spatial resection is a pre-requisite step to determine exterior orientation parameters. The existing spatial resection method is a non-linear equation that requires initial values of exterior orientation parameters and has a problem that a gimbal lock phenomenon may occur. On the other hand, the spatial resection using quaternion is a closed form solution that does not require initial values of EOP (Exterior Orientation Parameters) and is a method that can eliminate the problem of gimbal lock. In this study, to analyze the stability of the quaternion-based spatial resection, the exterior orientation parameters were determined according to the different layout of control points and were compared with the determined values using existing non-linear equation. As a result, it can be seen that the quaternionbased spatial resection is affected by the layout of the control points. Therefore, if the initial value of exterior orientation parameters could not be obtained, it would be more effective to estimate the initial exterior orientation values using the quaternion-based spatial resection and apply it to the collinearity equation-based spatial resection method.