• Journal of the Korean Society of Manufacturing Process Engineers
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• v.19 no.5
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• pp.27-37
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• 2020

Structural optimization problems with discrete design variables require more function calculations (or finite element analyses) than those in the continuous design space. In this study, a method to find an optimal solution in the discrete design of the truss structure is presented, reducing the number of function calculations. Because a continuous optimal solution is the Karush-Kuhn-Tucker point that satisfies the optimality condition, it is assumed that the discrete optimal solution is around the continuous optimum. Then, response values such as weight, displacement, and stress are predicted using approximate models-referred to as hybrid metamodels-within specified design ranges. The discrete design method using the hybrid metamodels is used as a post-process of the continuous optimization process. Standard truss design problems of 10-bar, 25-bar, 15-bar, and 52-bar are solved to show the usefulness of this method. The results are compared with those of existing methods.

• Geomechanics and Engineering
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• v.9 no.6
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• pp.815-827
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• 2015

The mechanical behavior of soil and soil-rock mixture is investigated via the discrete element method. A non-overlapping combination method of spheres is used to model convex polyhedron rock blocks of soil-rock mixture in the DEM simulations. The meso-mechanical parameters of soil and soil-rock interface in DEM simulations are obtained from the in-situ tests. Based on the Voronoi cell, a method representing volumtric strain of the sample at the particle scale is proposed. The numerical results indicate that the particle rotation, occlusion, dilatation and self-organizing force chains are a remarkable phenomena of the localization band for the soil and soil-rock mixture samples. The localization band in a soil-rock mixture is wider than that in the soil sample. The current research shows that the 3D discrete element method can effectively simulate the mechanical behavior of soil and soil-rock mixture.

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.529-548
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• 2007

The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.

• 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.

• International Journal of Aeronautical and Space Sciences
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• v.7 no.1
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• pp.106-117
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• 2006

The active vibration control of composite shell structure has been performed with the optimized sensor/actuator system. For the design of sensor/actuator system, a method based on finite element technique is developed. The nine-node Mindlin shell element has been used for modeling the integrated system of laminated composite shell with PVDF sensor/actuator. The distributed selective modal sensor/actuator system is established to prevent the effect of spillover. Electrode patterns and lamination angles of sensor/actuator are optimized using genetic algorithm. Continuous electrode patterns are discretized according to finite element mesh, and orientation angle is encoded into discrete values using binary string. Sensor is designed to minimize the observation spillover, and actuator is designed to minimize the system energy of the control modes under a given initial condition. Modal sensor/actuator for the first and the second mode vibration control of singly curved cantilevered composite shell structure are designed with the method developed on the finite element method and optimization. For verification, the experimental test of the active vibration control is performed for the composite shell structure. Discrete LQG method is used as a control law.

• Journal of the Korean Geotechnical Society
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• v.21 no.4
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• pp.115-122
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• 2005

In this paper, a new method composed of discrete element method and genetic algorithm has been introduced to estimate the safety factor and search critical slip surface on slope stability analysis. In case of estimating the safety factor, conventional methods of slope analysis based on the limit equilibrium do not satisfy the overall equilibrium condition; they must make assumptions regarding the inclination and location of the interstice forces. An alternative slope analysis method based on the discrete element method, which can consider the compatibility condition between force and displacement, is presented. Real-coded genetic algorithm is applied to the search for the minimum factor of safety in proposed analysis method. This search method is shown to be more robust than simple optimization routines, which are apt to find local minimum. Examples are also shown to demonstrate the applicability of the proposed method.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.717-737
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• 2014

We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise linear finite element methods for parabolic interface problems. Optimal $L^2(L^2)$ and $L^2(H^1)$ error estimates are shown to hold for semidiscrete problem under suitable regularity of the true solution in whole domain. Further, fully discrete scheme based on backward Euler method has also analyzed and optimal $L^2(L^2)$ norm error estimate is established. The error estimates are obtained for fitted finite element discretization based on straight interface triangles.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.16 no.2
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• pp.149-154
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• 2017

Numerous studies of the dynamic behavior of powders have been performed by Discrete Element Method (DEM). The behavior of powders can be analyzed using the DEM assuming that the powder is composed of spherical particles. Moreover, the assumption of spherical particle reduces the computing time significantly. However, the biggest problem with this assumption is the real shape of the particles. Some types of particles, such as calcium carbonate and colloidal copper, are needle shaped. Thus, analysis based on spherical particles can produce errors because of the incorrect assumption. In this research, we developed a new model to simulate needle-shaped particles using the DEM. In the model, a series of particles are connected and regarded as a rod. There is no relative motion among the particles. Thus, the behavior of the rod is rigid motion. To validate the developed model, we carried out the drop-and-bounce test with different initial angles. The results showed negligible error of less than 2%.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.17 no.3
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• pp.22-27
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• 2018

One problem of the Discrete Element Method is the assumption of a spherical particle shape, which reduces the computing time but significantly limits the application of the DEM to analysis. This limitation can be overcome by a recently developed rigid-rod model. However, the rigid-rod model has an essential problem related with friction: it always contains friction error because of the bumpy surface. To overcome this issue, we suggest a superposed rigid-rod model in this paper. The superposed rigid-rod model is notably consistent with the theoretical value in terms of the velocity and angular velocity after the collision. The estimated error is negligible(less than 2%). Then, the developed model is applied to hopper discharging. The developed model shows no problem in the discharging flow from the hopper.

• Computers and Concrete
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• v.5 no.4
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• pp.343-358
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• 2008

This article focuses on concrete structures submitted to impact loading and is aimed at predicting local damage in the vicinity of an impact zone as well as the global response of the structure. The Discrete Element Method (DEM) seems particularly well suited in this context for modeling fractures. An identification process of DEM material parameters from macroscopic data (Young's modulus, compressive and tensile strength, fracture energy, etc.) will first be presented for the purpose of enhancing reproducibility and reliability of the simulation results with DE samples of various sizes. The modeling of a large structure by means of DEM may lead to prohibitive computation times. A refined discretization becomes required in the vicinity of the impact, while the structure may be modeled using a coarse FE mesh further from the impact area, where the material behaves elastically. A coupled discrete-finite element approach is thus proposed: the impact zone is modeled by means of DE and elastic FE are used on the rest of the structure. The proposed approach is then applied to a rock impact on a concrete slab in order to validate the coupled method and compare computation times.