• Computational Structural Engineering
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• v.1 no.1
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• pp.67-78
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• 1988

A new method of element decomposition is suggested for simple, efficient, and generalized formulation of shell finite elements. The kernel of the method is to decompose conceptually the actual element into a translational element and a difference element. The actual element is obtained by combining the two component elements. The derived element can be classified into three basic types depending on how the element is decomposed. A few complementary measures, to remove locking phenomena and thus improve the performance of the elements, have been studied. They are reduced integration, addition of internal degrees of freedom, and mixed formulation. A rational method of controlling spurious zero energy modes has also been devised. Validity and efficiency of the element with or without complementary measures have been examined through a series of numerical studies.

• Computers and Concrete
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• v.3 no.5
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• pp.285-299
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• 2006

The free vibration of stiffened and damaged coupled shear walls is investigated using the mixed finite element method. The anisotropic damage model is adopted to describe the damage extent of the reinforced concrete shear wall element. The internal energy of a locally damaged shear wall element is derived. Polynomial shape functions established by Kwan are used to present the component of displacements vector on each point within the wall element. The principle of virtual work is employed to deduce the stiffness matrix of a damaged shear wall element. The stiffened system is reinforced by an additional stiffening beam at some level of the structure. This induces additional axial forces, and thus reduces the bending moments in the walls and the lateral deflection, and increases the natural frequencies. The effects of the damage extent and the stiffening beam on the free vibration characteristics of the structure are studied. The optimal location of the stiffening beam for increasing as far as possible the first natural frequency of vibration is presented.

• East Asian mathematical journal
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• v.31 no.5
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• pp.685-693
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• 2015

In this paper, we introduce fully discrete mixed discontinuous Galerkin approximations for parabolic problems. And we analyze the error estimates in $l^{\infty}(L^2)$ norm for the primary variable and the error estimates in the energy norm for the primary variable and the flux variable.

• Journal of Theoretical and Applied Mechanics
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• v.1 no.1
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• pp.97-109
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• 1995

In this paper, a finite viscoelastic continuum model for rubber and its finite element analysis are presented. This finite viscoelatic model based on continuum mechanics is an extended model of Johnson and Wuigley's 1-D model. In this extended model, continuum based kinematic measures are rigorously defied and by using this kinematic measures, elastic stage law and flow rule are introduced. In kinematics, three configuration are introduced. In kinematics, three configuration are introduced. They are reference, current and virtual visco configurations. In elastic state law, it is assumed that at a certain time, there exists an elastic potential which describes the recoverable elastic energy. From this elastic potential, elastic state law is derived. The proposed flow rule is based on phenomenological observation. The flow rule gives precise relaxation response. In finite element approximation, mixed Lagrangian description is used, where total and similar method of updated Lagrangian descriptions are used together. This approach reduces the numerical job and gives simple nonlinear syatem of equations. To satisfy the incompressible condition, penalty-type modified Mooney-Rivlin energy function is adopted. By this method nearly incompressible condition is obtain the virtual visco configuration. For verification, uniaxial stretch tests are simulated for various stretch rates. The simulated results show good agreement with experiments. As a practical experiments. As a preactical example, pressurized rubber plate is simulated. The result shows finite viscoelastic effects clearly.

• Interaction and multiscale mechanics
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• v.2 no.3
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• pp.277-293
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• 2009

The Enriched Free Mesh Method (EFMM) is a patch-wise procedure in which both a displacement field on an element and a stress/strain field on a cluster of elements connected to a node can be defined. On the other hand, the Superconvergent Patch Recovery (SPR) is known to be an efficient post-processing procedure of the finite element method to estimate the error norm at a node. In this paper, we discuss the relationship between solutions of the EFMM and those of the SPR through several convergence studies. In addition, in order to solve the demerit of the smoothing effect on the fracture mechanics fields, we implement a singular stress field to a local patch in the EFMM, and its effectiveness is investigated.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1592-1602
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• 1990

Mixed mode surface crack in finite-width plate subjected to uniform tension and bending has been analyzed in 3-D problem by using boundary element method. The calculations were carried out for the surface crack angles(.a/pha.) of 0.deg., 15.deg., 30.deg., 45.deg., 60.deg., and 75.deg., and for the aspect ratio(a/c) of 0.2, 0.4, 0.6 and 1.0 to get stress intensity factors at the boundary points of the surface crack. For the aspect ratio of 1.0 and the surface crack angles, finite element method was used to check the results in this study. Comparison of the results from both methods showed good agreement.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.3
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• pp.189-200
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• 2010

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.337-350
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• 2014

In this paper, we consider discontinuous Galerkin finite element methods with interior penalty term to approximate the solution of nonlinear parabolic problems with mixed boundary conditions. We construct the finite element spaces of the piecewise polynomials on which we define fully discrete discontinuous Galerkin approximations using the Crank-Nicolson method. To analyze the error estimates, we construct an appropriate projection which allows us to obtain the optimal order of a priori ${\ell}^{\infty}(L^2)$ error estimates of discontinuous Galerkin approximations in both spatial and temporal directions.

• Explosives and Blasting
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• v.42 no.3
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• pp.9-22
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• 2024

As buildings constructed in the 1980s during a period of rapid urbanization and economic growth have aged, the demand for demolition, especially of reinforced concrete structures, has increased. In large-scale structures such as industrial buildings, a mixed approach utilizing both mechanical demolition and explosive demolition methods is being employed. As the demand for demolition rises, so do safety concerns, making structural stability during demolition a crucial issue. In this study, drones and LiDAR were used to collect actual structural data, which was then used to build a simulation model. The analysis method employed was a combination of the Finite Element Method (FEM) and the Discrete Element Method (DEM), known as the Combined Finite-Discrete Element Method (FDEM), which was used to perform dynamic structural analysis during various demolition phases. The results were compared and analyzed with the commercial software ELS to assess its applicability.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.10
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• pp.1427-1435
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• 2010

A mixed finite element model was developed using the classical plate theory to analyze the nonlinear bending of a plate. The appropriate weight functions for the constraints integrated over the domain were determined by the Lagrange multiplier method by using the principle of minimum virtual energy; which provides the constitutive relations between force-like variables and strains. All of detail terms of element wise coefficient matrices and associate tangent matrices to be used in the Newton iterative method are presented. Then, the linear solutions of the current model and those of the traditional displacement model under the SS (simple support) boundary conditions were compared with the existing analytical solution. The post-processed images of the nonlinear results of the force-like variables are presented to show the continuity of the solutions at the joint of the element boundaries. Finally, the converged nonlinear finite element solutions of the current model are compared with those of existing traditional displacement model.