• International Journal of Aeronautical and Space Sciences
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• v.3 no.2
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• pp.46-58
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• 2002

An inverse method is introduced to construct benchmark problems for the numerical solution of initial value problems. Benchmark problems constructed through this method have a known exact solution, even though analytical solutions are generally not obtainable. The solution is constructed such that it lies near a given approximate numerical solution, and therefore the special case solution can be generated in a versatile and physically meaningful fashion and can serve as a benchmark problem to validate approximate solution methods. A smooth interpolation of the approximate solution is forced to exactly satisfy the differential equation by analytically deriving a small forcing function to absorb all of the errors in the interpolated approximate solution. A multi-variable orthogonal function expansion method and computer symbol manipulation are successfully used for this process. Using this special case exact solution, it is possible to directly investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for a given code and a given problem. Under the assumption that the original differential equation is well-posed with respect to the small perturbations, we thereby obtain valuable information about the optimal choice of the tuning parameters and the achievable accuracy of the numerical solution. Illustrative examples show the utility of this method not only for the ordinary differential equations (ODEs) but for the partial differential equations (PDEs).

• Structural Engineering and Mechanics
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• v.68 no.4
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• pp.399-408
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• 2018

Cable supported structures have been widely used in civil engineering. Cable tension estimation has great importance in cable supported structures' analysis, ranging from design to construction and from inspection to maintenance. Even though the Bernoulli-Euler beam element is commonly used in the traditional finite element method for calculation of frequency and cable tension estimation, many elements must be meshed to achieve accurate results, leading to expensive computation. To improve the accuracy and efficiency, a dynamic finite element method for estimation of cable tension is proposed. In this method, following the dynamic stiffness matrix method, frequency-dependent shape functions are adopted to derive the stiffness and mass matrices of an exact beam element that can be used for natural frequency calculation and cable tension estimation. An iterative algorithm is used for the exact beam element to determine both the exact natural frequencies and the cable tension. Illustrative examples show that, compared with the cable tension estimation method using the conventional beam element, the proposed method has a distinct advantage regarding the accuracy and the computational time.

• Advances in materials Research
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• v.3 no.2
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• pp.77-89
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• 2014

In the present article, the thermal buckling of zigzag single-walled carbon nanotubes (SWCNTs) is studied using a nonlocal refined shear deformation beam theory and Von-Karman geometric nonlinearity. The model developed simulates both small scale effects and higher-order variation of transverse shear strain through the depth of the nanobeam. Furthermore the present formulation also accommodates stress-free boundary conditions on the top and bottom surfaces of the nanobeam. A shear correction factor, therefore, is not required. The equivalent Young's modulus and shear modulus for zigzag SWCNTs are derived using an energy-equivalent model. The present study illustrates that the thermal buckling properties of SWCNTs are strongly dependent on the scale effect and additionally on the chirality of zigzag carbon nanotube. Some illustrative examples are also presented to verify the present formulation and solutions. Good agreement is observed.

• Geomechanics and Engineering
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• v.22 no.1
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• pp.11-23
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• 2020

In this study, a new analytical-numerical procedure is developed to give the stresses and strains around a circular tunnel in rock masses exhibiting different stress-strain behavior. The calculation starts from the tunnel wall and continues toward the unknown elastic-plastic boundary by a finite difference method in the annular discretized plastic zone. From the known stresses in the tunnel boundary, the strains are calculated using the elastic-plastic stiffness matrix in which three dimensional Hoek-Brown failure criterion (Jiang and Zhao 2015) and Mohr-Coulomb potential function with proper dilation angle (i.e., non-associated flow rule) are employed in terms of stress invariants. The illustrative examples give ground response curve and show correctness of the proposed approach. Finally, from the results of a great number of analyses, a simple relationship is presented to find out the closure of circular tunnel in terms of rock mass strength and tunnel depth. It can be valuable for the preliminary decision of tunnel support and for prediction of tunnel problems.

• The KIPS Transactions:PartD
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• v.11D no.7 s.96
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• pp.1443-1450
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• 2004

The clustering characteristics for a number of classes, and defining the inheritance relations between the classes is a difficult and complex problem in an early stage of object oriented software development. We discuss a traditional iterative approach for the reuse of the existing classes in a library and an integrated approach to creating a number of new classes presented in this study. This paper formulates a character-istic clustering problem for zero-one integer programming and presents a network solution method with illustrative examples and the basic rules to define the inheritance relations between the classes. The network solution method for a characteristic clustering problem is based on a distance parameter between every pair of objects with characteristics. We apply the approach to a real problem taken from industry.

• The Korean Journal of Applied Statistics
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• v.18 no.2
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• pp.381-393
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• 2005

As a promising technique for dimension reduction in regression analysis, Sliced Inverse Regression (SIR) and an associated chi-square test for dimensionality were introduced by Li (1991). However, Li's test needs assumption of Normality for predictors and found to be heavily dependent on the number of slices. We will provide a unified asymptotic test for determining the dimensionality of the SIR model which is based on the probabilistic principal component analysis and free of normality assumption on predictors. Illustrative results with simulated and real examples will also be provided.

• Steel and Composite Structures
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• v.13 no.1
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• pp.91-107
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• 2012

In this research, mechanical buckling of hybrid functionally graded plates is considered using a new four variable refined plate theory. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. Governing equations are derived from the principle of minimum total potential energy. The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. The effectiveness of the theories is brought out through illustrative examples.

• 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.

• Proceedings of the Korean Geotechical Society Conference
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• 2004.03b
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• pp.442-449
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• 2004

This paper describes a new concept of finite element analysis, which is based on neural network based material models (NNCMs) without invoking any pre-chosen mathematical framework. NNCMs have several advantages over conventional constitutive models (CCMs) and once plugged in a finite element (FE) engine, can be used for FE analysis in a manner similar to CCMs. The paper demonstrates a FE framework in which NNCMs are incorporated and also proposes a strategy for data enhancement by invoking the assumption of isotropy of the material. It is shown through some illustrative examples that this provides a better training environment for a generalized NNCM in which stress and strain components are used as effects and cause. Form this study, it appears that there is a prima facia case for developing NNCMs for materials for which mathematical theories become too complex and a large number of material parameters and constants have to be identified or determined.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.3
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• pp.515-522
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• 1994

The radiation characteristics of the conical corrugated feed horn are analyzed by the Gaussian beam mode theory. the electric field over the aperture can be expanded in terms of a set of Gaussian-Laguerre modes. It is proved that these modes are the solutions of the wave epuations for the paraxial approximation. A method, using the sum of the mode expansion coefficients instead of calculation only the fundamental mode, is presented in order to reduce the radiation pattern error. For illustrative examples, the radiation patterns of the corrugated horn antenna operting over C, Ku, and mm-wave band are calculated. Our results agree well with the results obtained by the vector potential method over each band, and also agree well with the measured value at 6.175GHz.