• Geophysics and Geophysical Exploration
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• v.15 no.3
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• pp.121-128
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• 2012

Absorbing boundary conditions are used to mitigate undesired reflections that can arise at the model's truncation boundaries. We apply a complex frequency shifted perfectly matched layer (CFS-PML) to elastic wave modeling in the frequency domain. Modeling results show that the performance of our implementation is superior to other absorbing boundaries. We consider the coefficients of CFS-PML to be optimal when the kinetic energy becomes to the minimum, and propose the modified CFS-PML that has the CFS-PML coefficient ${\alpha}_{max}$ defined as a function of frequency. Results with CFS-PML and modified CFS-PML are significantly improved compared with those of the classical PML technique suffering from large spurious reflections at grazing incidence.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.4
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• pp.367-380
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• 2019

A 1kW-class horizontal axis wind turbine (HAWT) rotor blade is taken into account to investigate elastic characteristics in 2-D. The elastic blade field is composed of symmetric cross-ply laminated composite material. Blade element momentum theory is applied to obtain the boundary conditions pressuring the blade, and the plane stress elasticity problem is formulated in terms of two displacement parameters with mixed boundary conditions. For the elastic characteristics a fair of differential equations are derived based on the elastic theory. The domain is divided by triangular and rectangular elements due to the complexity of the blade configuration, and a finite element method is developed for the governing equations to search approximate solutions. The results describe that the elastic behavior is deeply influenced by the layered angle of the middle laminate and the stability of the blade can be improved by controlling the layered angle of laminates, which can be evaluated by the mathematical approach.

• Geophysics and Geophysical Exploration
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• v.14 no.3
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• pp.220-226
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• 2011

In the elastic wave equations, both horizontal and vertical displacements are defined. Since we can measure both the horizontal and vertical displacements in field acquisition, these displacements compose a displacement vector. In this study, we propose a frequency-domain elastic waveform inversion technique taking advantage of the magnitudes of displacement vectors to define objective function. When we apply this displacement-vector objective function to the frequency-domain waveform inversion, the inversion process naturally incorporates the back-propagation algorithm. Through the inversion examples with the Marmousi model and the SEG/EAGE salt model, we could note that the RMS error of the solution obtained by our algorithm decreased more stably than that of the conventional method. Particularly, the density of the Marmousi model and the low-velocity sub-salt zone of the SEG/EAGE salt model were successfully recovered. Since the gradient direction obtained from the proposed objective function is numerically unstable, we need additional study to stabilize the gradient direction. In order to perform the waveform inversion using the displacementvector objective function, it is necessary to acquire multi-component data. Hence, more rigorous study should be continued for the multi-component land acquisition or OBC (Ocean Bottom Cable) multi-component survey.

• Journal of the Korean Society for Nondestructive Testing
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• v.3 no.1
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• pp.5-11
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• 1983

The impulse response function are studied using time domain Born approximation in two cases; firstly when the material parameters of a flaw are constant, secondly when the parameters are varying with positions. From the impulse response functions, characteristics can be learned about a flaw with high symmetry.

• Earthquakes and Structures
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• v.5 no.1
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• pp.49-65
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• 2013

This article presents the statistical characteristics of elastic floor acceleration spectra that represent the peak response demand of non-structural components attached to a nonlinear supporting frame. For this purpose, a set of stiff and flexible general moment resisting frames with periods of 0.3-3.6 sec. are analyzed using forty-nine near-field strong ground motion records. Peak accelerations are derived for each single degree of freedom non-structural component, supported by the above mentioned frames, through a direct-integration time-history analysis. These accelerations are obtained by Floor Acceleration Response Spectrum (FARS) method. They are statistically analyzed in the next step to achieve a better understanding of their height-wise distributions. The factors that affect FARS values are found in the relevant state of the art. Here, they are summarized to evaluate the amplification and/or reduction of FARS values especially when the supporting structures undergo inelastic behavior. The properties of FARS values are studied in three regions: long-period, fundamental-period and short-period. Maximum elastic acceleration response of non-structural component, mounted on inelastic frames, depends on the following factors: inelasticity intensity and modal periods of supporting structure; natural period, damping ratio and location of non-structural component. The FARS values, corresponded to the modal periods of supporting structure, are strongly reduced beyond elastic domain. However, they could be amplified in the transferring period domain between the mentioned modal periods. In the next step, the amplification and/or reduction of FARS values, caused by inelastic behavior of supporting structure, are calculated. A parameter called the response acceleration reduction factor ($R_{acc}$), has been previously used for far-field earthquakes. The feasibility of extending this parameter for near-field motions is focused here, suggested repeatedly in the relevant sources. The nonlinearity of supporting structure is included in ($R_{acc}$) for better estimation of maximum non-structural component absolute acceleration demand, which is ordinarily neglected in the seismic design provisions.

• Structural Engineering and Mechanics
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• v.28 no.4
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• pp.461-477
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• 2008

An adaptive finite element method for analyzing two-dimensional and axisymmetric nonlinear elastic fracture mechanics problems with cracks is presented. The J-integral is used as a parameter to characterize the severity of stresses and deformation near crack tips. The domain integral technique, for which all relevant quantities are integrated over any arbitrary element areas around the crack tips, is utilized as the J-integral solution scheme with 9-node degenerated crack tip elements. The solution accuracy is further improved by incorporating an error estimation procedure onto a remeshing algorithm with a solution mapping scheme to resume the analysis at a particular load level after the adaptive remeshing technique has been applied. Several benchmark problems are analyzed to evaluate the efficiency of the combined domain integral technique and the adaptive finite element method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.62-69
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• 1996

In this study, an equivalent domain integral (EDI) method is presented to estimate the track-till integral parameter, J-value, for two dimensional cracked elastic bodies which may quantify the severity of the crack-tit) stress fields. The conventional J-integral method based on line integral has been converted to equivalent area or domain integrals by using the divergence theorem. It is noted that the EDI method is very attractive because all the quantities necessary for computation of the domain integrals are readily available in a finite element analysis. The details and its implementation are extened to both h-version finite element model with 8-node isoparametric element and p-version finite element model with high order hierarchic element using Legendre type shape fuctions. The variations with respect to the different path of domain integrals from the crack-tip front and the choice of 5-function have been tested by several examples.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.6 s.183
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• pp.119-127
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• 2006

A non-destructive time domain approach to examine structural damage using parameterized partial differential equations and Galerkin approximation techniques is presented. The time domain analysis for damage detection is independent of modal parameters and analytical models unlike frequency domain methods which generally rely on analytical models. The time history of the vibration response of the structure was used to identify the presence of damage. Damage in a structure causes changes in the physical coefficients of mass density, elastic modulus and damping coefficients. This is a part of our ongoing effort on the general problem of modeling and parameter estimation for internal damping mechanisms in a composite beam. Namely, in detecting damage through time-domain or frequency-domain data from smart sensors, the common damages are changed in modal properties such as natural frequencies, mode shapes, and mode shape curvature. This paper examines the use of beam-like structures with piezoceramic sensors and actuators to perform identification of those physical parameters, and detect the damage. Experimental results are presented from tests on cantilevered composite beams damaged at different locations and different dimensions. It is demonstrated that the method can sense the presence of damage and obtain the position of a damage.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.2
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• pp.145-152
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• 2009

SGBEM(Symmetric Galerkin Boundary Element Method)-FEM alternating method has been proposed by Nikishkov, Park and Atluri. In the proposed method, arbitrarily shaped three-dimensional crack problems can be solved by alternating between the crack solution in an infinite body and the finite element solution without a crack. In the previous study, the SGBEM-FEM alternating method was extended further in order to solve elastic-plastic crack problems and to obtain elastic-plastic stress fields. For the elastic-plastic analysis the algorithm developed by Nikishkov et al. is used after modification. In the algorithm, the initial stress method is used to obtain elastic-plastic stress and strain fields. In this paper, elastic-plastic J integrals for three-dimensional cracks are obtained using the method. For that purpose, accurate values of displacement gradients and stresses are necessary on an integration path. In order to improve the accuracy of stress near crack surfaces, coordinate transformation and partitioning of integration domain are used. The coordinate transformation produces a transformation Jacobian, which cancels the singularity of the integrand. Using the developed program, simple three-dimensional crack problems are solved and elastic and elastic-plastic J integrals are obtained. The obtained J integrals are compared with the values obtained using a handbook solution. It is noted that J integrals obtained from the alternating method are close to the values from the handbook.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.4
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• pp.213-221
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• 2013

This paper introduces a mesh continuation scheme for a one-dimensional inverse medium problem to reconstruct the spatial distribution of elastic wave velocities in heterogeneous semi-infinite solid domains. To formulate the inverse problem, perfectly-matched-layers(PMLs) are introduced as wave-absorbing boundaries that surround the finite computational domain truncated from the originally semi-infinite extent. To tackle the inverse problem in the PML-truncated domain, a partial-differential-equations(PDE)-constrained optimization approach is utilized, where a least-squares misfit between calculated and measured surface responses is minimized under the constraint of PML-endowed wave equations. The optimization problem iteratively solves for the unknown wave velocities with their updates calculated by Fletcher-Reeves conjugate gradient algorithms. The optimization is performed using a mesh continuation scheme through which the wave velocity profile is reconstructed in successively denser mesh conditions. Numerical results showed the robust performance of the mesh continuation scheme in reconstructing target wave velocity profile in a layered heterogeneous solid domain.