• Journal of Theoretical and Applied Mechanics
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• v.3 no.1
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• pp.66-80
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• 2002

The bilinear formulation proposed earlier by Peters and Izadpanah to develop finite elements in time to solve undamped linear systems, Is extended (and found to be readily amenable) to develop time finite elements to obtain transient responses of both linear and nonlinear, and damped and undamped systems. The formulation Is used in the h-, p- and hp-versions. The resulting linear and nonlinear algebraic equations are differentiated to obtain the first- and second-order sensitivities of the transient response with respect to various system parameters. The present developments were tested on a series of linear and nonlinear examples and were found to yield, when compared with results obtained using other methods, excellent results for both the transient response and Its sensitivity to system parameters. Mostly. the results were obtained using the Legendre polynomials as basis functions, though. in some cases other orthogonal polynomials namely. the Hermite. the Chebyshev, and integrated Legendre polynomials were also employed (but to no great advantage). A key advantage of the time finite element method, and the one often overlooked in its past applications, is the ease In which the sensitivity of the transient response with respect to various system parameters can be obtained. The results of sensitivity analysis can be used for approximate schemes for efficient solution of design optimization problems. Also. the results can be applied to gradient-based parameter identification schemes.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.4
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• pp.583-594
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• 1989

The strong nonliner dynamic behavior of mechanical systems in the presence of clearances are studied. The nonlinearity is induced from the assumed symmetric piecewise-linear characteristics for stiffness and damping by the contact and uncontact. Based on Stoker's assertion concering the reasoning beyond the occurrence of subharmonics, the nonlinear differential equation is converted to four nonlinear algebraic equations form the boundary conditions at the contact points. For a single contact per half exciting period, under the assumption of symmetric response, the steady-state solutions obtained are in agreement with those of numerical integration. Also a nondimen-sionalized formulation is made for the purpose of parametric studies.

• Journal of the Korean Society of Safety
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• v.19 no.4 s.68
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• pp.155-160
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• 2004

A simply supported rectangular thin plate with temperature distribution varying over the thickness is analyzed. Since the thermal deflections are large compared to the plate thickness during bending and membrane stresses are developed md as such a nonlinear stress analysis is necessary. For the geometrically nonlinear, large deflection behavior of the plate, the classical von Karman equations are used. These equations are solved numerically by using the finite difference method. An iterative technique is employed to solve these quasi-linear algebraic equations. The results obtained from the suggested method are presented and discussed.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.111-120
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• 2018

This paper presents a new and simple solution for determining the natural frequencies of framed tube combined with shear-walls and tube-in-tube systems. The novelty of the presented approach is based on the bending moment function approximation instead of the mode shape function approximation. This novelty makes the presented solution very simpler and very shorter in the mathematical calculations process. The shear stiffness, flexural stiffness and mass per unit length of the structure are variable along the height. The effect of the structure weight on its natural frequencies is considered using a variable axial force. The effects of shear lag phenomena has been investigated on the natural frequencies of the structure. The whole structure is modeled by an equivalent non-prismatic shear-flexural cantilever beam under variable axial forces. The governing differential equation of motion is converted into a system of linear algebraic equations and the natural frequencies are calculated by determining a non-trivial solution for the system of equations. The accuracy of the proposed method is verified through several numerical examples and the results are compared with the literature.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.04a
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• pp.141-146
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• 2013

This research investigates the stability analysis for the rotating and the stationary grooved journal bearing. The dynamic coefficients of the journal bearing are calculated by using FEM and the perturbation method. When journal bearing is in whirling motion, the dynamic coefficients have time-varying components as a sine wave due to the reaction force of oil film toward the center of journal even in the steady state. The solutions for the equations of motion can be assumed as the Fourier series expansion. The equations of motion can be rewritten as the linear algebraic equations with respect to the Fourier coefficients. Then, stability of the grooved journal bearing can be calculated by Hill's infinite determinant. The periodic function of dynamic coefficients is derived using Fourier Fast Transform(FFT).The stability of journal bearing is determined as rotating speed increases and the stability of rotating grooved journal bearing is compared and discussed with the stability of stationary grooved journal bearing.

• The Journal of the Acoustical Society of Korea
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• v.19 no.1
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• pp.61-66
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• 2000

In this paper, we are proposing an efficient 3D source localization algorithm using 3 uniform linear subarrays. The proposed algorithm replaces 3D search required in conventional 3D MUSIC algorithm with 3 1D searches, and thus reduces computational burden. The estimate of the 1D conic angle obtained from a subarray under the far-field assumption satisfies a nonlinear algebraic equation of the true source bearing angle, elevation angle, and range. The proposed algorithm estimates source location by solving 3 algebraic equations obtained from 3 subarrays. Comparing 3D MUSIC spectrums of the estimated source locations, the proposed algorithm solves pairing problem for multiple sources localization.

• Coupled systems mechanics
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• v.8 no.2
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• pp.129-146
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• 2019

The main goal of this work is to develop a numerical simulator to study an isothermal single-phase two-component flow in a naturally fractured oil reservoir, taking into account advection and diffusion effects. We use the Peng-Robinson equation of state with a volume translation to evaluate the properties of the components, and the discretization of the governing partial differential equations is carried out using the Finite Difference Method, along with implicit and first-order upwind schemes. This process leads to a coupled non-linear algebraic system for the unknowns pressure and molar fractions. After a linearization and the use of an operator splitting, the Conjugate Gradient and Bi-conjugated Gradient Stabilized methods are then used to solve two algebraic subsystems, one for the pressure and another for the molar fraction. We studied the effects of fractures in both the flow field and mass transport, as well as in computing time, and the results show that the fractures affect, as expected, the flow creating a thin preferential path for the mass transport.

• Structural Engineering and Mechanics
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• v.17 no.1
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• pp.1-14
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• 2004

Numerical solution to linear bending analysis of circular plates is obtained by the method of harmonic differential quadrature (HDQ). In the method of differential quadrature (DQ), partial space derivatives of a function appearing in a differential equation are approximated by means of a polynomial expressed as the weighted linear sum of the function values at a preselected grid of discrete points. The method of HDQ that was used in the paper proposes a very simple algebraic formula to determine the weighting coefficients required by differential quadrature approximation without restricting the choice of mesh grids. Applying this concept to the governing differential equation of circular plate gives a set of linear simultaneous equations. Bending moments, stresses values in radial and tangential directions and vertical deflections are found for two different types of load. In the present study, the axisymmetric bending behavior is considered. Both the clamped and the simply supported edges are considered as boundary conditions. The obtained results are compared with existing solutions available from analytical and other numerical results such as finite elements and finite differences methods. A comparison between the HDQ results and the finite difference solutions for one example plate problem is also made. The method presented gives accurate results and is computationally efficient.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.8
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• pp.1429-1437
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• 1992

A new finite element formulation based on the relaxation type hereditary integral is presented for a time-domain analysis of isotropic, linear viscoelastic problems. The semi-discrete variational approximation and elastic-viscoelastic correspondence principle are used in the theoretical development of the proposed method. In a time-stepping procedure of final, linear algebraic system equations, only a small additional computation for past history is required since the equivalent stiffness matrix is constant. The viscoelasticity matrices are derived and the stress computation algorithm is given in matrix form. The effect of time increment and Gauss point numbers on the numerical accuracy is examined. Two dimensional numerical examples of plane strain and plane stress are solved and compared with the analytical solutions to demonstrate the versatility and accuracy of the present method.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.33 no.2
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• pp.211-222
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• 2023

Multivariate quadratic equations (MQ)-based public-key cryptographic algorithms are one of promising post-quantumreplacements for currently used public-key cryptography. After selecting to NIST Post-Quantum Cryptography StandardizationRound 3 as one of digital signature finalists, Rainbow was cryptanalyzed by advanced algebraic attacks due to its multiple layered structure. The researches on MQ-based schemes are focusing on UOV with a single layer. In this paper, we propose a new MQ-signature scheme based on UOV using the combinations of the special structure of linear equations, spare polynomials and random polynomials to reduce the secret key size. Our scheme uses the block inversion method using half-sized blockmatrices to improve signing performance. We then provide security analysis, suggest secure parameters at three security levels and investigate their key sizes and signature sizes. Our scheme has the shortest signature length among post-quantumsignature schemes based on other hard problems and its secret key size is reduced by up to 97% compared to UOV.