• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.9-22
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• 2002

We consider the hp-version to solve non-constant coefficient elliptic equations with Dirichlet boundary conditions on a bounded, convex polygonal domain $\Omega$ in $R^{2}.$ To compute the integrals in the variational formulation of the discrete problem we need the numerical quadrature rule scheme. In this paler we consider a family $G_{p}= {I_{m}}$ of numerical quadrature rules satisfying certain properties. When the numerical quadrature rules $I_{m}{\in}G_{p}$ are used for calculating the integrals in the stiffness matrix of the variational form we will give its variational fore and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_0,{\Omega}'$.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.556-562
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• 2000

This paper presents new sensitivity analysis algorithm for the dynamic response of three dimensional rectilinear type structure. This method is derived from a combination of the transfer stiffness coefficient method(TSCM) and the Newmark method. We developed dynamic response analysis algorithm by TSCM. This method has more safe computational precision and time than transfer matrix method(TMM). We defined new design variable and object function, and computated simple three dimensional computation model by TSCM. The presented analysis algorithm was validated by results of changing design variable.

• Proceedings of the Acoustical Society of Korea Conference
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• 1994.06a
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• pp.734-739
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• 1994

Elastic wave propagation in discrete random medium is studied to evaluate the effects of particle resonance on dispersion and attenuation of composite materials containing spherical inclusions. The frequency-dependent wave speed and attenuation coefficient can be obtained from proposed self-consistent method. It can be observed that the abrupt increase of effective wave speed and the concurrent peak of attenuation at low frequency is due to the lowest resonance of particles, whereas those in high frequency region are due to higher ones. The lowest resonance is mainly caused by the density mismatch and higher resonances by the stiffness mismatch between matrix and particles. The dispersion and attenuation of elastic waves in particulate composites are affected by the lowest resonance much than by higher ones.

• Advances in nano research
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• v.16 no.2
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• pp.175-186
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• 2024

Dynamical behaviors of one-dimensional (1D) nano-sized structures are of great importance in nanotechnology applications. Therefore, the torsional dynamic response of functionally graded nanorods which could be used to model the nano electromechanical systems or micro electromechanical systems with torsional motion about the center of twist is examined based on the theory of strain gradient nonlocal elasticity in this work. The mathematical background is constructed based on both strain gradient theory and Eringen's nonlocal elasticity theory. The equation of motions and boundary conditions of radially functionally graded nanorods are derived using Hamilton's principle and then transformed into the eigenvalue analysis by using Fourier sine series. A general coefficient matrix is obtained to assemble the Stokes' transformation. The case of a restrained functionally graded nanorod embedded in two elastic springs against torsional rotation is then deeply investigated. The effect of changing the functionally graded index, the stiffness of elastic boundary conditions, the length scale parameter and nonlocal parameter are investigated in detail.

• Journal of the Korean Geotechnical Society
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• v.26 no.1
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• pp.45-54
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• 2010

It is important to calculate the natural frequency of a piled structure in the design stage in order to prevent resonance-induced damage to the pile foundation and analyze the dynamic behavior of the piled structure during an earthquake. In this paper, a simple but relatively accurate method employing a mass-spring model is presented for the evaluation of the natural frequency of a pile-soil system. Greatly influencing the calculation of the natural frequency of a piled structure, the spring stiffness between a pile and soil was evaluated by using the coefficient of subgrade reaction, the p-y curve, and the subsoil elastic modulus. The resulting natural frequencies were compared with those of 1-g shaking table tests. The comparison showed that the natural frequency of the pile-soil system could be most accurately calculated by constructing a stiffness matrix with the spring stiffness of the Reese (1974) method, which utilizes the coefficient of the subgrade reaction modulus, and Yang's (2009) dynamic p-y backbone curve method. The calculated natural frequencies were within 5% error compared with those of the shaking table tests for the pile system in dry dense sand deposits and 5% to 40% error for the pile system in saturated sand deposits depending on the occurrence of excess pore water pressure in the soil.

• Geomechanics and Engineering
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• v.5 no.2
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• pp.119-142
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• 2013

Pile load tests using Osterberg cells (O-cell) were conducted on cast-in-place concrete piles founded in oil sand fill and in situ oil sand at an industrial plant site in Fort McMurray, Alberta, Canada. Interpreted pile test results show that very high pile shaft resistance (with the Bjerrum-Burland or Beta coefficient of 2.5-4.5) against oil sand could be mobilized at small relative displacements of 2-3% of shaft diameter. Finite element simulations based on linear elastic and elasto-plastic models for oil sand materials were used to analyze the pile load test measurements. Two constitutive models yield comparable top-down load versus pile head displacement curves, but very different behaviour in mobilization of pile shaft and end bearing resistances. The elasto-plastic model produces more consistent matching in both pile shaft and end bearing resistances whereas the linear elastic under- and over-predicts the shaft and end bearing resistances, respectively. The mobilization of high shaft resistance in oil sand under pile load is attributed to the very dense and interlocked structure of oil sand which results in high matrix stiffness, high friction angle, and high shear dilation.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.1-10
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• 1991

Two-dimensional explicit finite element code was developed. The transient dynamics code can analyse large deformations of non-linear materials subjected to extremely high strain rates. The Lagrangian finite element program uses an explicit time integration operator to integrate the equations of motion, thus the stiffness matrix is not introduced. Cylinder upsetting and ring compression problems are simulated to check the effects of friction and inertia force. It is shown that (1) calculated results agree very well with experimental results, (2) constant shear friction method overestimates the decrease of inner ring radius and then underestimates after on in comparison with the Coulomb friction method, and (3) the effect of the increase in initial strain rate is similar to the effect of higher frictional coefficient.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.5
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• pp.1091-1096
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• 1994

Since horizontal movements due to shrinkage and thermal gradients in concrete pavements involve no actual load, the stresses induced will be those due to closing of the pavement joints and subbase friction. Consequently, complete derivations of stiffness matrix and equivalent nodal loads due to planar effects on the concrete pavements was throughly undertaken using the finite rectangular elements with two degrees of freedom at each node. The numerical example shows that the tensile stress induced in a pavement due to concrete shrinkage might be negligible except at very long slab and very high coefficient of frictions. However the stresses in conjunction with principal traffic loads might cause cracking problems.

• Wind and Structures
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• v.24 no.4
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• pp.351-365
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• 2017

The minimization method is widely used to predict the dynamic characteristics of a system. Generally, data recorded by experiment (for example displacement) tends to contain noise, and the error in the properties of the system is proportional to the noise level (NL). In addition, the accuracy of the results depends on various factors such as the signal character, filtering method or cut off frequency. In particular, coupled terms in multimode systems show larger differences compared to the true value when measured in an environment with a high NL. The iterative least square (ILS) method was proposed to reduce these errors that occur under a high NL, and has been verified in previous research. However, the ILS method might be sensitive to the signal processing, including the determination of cutoff frequency. This paper focused on improving the accuracy of the ILS method, and proposed the modified ILS (MILS) method, which differs from the ILS method by the addition of a new calculation process based on correlation coefficients for each degree of freedom. Comparing the results of these systems with those of a numerical simulation revealed that both ILS and the proposed MILS method provided good prediction of the dynamic properties of the system under investigation (in this case, the damping ratio and damped frequency). Moreover, the proposed MILS method provided even better prediction results for the coupling terms of stiffness and damping coefficient matrix.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.5 s.98
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• pp.527-535
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• 2005

This paper explains a general coupling system in terms of the system parameters. impedance of a cavity or mobility of a structure. To easily access the mechanism of the structural-acoustic coupled system, a simple expression is derived. A general coupled equation is also derived of a general coupled problem constituted a flexible structure and an opening boundary in terms of vector and matrix notation, and is analyzed the coupling phenomena using the understanding acquired simple coupled system. The paper shows that the general coupled equation is expanded version of the simple coupled equation by some limiting checks. The paper also shows that the degree of coupling is proportioned to a stiffness of the acoustic system and a modal coupling coefficient, but is in inverse proportion to a mass of the structural system and the difference of the excitation frequency and resonant frequency of the acoustic or structural system.