• Bulletin of the Society of Naval Architects of Korea
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• v.13 no.1
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• pp.17-23
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• 1976

Some methods of analysis of rectangular plates under distributed load of various intensity with interior supports are presented herein. Analysis of many structures such as bottom, side shell, and deck plate of ship hull and flat slab, with or without internal supports, Floor systems of bridges, included crthotropic bridges is a problem of plate with elastic supports or continuous edges. When the four edges of rectangular plate is simply supported, the double Fourier series solution developed by Navier can represent an exact result of this problem. If two opposite edges are simply supported, Levy's method is available to give an "exact" solution. When the loading condition and supporting condition of a plate does not fall into these cases, no simple analytic method seems to be feasible. Analysis of a simply supported rectangular plate under irregularly distributed loads of various intensity with internal supports is carried out by applying Navier solution well as the "Principle of Superposition." Finite difference technique is used to solve plates under irregularly distributed loads of various intensity with internal supports and with various boundary conditions. When finite difference technique is applied to the Lagrange's plate bending equation, any of fourth order derivative term in this equation produces at least five pivotal points leading to some troubles when the resulting linear algebraic equations are to be solved. This problem was solved by reducing the order of the derivatives to two: the fourth order partial differential equation with one dependent variable, namely deflection, is changed to an equivalent pair of second order partial differential equations with two dependent variables. Finite difference technique is then applied to transform these equations to a set of simultaneous linear algebraic equations. Principle of Superposition is then applied to handle the problems caused by concentrated loads and interior supports. This method can be used for the cases of plates under irregularly distributed loads of various intensity with arbitrary conditions such as elastic supports, or continuous edges with or without interior supports, and this method can also be solve the influence values of deflection, moment and etc. at arbitrary position of plates under the live load.

• Journal of Korean Society of Steel Construction
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• v.23 no.3
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• pp.397-404
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• 2011

In this paper, a research for the dynamic wheel loads of a 3D vehicle model, which relates to a tire-enveloping model, is carried out. A single truck with four axles is modeled as a 10-D.O.F. vehicle by modeling both contact length of tires and pitching of tandem spring axles. The dynamic equations of the vehicle are obtained using the Lagrange's equation, the solution of the equations is calculated by Newmark-${\beta}$ method. The validity of the developed 3D vehicle model is demonstrated by comparing results obtained from the proposed method with those from experimental data. The maximum impact factors of tire force are evaluated according to the various step bumps on which a 24-ton dump truck is running.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.4
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• pp.191-197
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• 2021

To calculate the induced charge of atoms in molecular dynamics, linear equations for the induced charges need to be solved. As induced charges are determined at each time step, the process involves considerable computational costs. Hence, an efficient method for calculating the induced charge distribution is required when analyzing large systems. This paper introduces the Uzawa method for solving saddle point problems, which occur in linear systems, for the solution of the Lagrange equation with constraints. We apply the accelerated Uzawa algorithm, which reduces computational costs noticeably using the Schur complement and preconditioned conjugate gradient methods, in order to overcome the drawback of the Uzawa parameter, which affects the convergence speed, and increase the efficiency of the matrix operation. Numerical models of molecular dynamics in which two gold nanoparticles are placed under external electric fields reveal that the proposed method provides improved results in terms of both convergence and efficiency. The computational cost was reduced by approximately 1/10 compared to that for the Gaussian elimination method, and fast convergence of the conjugate gradient, as compared to the basic Uzawa method, was verified.

• Proceedings of the ESK Conference
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• 1997.04a
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• pp.165-175
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• 1997

Brain potential is described by using Euler Lagrange equation derived from Lagrangian based on SMNI(Statistical Mechanics of Neocortical Interaction). It is assumed that excitatory neuron firing is amplitude-modulated dominantly by the sum of two modes of frequency ${\omega}and 2 {\omega}$ . Time series of this neuron firing is numerically calculated. $I_{L}$related to low frequency distribution of power spectrum, $I_{H}$high frequency, and S(standard deviation) are introduced for the effective extraction of the dynamic property in this simulated brain potential. $I_{L}$,$I_{H}$, and S are obtained from EEG of 4 persons in rest state and are compared with thoretical results. It is of importance in various fields related to human well-being such as comfort-pursued industrial design, psychology, medicine to characterize human emotional states by EEG analysis. The pleasant and unpleasant sensation among various emotional states would be demonstrated to be determined in terms of ${\epsilon}$ and ${\gamma}$ parameters estimated by the simulated $I_{L}$-$I_{H}$-S relations.

• Steel and Composite Structures
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• v.15 no.4
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• pp.379-397
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• 2013

Conoidal shells are doubly curved stiff surfaces which are easy to cast and fabricate due to their singly ruled property. Application of laminated composites in fabrication of conoidal shells reduces gravity forces and mass induced forces compared to the isotropic constructions due to the high strength to weight ratio of the material. These light weight shells are preferred in the industry to cover large column free open spaces. To ensure design reliability under service conditions, detailed knowledge about different behavioral aspects of conoidal shell is necessary. Hence, in this paper, static bending, free and forced vibration responses of composite conoidal shells are studied. Lagrange's equation of motion is used in conjunction with Hamilton's principle to derive governing equations of the shell. A finite element code using eight noded curved quadratic isoparametric elements is developed to get the solutions. Uniformly distributed load for static bending analysis and three different load time histories for solution of forced vibration problems are considered. Eight different stacking sequences of graphite-epoxy composite and two different boundary conditions are taken up in the present study. The study shows that relative performances of different shell combinations in terms of static behaviour cannot provide an idea about how they will relatively behave under dynamic loads and also the fact that the points of occurrence of maximum static and dynamic displacement may not be same on a shell surface.

• Advances in Computational Design
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• v.5 no.4
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• pp.363-380
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• 2020

In this paper, a cylindrical shell is immersed in a non-viscous fluid using first order shell theory of Sander. These equations are partial differential equations which are solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the Rayleigh-Ritz procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. Throughout the computation, simply supported edge condition is used. Expressions for modal displacement functions, the three unknown functions are supposed in such way that the axial, circumferential and time variables are separated by the product method. Comparison is made for empty and fluid-filled cylindrical shell with circumferential wave number, length- and height-radius ratios, it is found that the fluid-filled frequencies are lower than that of without fluid. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

• Journal of the Korean Institute of Gas
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• v.6 no.1 s.17
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• pp.1-9
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• 2002

This paper presents simple models for flow and the PIG dynamics when it passes through a $90^{\circ}$ curved section of pipeline. The simulation has been done with two different operational boundary conditions. The solution fur non-linear hyperbolic partial equations for flow is given by using MOC. The Runge-Kuta method is used to solve the initial condition equation fur flow and the PIG dynamics equation. The simulation results show that the proposed model and solution can be used fur estimating the PIG dynamics when the pig runs in the pipeline including curved section. In this paper, dynamic modeling and its analysis for the PIG flow through $90^{\circ}$ curved pipe with compressible and unsteady flow are studied. The PIG dynamics model is derived by using Lagrange equation under assumption that it passes through 3 different sections in the curved pipeline such that it moves into, inside and out of the curved section. The downstream and up stream flow dynamics including the curved sections are solved using MOC. The effectiveness of the derived mathematical models is estimated by simulation results fur a low pressure natural gas pipeline including downward and upward curved sections. The simulation results show that the proposed model and solution can be used for estimating the PIG dynamics when we pig the pipeline including curved section.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.298-309
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• 1990

In this paper, a new method is suggested to analyze impulsive stresses at loading poing of concentrated impact load under certain impact conditions determined by impact velocity, stiffness of plate and mass of impact body, etc. The impulsive stresses are analyzed by using the three dimensional dynamic theory of elasticity so as to analytically clarify the generation phenomenon of cone crack at the impact fracture of fragile materials (to be discussed if the second paper). The Lagrange's plate theory and Hertz's law of contact theory are used for the analysis of impact load, and the approximate equation of impact load is suggested to analyze the impulsive stresses at the impact point to decide the ranage of impact load factor. When impact load factors are over and under 0.263, approximate equations are suggested to be F(t)=Aexp(-Bt)sinCt and F(t)=Aexp(-bt) {1-exp(Ct)} respectively. Also, the inverse Laplace transformation is done by using the F.F.T.(fast fourier transform) algorithm. And in order to clarity the validity of stress analysis method, experiments on strain fluctuation at impact point are performed on a supported square glass plate. Finally, these analytical results are shown to be in close agreement with experimental results.

• 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.

• Journal of Aerospace System Engineering
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• v.11 no.6
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• pp.26-33
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• 2017

We propose a variable frame structure connected with telescopic mast-shaped shaft for a robot displaying outstanding ability to cross obstacles, and for effective traction control. The wireless control system was built to extend and contract a deployable mechanism, which is shaped into a hoberman sphere assembled with frame structures. In order to develop important parameters for efficient locomotion, we derived an Euler-Lagrange equation for the spherical robot. According to the equation, the DC motor was selected. A prototype mechanism was tested and a Finite-Element Analysis (FEA) was conducted in parallel. Using these data, we constructed a deployable spherical robot with structural stability. The deployable robot moved at a speed of 0.85 m/s from 520 mm to 650 mm.