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

• International Journal of Safety
• /
• v.2 no.1
• /
• pp.17-22
• /
• 2003

In order to analyze general three dimensional cracks in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear is used. A crack is modelled as distribution of displacement discontinuities, and the governing equation is formulated as singularity-reduced integral equations. With the proposed method several example problems for three dimensional cracks in an infinite solid, as well as their growth under fatigue, are solved and the accuracy and efficiency of the method are demonstrated.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.24 no.10B
• /
• pp.1885-1894
• /
• 1999

The higher mode cutoff frequencies in Crawford TEM cells computed by the Galerkin method(GM) describe in this paper. The authors also report the half mode boundaries to solve not only the cut-off frequencies of symmetric TEM cells and those of asymmetric TEM cells. It is shown that the measured resonant frequencies of the present symmetric TEM cells and a designed asymmetric TEM cell are agreed with the calculated results.

• Steel and Composite Structures
• /
• v.24 no.5
• /
• pp.523-536
• /
• 2017

A layerwise (LW) formulation based on the Galerkin method is presented to investigate the three-dimensional stress state in long sandwich plate which is subjected to tension force and pure bending moment. Based on the Galerkin method and the LW discretization approach, the equilibrium equations of elasticity for the long plate are written in the weak form and discretized through the thickness of the plate. The discretized equations are written in terms of displacement components of the numerical layers. The governing equations of the plate are solved analytically for the free edge boundary conditions. The distribution of stress state especially the 3D stress state in the vicinity of the edges of the sandwich plate which is subjected to tension and pure bending is studied. In order to increase the accuracy, the out of plane stresses are obtained by integrating the equilibrium equations of elasticity. The convergence and accuracy of the predictions are studied and various numerical results are presented for distribution of the in-plane and out of plane stresses in symmetric and un-symmetric sandwich plates.

• East Asian mathematical journal
• /
• v.26 no.5
• /
• pp.615-626
• /
• 2010

In this paper, we analyze discontinuous Galerkin methods with penalty terms, namly symmetric interior penalty Galerkin methods, to solve nonlinear parabolic equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ${\ell}^{\infty}$ ($L^2$) error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.953-966
• /
• 2010

In this paper, we develop discontinuous Galerkin methods with penalty terms, namaly symmetric interior penalty Galerkin methods to solve nonlinear parabolic equations. By introducing an appropriate projection of u onto finite element spaces, we prove the optimal convergence of the fully discrete discontinuous Galerkin approximations in ${\ell}^2(L^2)$ normed space.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.5
• /
• pp.897-915
• /
• 2011

In this paper, we develop a symmetric Galerkin method with interior penalty terms to construct fully discrete approximations of the solution for nonlinear Sobolev equations. To analyze the convergence of discontinuous Galerkin approximations, we introduce an appropriate projection and derive the optimal $L^2$ error estimates.

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1221-1234
• /
• 2009

In this paper, we construct fully discrete discontinuous Galerkin approximations to the solution of linear Sobolev equations. We apply a symmetric interior penalty method which has an interior penalty term to compensate the continuity on the edges of interelements. The optimal convergence of the fully discrete discontinuous Galerkin approximations in ${\ell}^{\infty}(L^2)$ norm is proved.

• Structural Engineering and Mechanics
• /
• v.74 no.5
• /
• pp.679-698
• /
• 2020

In this paper, the meshless local Petrov-Galerkin (MLPG) method is developed for dynamic analysis of non-symmetric nanocomposite cylindrical shell equations of elastic wave motion with nonlinear grading patterns under shock loading. The mechanical properties of the nanocomposite cylinder are obtained based on a micro-mechanical model. In this study, four kinds of grading patterns are assumed for carbon nanotube mechanical properties. The displacements can be approximated using shape function so, the multiquadrics (MQ) Radial Basis Functions (RBF) are used as the shape function. In order to discretize the derived equations in time domains, the Newmark time approximation scheme with suitable time step is used. To demonstrate the accuracy of the present method for dynamic analysis, at the first a problem verifies with analytical solution and then the present method compares with the finite element method (FEM), finally, the present method verifies by using the element free Galerkin (EFG) method. The comparison shows the high capacity and accuracy of the present method in the dynamic analysis of cylindrical shells. The capability of the present method to dynamic analysis of non-symmetric nanocomposite cylindrical shell is demonstrated by dynamic analysis of the cylinder with different kinds of grading patterns and angle of nanocomposite reinforcements. The present method shows high accuracy, efficiency and capability to dynamic analysis of non-symmetric nanocomposite cylindrical shell, which it furnishes a ground for a more flexible design.

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