• Structural Engineering and Mechanics
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• v.15 no.3
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• pp.331-344
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• 2003

The plane contact problem for two infinite elastic layers whose elastic constants and heights are different is considered. The layers lying on a Winkler foundation are acted upon by symmetrical distributed loads whose lengths are 2a applied to the upper layer and uniform vertical body forces due to the effect of gravity in the layers. It is assumed that the contact between two elastic layers is frictionless and that only compressive normal tractions can be transmitted through the interface. The contact along the interface will be continuous if the value of the load factor, ${\lambda}$, is less than a critical value. However, interface separation takes place if it exceeds this critical value. First, the problem of continuous contact is solved and the value of the critical load factor, ${\lambda}_{cr}$, is determined. Then, the discontinuous contact problem is formulated in terms of a singular integral equation. Numerical solutions for contact stress distribution, the size of the separation areas, critical load factor and separation distance, and vertical displacement in the separation zone are given for various dimensionless quantities and distributed loads.

• International Journal of Control, Automation, and Systems
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• v.5 no.5
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• pp.547-558
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• 2007

This paper proposes a simpler solution to the stabilization problem of a special class of nonlinear underactuated mechanical systems which includes widely studied benchmark systems like Inertia Wheel Pendulum, TORA and Acrobot. Complex internal dynamics and lack of exact feedback linearizibility of these systems makes design of control law a challenging task. Stabilization of these systems has been achieved using Energy Shaping and damping injection and Backstepping technique. Former results in hybrid or switching architectures that make stability analysis complicated whereas use of backstepping some times requires closed form explicit solutions of highly nonlinear equations resulting from partial feedback linearization. It also exhibits the phenomenon of explosions of terms resulting in a highly complicated control law. Exploiting recently introduced Dynamic Surface Control technique and using control Lyapunov function method, a novel nonlinear controller design is presented as a solution to these problems. The stability of the closed loop system is analyzed by exploiting its two-time scale nature and applying concepts from Singular Perturbation Theory. The design procedure is shown to be simpler and more intuitive than existing designs. Design has been applied to important benchmark systems belonging to the class demonstrating controller design simplicity. Advantages over conventional Energy Shaping and Backstepping controllers are analyzed theoretically and performance is verified using numerical simulations.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.4
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• pp.509-517
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• 1997

Results of flat plate compressible boundary layer calculation, based on discrete formulation of DSMC method, are presented in low Mach number and low Knudsen number range. The free stream is a uniform flow of pure nitrogen at various Mach numbers in low pressures (i.e. rarefied gas). Complete thermal accommodation and diffuse molecular reflections are used as the wall boundary condition, replacing unreal no-slip condition used in continuum calculations. In the discrete formulation of DSMC method, there is no need to use ad hoc assumptions on transport properties like viscosity and thermal conductivity, instead viscosity is calculated from values of other field variables (velocity and shear stress). Also the results are compared with existing self-similar continuum solutions. In all Mach number cases computed, velocity slip is most pronounced in regions near the leading edge where continuum formulation renders the solution singular. As the boundary layer develops further downstream, velocity slips asymptote to values that are between 10 to 20% of the magnitude of free stream velocity. When the free stream number density is reduced, so the gas more rarefied, the velocity slip increases as expected.

• Transactions of the Korean Society of Mechanical Engineers
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• v.8 no.3
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• pp.232-240
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• 1984

The plane elastostatic boundary value problem with the sharp V-notched singularity is formulated by a contour integral method for determining numerically the stress intensity factors. The integral formula is based on Somigliana type of reciprocal work in terms of displacement and traction vectors on the plate boundary. The characteristic singular solutions can be identified on the basis of traction free boundary conditions of two radial notch edges. Two numerical example examples are treated in detail; a symmetric mode-I type of notched plate with various interior angles and a mixed mode type of cantilever subjected to end shear.

• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.607-622
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• 2015

This paper presents a comparative study of analytical method and finite element method (FEM) for analysis of a continuous contact problem. The problem consists of two elastic layers loaded by means of a rigid circular punch and resting on semi-infinite plane. It is assumed that all surfaces are frictionless and only compressive normal tractions can be transmitted through the contact areas. Firstly, analytical solution of the problem is obtained by using theory of elasticity and integral transform techniques. Then, finite element model of the problem is constituted using ANSYS software and the two dimensional analysis of the problem is carried out. The contact stresses under rigid circular punch, the contact areas, normal stresses along the axis of symmetry are obtained for both solutions. The results show that contact stresses and the normal stresses obtained from finite element method (FEM) provide boundary conditions of the problem as well as analytical results. Also, the contact areas obtained from finite element method are very close to results obtained from analytical method; disagree by 0.03-1.61%. Finally, it can be said that there is a good agreement between two methods.

• Steel and Composite Structures
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• v.39 no.5
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• pp.511-528
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• 2021

There are recently some advances in solving numerically topology optimization problems for large-scaled trusses based on ground structure approach. A disadvantage of this approach is that the final design usually includes many bars, which is difficult to be produced in practice. One of efficient tools is a so-called filter scheme for the ground structure to reduce this difficulty and determine several distinct bars. In detail, this technique is valuable for practical uses because unnecessary bars are filtered out from the ground structure to obtain a well-defined structure during the topology optimization process, while it still guarantees the global equilibrium condition. This process, however, leads to a singular system of equilibrium equations. In this case, the minimization of least squares with Tikhonov regularization is adopted. In this paper, a proposed algorithm in controlling optimal Tikhonov parameter is considered in combination with the filter scheme due to its crucial role in obtaining solution to remove numerical singularity and saving computational time by using sparse matrix, which means that the discrete optimal topology solutions depend on choosing the Tikhonov parameter efficiently. Several numerical examples are investigated to demonstrate the efficiency of the filter parameter control algorithm in terms of the large-scaled optimal topology designs.

• Structural Engineering and Mechanics
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• v.86 no.4
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• pp.535-546
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• 2023

In the present paper, multiple interface cracks between a functionally graded orthotropic coating and an orthotropic half-plane substrate under concentrated loading are considered by means of the distribution dislocation technique (DDT). With the use of integration of Fourier transform the problem is reduced to a system of Cauchy-type singular integral equations which are solved numerically to compute the dislocation density on the surfaces of the cracks. The distribution dislocation is a powerful method to calculate accurate solutions to plane crack problems, especially this method is very good to find SIFs for multiple unequal cracks located at the interface. Hence this technique allows considering any number of interface cracks. The primary objective of this paper is to investigate the effects of the interaction of multiple interface cracks, load location, material orthotropy, nonhomogeneity parameters and geometry parameters on the modes I and II SIFs. Numerical results show that modes I/II SIFs decrease with increasing the nonhomogeneity parameter and the highest magnitude of SIF occurs where distances between the load location and crack tips are minimal.

• Journal of the Korean Electrochemical Society
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• v.15 no.4
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• pp.256-263
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• 2012

This study was performed to investigate the separation of cesium cations by using an electrochemical ion exchanger of nickel hexacyanoferrate($KNiFe(CN)_6$) film electrode. Potential, current, and charge passing through the cyclic voltammograms were measured in singular and binary solutions of 1.0M $NaNO_3$ and 1.0M $CsNO_3$. Before and after each experiment, the structural morphology and atomic composition of $KNiFe(CN)_6$ were analyzed by SEM and EDS, respectively. The ion selectivity of $KNiFe(CN)_6$ was also observed by the voltammograms and atomic compositions measured in the solution alternated between sodium and cesium. As the result of this study, it was found that the electrically switched $KNiFe(CN)_6$ ion exchanger had the significant advantage of 40 times or longer durability than conventional organic or inorganic ion exchanger. It was also shown that the $KNiFe(CN)_6$ ion exchanger had high selectivity for cesium over sodium.

• Journal of computational fluids engineering
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• v.22 no.1
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• pp.59-66
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• 2017

The guideline of selecting the number of snapshot dataset, $N_s$ in proper orthogonal decomposition(POD) was presented via the analysis of Eigen values based on the singular value decomposition(SVD). In POD, snapshot datasets from the solutions of Euler or Navier-Stokes equations are utilized to SVD and a reduced order model(ROM) is constructed as the combination of Eigen vectors. The ROM is subsequently applied to reconstruct the flowfield data with new set of flow conditions, thereby enhancing the computational efficiency. The overall computational efficiency and accuracy of POD is dependent on the number of snapshot dataset; however, there is no reliable guideline of determining $N_s$. In order to resolve this problem, the order of maximum to minimum Eigen value ratio, O(R) from SVD was analyzed and presented for the decision of $N_s$; in case of steady flow, $N_s$ should be determined to make O(R) be $10^9$. For unsteady flow, $N_s$ should be increased to make O(R) be $10^{11\sim12}$. This strategy of selecting the snapshot dataset was applied to two dimensional NACA0012 airfoil and vortex flow problems including steady and unsteady cases and the numerical accuracies according to $N_s$ and O(R) were discussed.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.4
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• pp.389-396
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• 1994

We analyze existing time-dependent mild-slope equations, which were developed by Smith and Sprinks (1975) (or, equivalently, Radder and Dingemans (1985)) and Kubo et al. (1992), in terms of the dispersion relation and energy transport. One-dimensionally in the horizontal direction, we compare the modulation of wave amplitudes for the time-dependent mild-slope equations against the linear Scrodinger equation. In view of the dispersion relation and modulation of wave amplitudes, Smith and Sprinks' model is more accurate in shallower water (kh$\leq$0.2$\pi$) and satisfies the linear Scrodinger equation in very shallow water (kh>0.2$\pi$) and satisfies the linear Scrodinger equation at a point of intermediate water depth (kh=0.3$\pi$). In view of the energy transport, Kubo et al.'s model is more accurate but yields singular solutions at some higher frequency range.