• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.507-512
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• 2007

A new type of extended element-free Galerkin method (XFEM) is proposed on this paper. The blending region which was inevitable in the extended finite element method and the extended meshfree method is removed in this method. For this end, two different techniques are developed. The first one is the modification of the domain of influence so that the crack tip is always placed on the edge of a domain of influence. The second method is the use of the Lagrange multiplier. The crack is virtually extended beyond the actual crack tip. The virtual extension was forced close by the Lagrange multiplier. The first method can be applied to two dimensional problems only Lagrange multiplier method can be used in both two and three dimensions.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.4
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• pp.174-186
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• 1998

A Galerkin's finite element model incorporating infinite elements for modeling of radiation condition at infinity has been developed, which is based on an extended mild-slope equation. To illustrate the validity and applicability of the present model, the example analyses were carried out for a resonance problem in the rectangular harbor of Ippen and Goda (1963) and for wave transformations over circular shoals of Sharp (1968) and Chandrasekera and Cheung (1997). Comparisons with the results obtained by hydraulic experiments and hybrid element method showed that the present model gives very good results in spite of the rapidly varying topography. Numerical experiments were also performed for wave transformations over a circular concave well which may be an alternative to conventional wave barriers.

• The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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• v.12 no.3
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• pp.133-141
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• 2007

A finite element model is developed for the extended Boussinesq equations that is capable of simulating the dynamics of long and short waves. Galerkin weighted residual method and the introduction of auxiliary variables for 3rd spatial derivative terms in the governing equations are used for the model development. The Adams-Bashforth-Moulton Predictor Corrector scheme is used as a time integration scheme for the extended Boussinesq finite element model so that the truncation error would not produce any non-physical dispersion or dissipation. This developed model is applied to the problems of solitary wave propagation. Predicted results is compared to available analytical solutions and laboratory measurements. A good agreement is observed.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.658-663
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• 2001

The dynamic response of an axially deploying beam is studied when the beam has geometric non-linearity and translating acceleration. Based upon the von Karman strain theory, the governing equations and the boundary conditions of a deploying beam are derived by using extended Hamilton's principle considering the longitudinal and transverse deflections. The equations of motion are discretized by using the Galerkin approximate method. From the discretized equations, the dynamic responses are computed by the Newmark time integration method.

• Journal of the Korean Society of Safety
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• v.19 no.1
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• pp.38-43
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• 2004

Many analysis methods, including finite element method, have been suggested and used for assessing the integrity of cracked structures. In the paper, in order to analyze arbitrary three dimensional cracks, the finite element alternating method is extended. The crack is modeled by the symmetric Galerkin boundary element method as a distribution of displacement discontinuities, which is formulated as singularity-reduced integral equations. And the finite element method is used to calculate the stress values for the uncracked body only. Applied the proposed method to several example problems for planner cracks in finite bodies, the accuracy and efficiency of the method were demonstrated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.10a
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• pp.136-142
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• 2011

The equations of motion for composite plates incorporating magneto-thermo-elastic effects have been derived via Hamilton's principle. In order to get the insight into the implications of a number of geometrical and physical features of the system, the vibrational responses of finite composite rectangular plates immersed in a transversal magnetic field are investigated by applying the extended Galerkin method. The vibration response characteristics of a composite plate are exploited in connection with the magnetic field intensity, thermal load, and electric conductivity of fibrous composite materials. Some pertinent conclusions, which highlight the various effects induced by the magneto-thermo-elastic couplings, are outlined.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.9
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• pp.797-805
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• 2013

In this paper vibration and stability analysis of laminated composite shells based on the first order shear deformation theory(FSDT) for two different boundary conditions(clamped-clamped, simply supported) are performed. Structural model of cross-ply symmetric laminated composite cylindrical shells subjected to a combination of magnetic and thermal fields is developed via Hamilton's variational principle. These coupled equations of motion are based on the electromagnetic equations(Faraday, Ampere, Ohm, and Lorenz equations)and thermal equations which are involved in constitutive equations. Extended Galerkin method is adopted to obtain the discretized equations of motion. Variations of dynamic characteristics of composite shells with applied magnetic field, temperature gradient, laminate thickness-ratio and radius ratio for two boundary conditions are investigated and pertinent conclusions are derived.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.15 no.3
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• pp.159-166
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• 2003

In this study, we develop a finite element model to directly solve the Laplace equation while keeping the same computational efficiency as the models based on the extended mild-slope equation which has been widely used for calculation of wave transformation in shallow water. For this, the computational domain is discretized into finite elements with a single layer in the vertical direction. The velocity potential in the element is then expressed in terms of the potentials at the nodes located at water surface, and the Galerkin method is used to construct the numerical model. A common shape function is adopted in horizontal direction, and the cosine hyperbolic function in vertical direction, which describes the vertical behavior of progressive waves. The model was developed for vertical two-dimensional problems. In order to verify the developed model, it is applied to vertical two-dimensional problems of wave reflection and transmission. It is shown that the present finite element model is comparable to the models based on extended mild-slope equations in both computational efficiency and accuracy.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.10
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• pp.1009-1016
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• 2007

Finite element alternating method has been suggested and used effectively to obtain the fracture parameters in assessing the integrity of cracked structures. The method obtains the solution from alternating independently between the FEM solution for an uncracked body and the crack solution in an infinite body. In the paper, the finite element alternating method is extended in order to obtain the elastic-plastic stress fields of a three dimensional inner crack. The three dimensional crack solutions for an infinite body were obtained using symmetric Galerkin boundary element method. As an example of a three dimensional inner crack, a penny-shaped crack in a finite body was analyzed and the obtained elastc-plastic stress fields were compared with the solution obtained from the finite element analysis with fine mesh. It is noted that in the region ahead of the crack front the stress values from FEAM are close to the values from FEM. But large discrepancy between two values is observed near the crack surfaces.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.341-348
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• 2004

This paper presents a modeling technique of cracks by combined extended and superposed finite element method (XSFEM) which is a combination of the extended finite element method (XFEM) and the mesh superposition method (sversion FEM). In the proposed method, the near-tip field is modeled by a superimposed patch consisting of quarter point elements and the rest of the discontinuity is treated by the XFEM. The actual crack opening in this method is measured by the sum of the crack openings of XFEM and SFEM in transition region. This method retains the strong point of the XFEM so it can avoid remeshing in crack evolution and trace the crack growth by translation or rotation of the overlaid mesh and the update of the nodes to be enriched by step functions. Moreover, the quadrature of the Galerkin weak form becomes simpler. Numerical experiments are provided to demonstrate the effectiveness and robustness of the proposed method.