• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.545-565
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• 2014

In this paper we derive a priori $L^{\infty}(L^2)$ error estimates for expanded mixed finite element formulations of semilinear Sobolev equations. This formulation expands the standard mixed formulation in the sense that three variables, the scalar unknown, the gradient and the flux are explicitly treated. Based on this method we construct finite element semidiscrete approximations and fully discrete approximations of the semilinear Sobolev equations. We prove the existence of semidiscrete approximations of u, $-{\nabla}u$ and $-{\nabla}u-{\nabla}u_t$ and obtain the optimal order error estimates in the $L^{\infty}(L^2)$ norm. And also we construct the fully discrete approximations and analyze the optimal convergence of the approximations in ${\ell}^{\infty}(L^2)$ norm. Finally we also provide the computational results.

• Computers and Concrete
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• v.34 no.2
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• pp.231-245
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• 2024

A 3D discrete element model integrating the rough surface contact concept with the flat-joint model is suggested to examine the mechanical characteristics of the interfacial transition zone (ITZ) in concrete. The essential components of our DEM procedure include the calculation of the actual contact area in an element contact-pair related to the bonded factor using a Gaussian probability distribution of asperity height, as well as the determination of the contact probability-relative displacement form using the least square method for further computing the force-displacement of ITZs. The present formulations are implemented in MUSEN, an open source development environment for discrete element analysis that is optimized for high performance computation. The model's meso-parameters are calibrated by using uniaxial compression and splitting tensile simulations, as well as laboratory tests of concrete from the literature. The present model's DEM predictions accord well with laboratory experimental tests of pull-out concrete specimens published in the literature.

• Journal of the Korea Concrete Institute
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• v.11 no.3
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• pp.181-192
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• 1999

The progressive failure following strain localization in concrete can be analyzed effectively using finite element modeling of fracture process zone of concrete with a finite element embedded discontinuity. In this study, a finite element with embedded discontinuous line is utilized for the analysis of progressive failure in concrete. The finite element with embedded discontinuity is a kind of discrete crack element, but the difficulties in discrete crack approach such as remeshing or adding new nodes along with crack growth can be avoided. Using a discontinuous shape function for this element, the displacement discontinuity is embedded within an element and its constitutive equation is modeled from the modeling of fracture process zone. The element stiffness matrix is derived and its dual mapping technique for numerical integration is employed. Then, a finite element analysis program with employed algorithms is developed and failure analysis results using developed finite element program are verified through the comparison with experimental data and other analysis results.

• Computers and Concrete
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• v.6 no.2
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• pp.133-153
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• 2009

Discrete element modeling (DEM) in concrete technology is concerned with design and use of models that constitute a schematization of reality with operational potentials. This paper discusses the material science principles governing the design of DEM systems and evaluates the consequences for their operational potentials. It surveys the two families in physical discrete element modeling in concrete technology, only touching upon probabilistic DEM concepts as alternatives. Many common DEM systems are based on random sequential addition (RSA) procedures; their operational potentials are limited to low configuration-sensitivity features of material structure, underlying material performance characteristics of low structure-sensitivity. The second family of DEM systems employs concurrent algorithms, involving particle interaction mechanisms. Static and dynamic solutions are realized to solve particle overlap. This second family offers a far more realistic schematization of reality as to particle configuration. The operational potentials of this family involve valid approaches to structure-sensitive mechanical or durability properties. Illustrative 2D examples of fresh cement particle packing and pore formation during maturation are elaborated to demonstrate this. Mainstream fields of present day and expected application of DEM are sketched. Violation of the scientific knowledge of to day underlying these operational potentials will give rise to unreliable solutions.

• Nuclear Engineering and Technology
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• v.52 no.6
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• pp.1137-1147
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• 2020

The discrete ordinates method (S_N) is one of the major shielding calculation method, which is suitable for solving deep-penetration transport problems. Our objective is to explore the available quadrature sets and to improve the accuracy in shielding problems involving strong anisotropy. The linear discontinuous finite-element (LDFE) quadrature sets based on the icosahedron (in short, ICLDFE quadrature sets) are developed by defining projected points on the surfaces of the icosahedron. Weights are then introduced in the integration of the discontinuous finite-element basis functions in the relevant angular regions. The multivariate secant method is used to optimize the discrete directions and their corresponding weights. The numerical integration of polynomials in the direction cosines and the Kobayashi benchmark are used to analyze and verify the properties of these new quadrature sets. Results show that the ICLDFE quadrature sets can exactly integrate the zero-order and first-order of the spherical harmonic functions over one-twentieth of the spherical surface. As for the Kobayashi benchmark problem, the maximum relative error between the fifth-order ICLDFE quadrature sets and references is only -0.55%. The ICLDFE quadrature sets provide better integration precision of the spherical harmonic functions in local discrete angle domains and higher accuracy for simple shielding problems.

• Journal of the Korean Geosynthetics Society
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• v.10 no.2
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• pp.55-66
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• 2011

This paper presents the results of an investigation on the failure mechanism of geosynthetic reinforced soil walls in back-to-back configuration using 1-g reduced-scale model tests as well as discrete element method-based numerical investigation. In the 1-g reduced scale model tests, 1/10 scale back-to-back walls were constructed so that the wall can be brought to failure by its own weight and the effect of reinforcement length on the failure mechanism was investigated. In addition, a validated discrete element method-based numerical model was used to further investigate the failure mechanism of back-to-back walls with different boundary conditions. The results were then compared with the failure mechanisms defined in the FHWA design guideline.

• Geomechanics and Engineering
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• v.34 no.5
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• pp.577-595
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• 2023

A dynamic triaxial discrete element numerical model of lightweight soil was established using the discrete element method to study the microscopic mechanism of expanded polystyrene (EPS) particles in the soil under cyclic loading. The microscopic parameters of the discrete element model of the lightweight soil were calibrated depending on the dynamic triaxial test hysteresis curves. Based on the calibration results, the effects of the EPS particles volume ratio and amplitude on the contact force, displacement field, and velocity field of the lightweight soil under different accumulated strains were studied. The results showed that the hysteresis curves of lightweight soil exhibit nonlinearity, hysteresis, and strain accumulation. The strain accumulated in remolded soil is mainly tensile strain, and that in lightweight soil is mainly compressive strain. As the volume ratio of EPS particles increased, the contact force first increased and then decreased, and the displacement and velocity of the particles increased accordingly. With an increase in amplitude, the dynamic stress of the particle system increased, and the accumulation rate of the dynamic strain of the samples also increased. At 5% compressive strain, the contact force of the particles changed significantly and the number of particles deflected in the direction of velocity also increased considerably. These results indicated that the cemented structure of the lightweight soil began to fail at a compressive strain of 5%. Thus, a compressive strain of 5% is more reasonable than the dynamic strength failure standard of lightweight soil.

• Earthquakes and Structures
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• v.12 no.2
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• pp.223-236
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• 2017

Seismic assessment and rehabilitation of Monumental Buildings constitute an important issue in many regions around the world to preserve cultural heritage. On the contrary, many recent earthquakes have demonstrated the high vulnerability of this type of structures. The high nonlinear masonry behaviour requires ad hoc refined finite element numerical models, whose complexity and computational costs are generally unsuitable for practical applications. For these reasons, several authors proposed simplified numerical strategies to be used in engineering practice. However, most of these alternative methods are oversimplified being based on the assumption of in-plane behaviour of masonry walls. Moreover, they cannot be used for modelling the monumental structures for which the interaction between plane and out-plane behaviour governs the structural response. Recently, an innovative discrete-modelling approach for the simulation of both in-plane and out of-plane response of masonry structures was proposed and applied to study several typologies of historic structures. In this paper the latter model is applied with reference to a real case study, and numerically compared with an advanced finite element modelling. The method is applied to the St.Venerio church in Reggiolo (Italy), damaged during the 2012 Emilia-Romagna earthquake and numerically investigated in the literature.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.223-235
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• 2006

By applying the Landau-type transformation, we transform a Stefan problem with nonlinear free boundary condition into a system consisting of a parabolic equation and the ordinary differential equations. Fully discrete finite element method is developed to approximate the solution of a system of a parabolic equation and the ordinary differential equations. We derive optimal orders of convergence of fully discrete approximations in $L_2,\;H^1$ and $H^2$ normed spaces.

• Computational Structural Engineering
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• v.5 no.2
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• pp.105-118
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• 1992

Static performance was compared for the triangular plate elements through some numerical experiments. Four Kirchhoff elements and six Mindlin elements were selected for the comparison. Numerical tests were executed for the problems of rectangular plates with regular and distorted meshes, rhombic plates, circular plates and cantilever plates. Among the Kirchhoff 9 DOF elements, the discrete Kirchhoff theory element was the best. Element distortion and the aspect ratio were shown to have negligible effects on the displacement behaviour. The Specht's element resulted in better results than the Bergan's but it was sensitive to the aspect ratio. The element based on the hybrid stress method also resulted in good results but it assumed to be less reliable. Among the linear Mindlin elements, the discrete shear triangle was the best in view of reliability, accuracy and convergence. Since the thin plate behaviour of it was as good as the DKT element, it can be used effectively in the finite element code regardless of the thickness. As a quadratic Mindlin element, the MITC7 element resulted in best results in almost all cases considered. The results were at least as good as those of doubly refined meshes of linear elements.