• Advances in aircraft and spacecraft science
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• v.3 no.1
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• pp.1-14
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• 2016

The Carrera Unified Formulation (CUF) is here extended to perform free-vibrational analyses of rotating structures. CUF is a hierarchical formulation, which enables one to obtain refined structural theories by writing the unknown displacement variables using generic functions of the cross-section coordinates (x, z). In this work, Taylor-like expansions are used. The increase of the theory order leads to three-dimensional solutions while, the classical beam models can be obtained as particular cases of the linear theory. The Finite Element technique is used to solve the weak form of the three-dimensional differential equations of motion in terms of "fundamental nuclei", whose forms do not depend on the adopted approximation. Including both gyroscopic and stiffening contributions, structures rotating about either transversal or longitudinal axis can be considered. In particular, the dynamic characteristics of thin-walled cylinders and composite blades are investigated to predict the frequency variations with the rotational speed. The results reveal that the present one-dimensional approach combines a significant accuracy with a very low computational cost compared with 2D and 3D solutions. The advantages are especially evident when deformable and composite structures are analyzed.

• Smart Structures and Systems
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• v.13 no.4
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• pp.659-683
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• 2014

The static analysis of structures with arbitrary cross-section geometry and material lamination via a refined one-dimensional (1D) approach is presented in this paper. Higher-order 1D models with a variable order of expansion for the displacement field are developed on the basis of Carrera Unified Formulation (CUF). Classical Euler-Bernoulli and Timoshenko beam theories are obtained as particular cases of the first-order model. Numerical results of displacement, strain and stress are provided by using the finite element method (FEM) along the longitudinal direction for different configurations in excellent agreement with three-dimensional (3D) finite element solutions. In particular, a layered thin-walled cylinder is considered as first assessment with a laminated conventional cross-section. An atherosclerotic plaque is introduced as a typical structure with arbitrary cross-section geometry and studied for both the homogeneous and nonhomogeneous material cases through the 1D variable kinematic models. The analyses highlight limitations of classical beam theories and the importance of higher-order terms in accurately detecting in-plane cross-section deformation without introducing additional numerical problems. Comparisons with 3D finite element solutions prove that 1D CUF provides remarkable three-dimensional accuracy in the analysis of even short and nonhomogeneous structures with arbitrary geometry through a significant reduction in computational cost.

• Current Optics and Photonics
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• v.2 no.3
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• pp.250-260
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• 2018

A pressure wave created by the photoacoustic effect is affected by the medium and by laser parameters. The effect of these parameters on the generated pressure wave can be seen by solving the photoacoustic wave equation. These solutions which are examined in the time domain and the frequency domain should be considered by researchers in acoustic sensor design. In particular, frequency domain analysis contains significant information for designing the sensor. The most important part of this information is the determination of the operating frequency of the sensor. In this work, the laser parameters to excite the medium, and the acoustic signal parameters created by the medium are analyzed. For the first time, we have obtained solutions for situations which have no frequency domain solutions in the literature. The main focal point in this work is that the frequency domain solutions of the acoustic wave equation are performed and the effects of the frequency analysis of the related parameters are shown comparatively from the viewpoint of using them in acoustic sensor designs.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.1
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• pp.26-33
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• 2003

Based on detailed FE limit analyses, the present paper provides tractable approximations fer plastic limit pressure solutions fur axially through-wall-cracked pipe; axially (inner) surface-cracked pipe; circumferentially through-wall-cracked pipe; and circumferentially (inner) surface-cracked pipe. In particular, for surface crack problems, the effect of the crack shape, the semi-elliptical shape or the rectangular shape, on the limit pressure is quantified. Comparisons with existing analytical and empirical solutions show a large discrepancy in circumferential short through-wall cracks and in surface cracks (both axial and circumferential). Being based on detailed 3-D FE limit analysis, the present solutions are believed to be the most accurate, and thus to be valuable information not only for plastic collapse analysis of pressurised piping but also for estimating non-linear fracture mechanics parameters based on the reference stress approach.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.185-196
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• 1988

We study existence of polynomial integrating factors and solutions F(x, y)=c of first order nonlinear differential equations. We characterize the homogeneous case, and give algorithms for finding existence of and a basis for polynomial solutions of linear difference and differential equations and rational solutions or linear differential equations with polynomial coefficients. We relate singularities to nature of the solution. Solution of differential equations in closed form to some degree might be called more an art than a science: The investigator can try a number of methods and for a number of classes of equations these methods always work. In particular integrating factors are tricky to find. An analogous but simpler situation exists for integrating inclosed form, where for instance there exists a criterion for when an exponential integral can be found in closed form. In this paper we make a beginning in several directions on these problems, for 2 variable ordinary differential equations. The case of exact differentials reduces immediately to quadrature. The next step is perhaps that of a polynomial integrating factor, our main study. Here we are able to provide necessary conditions based on related homogeneous equations which probably suffice to decide existence in most cases. As part of our investigations we provide complete algorithms for existence of and finding a basis for polynomial solutions of linear differential and difference equations with polynomial coefficients, also rational solutions for such differential equations. Our goal would be a method for decidability of whether any differential equation Mdx+Mdy=0 with polynomial M, N has algebraic solutions(or an undecidability proof). We reduce the question of all solutions algebraic to singularities but have not yet found a definite procedure to find their type. We begin with general results on the set of all polynomial solutions and integrating factors. Consider a differential equation Mdx+Ndy where M, N are nonreal polynomials in x, y with no common factor. When does there exist an integrating factor u which is (i) polynomial (ii) rational? In case (i) the solution F(x, y)=c will be a polynomial. We assume all functions here are complex analytic polynomial in some open set.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.179-189
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• 1991

Composite materials are generally treated as anisotropic or an orthotropic materials. Unlike isotropic materials, the orthotropic materials can divided three groups depending upon the relationship of the four material constants or depending upon the characteristic roots of orthotropic materials. In particular, the fundamental solutions of two dimensional BEM for composite materials (orthotropic or anisotropic material) generally have a singularity in the conventional method when the characteristic roots are equal. In consideration of this singularity in the conventional method when the characteristic roots are equal. In consideration of this singular problems, in this paper, the fundamental solutions of BEM are systematically analysed for orthotropic materials. And the stress and displacement fields for a crack in an orthotropic materials are singular when the characteristic roots of orthotropic materials are equal. Therefore, these fields for a crack in an orthotropic materials are analysed by the analogous method to isotropic materials when the characteristic roots are equal.

• International Journal of Air-Conditioning and Refrigeration
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• v.12 no.2
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• pp.97-107
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• 2004

Wall/floor intersection is important parts of a building envelope system. These intersections can be sources of thermal bridging effects and/or moisture condensation problems. This paper provides a detailed analysis of the thermal performance of wall/floor intersection. In particular, two-dimensional steady-state and transient solutions of the heat conduction within the wall/floor joint are presented. Various insulation configurations are considered to determine the magnitude of heat transfer increase due to wall/floor joint construction.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.3-10
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• 1997

Meshless particle method is a numerical technique which does not use the concept of element. This method can easily handle special engineering problems which cause difficulty in the use of finite element method, however it has a drawback that essential boundary condition is not satisfied. In this paper, several studies for satisfying essential boundary conditions and enhancing the accuracy of solutions are discussed. Particular emphasis is placed on a new numerical technique in which finite elements are used on the boundaries to satisfy the essential boundary conditions and meshless particle method is used in the interior domain. For coupling of the two methods interface elements are introduced into the zone between the subdomains using meshless particle method and finite element method. The shape functions and the approximated displacement functions of the interface element are derived with the ramp function based on the shape function of finite elements. The whole numerical procedures are formulated by Galerkin method. Several numerical examples for enhancing the accuracy of solution in the meshless particle method and a new coupling method are presented.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.51-64
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• 1998

Conflict resolution methodology is discussed with fuzzified Pareto frontier. Four solution concepts namely the Nash solution the generalized nash solution the kalai-Smorodinsky concept and a solution method based on a special bargaining process are examined. The solutions are also fuzzy, the corresponding payoff values are fyzzy numbers the membership functions of which are determined. Three particular cases are considered in the paper. Linear quadratic, and general nonlinear pareto frontiers with known shape are examined.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.11B
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• pp.961-967
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• 2008

Congestion control is one of major mechanisms to avoid dropped packets. Many researchers use optimization theories to find an efficient way to reduce congestion in networks, but they do not consider robustness that may lead to unstable network utilities. This paper proposes a new methodology in order to solve a congestion control problem for wired networks by using a robust design principle. In our particular numerical example, the proposed method provides robust solutions that guarantee high and stable network utilities.