• Computers and Concrete
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• v.27 no.3
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• pp.199-210
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• 2021

The aim of this paper was to examine the continuous and discontinuous contact problems between the functionally graded (FG) layer pressed with a uniformly distributed load and homogeneous half plane using an analytical method and FEM. The FG layer is made of non-homogeneous material with an isotropic stress-strain law with exponentially varying properties. It is assumed that the contact at the FG layer-half plane interface is frictionless, and only the normal tractions can be transmitted along the contacted regions. The body force of the FG layer is considered in the study. The FG layer was positioned on the homogeneous half plane without any bonds. Thus, if the external load was smaller than a certain critical value, the contact between the FG layer and half plane would be continuous. However, when the external load exceeded the critical value, there was a separation between the FG layer and half plane on the finite region, as discontinuous contact. Therefore, there have been some steps taken in this study. Firstly, an analytical solution for continuous and discontinuous contact cases of the problem has been realized using the theory of elasticity and Fourier integral transform techniques. Then, the problem modeled and two-dimensional analysis was carried out by using ANSYS package program based on FEM. Numerical results for initial separation distance and contact stress distributions between the FG layer and homogeneous half plane for continuous contact case; the start and end points of separation and contact stress distributions between the FG layer and homogeneous half plane for discontinuous contact case were provided for various dimensionless quantities including material inhomogeneity, distributed load width, the shear module ratio and load factor for both methods. The results obtained using FEM were compared with the results found using analytical formulation. It was found that the results obtained from analytical formulation were in perfect agreement with the FEM study.

• KCI Concrete Journal
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• v.12 no.2
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• pp.23-30
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• 2000

This paper presents behavior of concrete pavement at transverse joint subject to static test load. The test was conducted on 1/10 scale model in the laboratory. Load transfer across the crack is developed either by the interlocking action of the aggregate particles at the faces of the joint or by a combination of aggregate interlock and mechanical devices such as dowel bars. In this study, significant three variables considered to the performance of joints were selected. : (a)diameter of dowel bars(2.5mm, 3.0mm, 4.0mm), (b)presence or absence of dowel bars, (c)aggregate types(crushed stone, round stone). Experimental results were analyzed to find relationships among displacement of discontinuous plane at jointed slab, load transfer efficiency and joint opening, etc. Displacement of discontinuous plane at joint was decreased according to the increase of dowel bar diameter. In addition, it is found that model slabs made using crushed stone had better load transfer characteristics by aggregate interlock than model slabs made using similarly graded round stone. Displacement of discontinuous plane was increased according to the increase of loading. In addition, it was decreased as dowel diameter(2.5mm, 3.0mm, 4.0mm) was increased. In the case of slab without dowel bars, displacement of discontinuous plane was greatly increased and load transfer effciency of slab applied crushed stone was shown 30 percent greater than round stone. In addition, load transfer efficiency of slabs, which were made using crushed and round stone without dowel bars, was decreased to 20 percent and 30 percent, respectively as it was compared with slabs made us-ing dowel bars.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.16 no.1
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• pp.64-71
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• 2016

This paper proposes nonlinear behavior in a love model for Romeo and Juliet with an external force of discontinuous time. We investigated the periodic motion and chaotic behavior in the love model by using time series and phase portraits with respect to some variable and fixed parameters. The computer simulation results confirmed that the proposed love model with an external force of discontinuous time shows periodic motion and chaotic behavior with respect to parameter variation.

• Computers and Concrete
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• v.29 no.4
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• pp.247-253
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• 2022

In this study, the problem of discontinuous contact in two functionally graded (FG) layers resting on a rigid plane and loaded by two rigid blocks is solved by the finite element method (FEM). Separate analyzes are made for the cases where the top surfaces of the problem layers are metal, the bottom surfaces are ceramic and the top surfaces are ceramic and the bottom surfaces are metal. For the problem, it is accepted that all surfaces are frictionless. A two-dimensional FEM analysis of the problem is made by using a special macro added to the ANSYS package program The solution of this study, which has no analytical solution in the literature, is given with FEM. Analyzes are made by loading different Q and P loads on the blocks. The normal stress (σy) distributions at the interfaces of FG layers and between the substrate and the rigid plane interface are obtained. In addition, the starting and ending points of the separations between these surfaces are determined. The normal stresses (σx, σy) and shear stresses (τxy) at the point of separation are obtained along the depth. The results obtained are shown in graphics and tables. With this method, effective results are obtained in a very short time. In addition, analytically complex and long problems can be solved with this method.

• Journal of the Korea Concrete Institute
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• v.12 no.6
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• pp.83-90
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• 2000

This paper presents an analytical prediction of the elastic behavior of discontinuous displacement in reinforced concrete column-footing joint under earthquake. Material nonlinearity is taken into account by comprising tensile, compressive and shear models of cracked concrete and a model of reinforcing steel. The smeared crack approach is incorporated. In boundary plane at which each member with different thickness is connected, local discontinuous deformation due to the abrupt change in their stiffness can be taken into account by introducing interface element. The proposed numerical method for hysteretic behavior of discontinuous displacement in reinforced concrete column-footing joint will be verified by comparison with reliable experimental results.

• Structural Engineering and Mechanics
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• v.25 no.4
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• pp.383-403
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• 2007

The contact problem for an elastic layer resting on an elastic half plane is considered according to the theory of elasticity with integral transformation technique. External loads P and Q are transmitted to the layer by means of two dissimilar rigid flat punches. Widths of punches are different and the thickness of the layer is h. All surfaces are frictionless and it is assumed that the layer is subjected to uniform vertical body force due to effect of gravity. The contact along the interface between elastic layer and half plane will be continuous, if the value of load factor, ${\lambda}$, is less than a critical value, ${\lambda}_{cr}$. However, if tensile tractions are not allowed on the interface, for ${\lambda}$ > ${\lambda}_{cr}$ the layer separates from the interface along a certain finite region. First the continuous contact problem is reduced to singular integral equations and solved numerically using appropriate Gauss-Chebyshev integration formulas. Initial separation loads, ${\lambda}_{cr}$, initial separation points, $x_{cr}$, are determined. Also the required distance between the punches to avoid any separation between the punches and the layer is studied and the limit distance between punches that ends interaction of punches, is investigated. Then discontinuous contact problem is formulated in terms of singular integral equations. The numerical results for initial and end points of the separation region, displacements of the region and the contact stress distribution along the interface between elastic layer and half plane is determined for various dimensionless quantities.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.429-434
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• 2002

The differential equations governing in-plane free vibrations of stepped circular arcs, including the effects of axial deformation, rotatory inertia and shear deformation, are derived and solved numerically to obtain frequencies and mode shapes. Numerical results are calculated for the clamped-clamped symmetric and unsymmetric circular arcs with thickness varying in a discontinuous fashion. The lowest four natural frequencies and mode shapes are presented over a range of non-dimensional system parameters: the subtended angle, the slenderness ratio, the section ratio and the ratio of discontinuous section.

• Proceedings of the Korean Geotechical Society Conference
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• 2006.03a
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• pp.1-11
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• 2006

To be design the slope, the area distributed the shale or mica schist which was metamorphosed by shale must carefully consider the stability. The shale has the detrital materials of which the grain size are 1/256mm and fissility. As the reason the slope of shale is always unstable by bedding slip and fissility but also the joint and fault. Mica schist is also another unstable rock for slope by schistosity, cleavage, axial plane of a fold etc. In general shale and mica schist contain the swelling clay minerals such as smectite, vermiculite and montmorillonite. These minerals make the slope unstable. At OO tunnel construction area for the rail way of the Kyungbu high speed train, the slope of mica schist is very unstable by the distribution phenomena of the discontinuous plane such as joints which are 1-5cm spacing and thrust and strike-slip fault. By the drilling core of this area, most RQD have 0-20%.

• Tunnel and Underground Space
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• v.12 no.3
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• pp.158-170
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• 2002

Since the development of Discontinuous Deformation Analysis (DDA) by Shi (1984), there has been much improvement in the theory and programs. These, however, are all based on the assumption of a two-dimensional plane strain or plane stress state; and because a rock block system is a three-dimensional problem, a two-dimensional analysis has limited application. So a three-dimensional analysis is required in the design of rock slopes and underground spaces where three-dimensional discontinuities dominate stability. In this study three-dimensional DDA program is developed using the Shi's two-dimensional theory and program, and the two cases of three-dimensional block are analysed. The program is applied to one sliding-face blocks and wedge sliding and it gives the good results comparing to the exact solution. Multi-block cases will be analysed for many other application soon.

• KIEAE Journal
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• v.13 no.6
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• pp.121-128
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• 2013

This study attempted to explore the MC design methods of modular construction using discontinuous double module grids and further, the design methods of walls. Modular construction is generally characterized with multiple units called modules with a module dimension of 3M(300mm) appearing in the form of double grids. The discontinuous double grids including correction values and gap values occurs inevitably in the modular construction where units are joined horizontally. Therefore, it is desirable to carry out the MC design taking into account these discontinuous double grids. In this study, the MC design was applied to the plane of wooden houses in modular construction, going through a process of setting the size of pillars and inside dimensions, of determining the dimension of discontinuous double grids that occur during the assembly of units, and of setting the dimension of outer walls in conjunction with the derived dimensions. The dimension of outer walls was applied differently depending on the range of regional use by analyzing the energy performance with the materials used. Consequently, the materials and components of factory-produced buildings can be used directly without processing, and the suitability of the outer wall design can be pre-determined by previewing the calculation of the cross-sectional configuration and heat transmission coefficients of outer walls in modular construction, allowing to be used as a decision-making tool of design.