• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.3 no.2
• /
• pp.1-4
• /
• 1999

The Helmholtz equation is very important in physics and engineering. However, solution of the Helmholtz equation is in general known as a very difficult phenomenon. For if the ${\omega}$ is negative, the FDM discretized linear system becomes indefinite, whose solution by iterative method requires a very clever preconditioner. In this paper we assume that ${\omega}$ is nonnegative, and determine the optimal ${\rho}$ parameter for the three dimensional ADI iteration for the Helmholtz equation. The ADI(Alternating Direction Implicit) method is also getting new attentions due to the fact that it is very suitable to the vector/parallel computers, for example, as a preconditioner to the Krylov subspace methods. However, classical ADI was developed for two dimensions, and for three dimensions it is known that its convergence behaviour is quite different from that in two dimensions. So far, in three dimensions the so-called Douglas-Rachford form of ADI was developed. It is known to converge for a relatively wide range of ${\rho}$ values but its convergence is very slow. In this paper we determine the necessary conditions of the ${\rho}$ parameter for the convergence and optimal ${\rho}$ for the three dimensional ADI iteration of the Peaceman-Rachford form for the real Helmholtz equation with nonnegative ${\omega}$. Also, we conducted some experiments which is in close agreement with our theory. This straightforward extension of Peaceman-rachford ADI into three dimensions will be useful as an iterative solver itself or as a preconditioner to the the Krylov subspace methods, such as CG(Conjugate Gradient) method or GMRES(m).

• Journal of Korean Association for Spatial Structures
• /
• v.4 no.4 s.14
• /
• pp.113-128
• /
• 2004

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid paraboloidal and complete (that is, without a top opening) paraboloidal shells of revolution with variable wall thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. The ends of the shell may be free or may be subjected to any degree of constraint. Displacement components $u_r,\;u_{\theta},\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in ${\theta}$, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the paraboloidal shells of revolution are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the complete, shallow and deep paraboloidal shells of revolution with variable thickness. Numerical results are presented for a variety of paraboloidal shells having uniform or variable thickness, and being either shallow or deep. Frequencies for five solid paraboloids of different depth are also given. Comparisons are made between the frequencies from the present 3-D Ritz method and a 2-D thin shell theory.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.21 no.3
• /
• pp.423-429
• /
• 1997

A simplified method for determining the mode components of the strain energy release rate of free-edge delaminations in laminated composite is proposed. The interlaminar stresses are evaluated as an interface moment and interface shear forces that are obtained from the equilibrium equations at the interface between the adjacent layers. Deformation of an edge-delaminated laminate is calculated by using a generalized quasi-three dimensional classical laminated plate theory developed by the authors. The analysis provides closed-form expression for the three components of the strain energy release rate. Comparison of results with a finite element solution using the virtual crack closure technique shows good agreement. In the present study, laminated composite with stacking sequences of [30/-30/90]$_{s}$ were examined. The simple nature of the method makes it suitable for primary design analysis for the delaminations of laminated composite.e.

• Advances in aircraft and spacecraft science
• /
• v.7 no.2
• /
• pp.115-134
• /
• 2020

This paper proposes a bending analysis for a functionally graded piezoelectric (FGP) plate through utilizing a two-variable shear deformation plate theory under simply-supported edge conditions. The number of unknown functions used in this theory is only four. The electric potential distribution is assumed to be a combination of a cosine function along the cartesian coordinate. Applying the analytical solutions of FGP plate by using Navier's approach and the principle of virtual work, the equilibrium equations are derived. The paper also discusses thoroughly the impact of applied electric voltage, plate's aspect ratio, thickness ratio and inhomogeneity parameter. Results are compared with the analytical solution obtained by classical plate theory, first-order-shear deformation theory, higher-order shear deformation plate theories and quasi-three-dimensional sinusoidal shear deformation plate theory.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.28 no.3
• /
• pp.296-303
• /
• 2004

Recently, the ultra light metal structure with periodic and three dimensional truss elements takes attention because of its multi-functionality and substantial heat resistance. However, the complicated fabrication process leading to high cost has been a major obstacle to wide applications. In this paper, a new idea to construct an ultra light structure with periodic, three dimensional truss using metal wires is presented. To prove the practical validity, a Kagome-like structure was fabricated from stamped wires and punched face sheets. It was assembled by soldering. Through three-point bending and compression tests, the strength was evaluated and compared with the theory.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 2004.03a
• /
• pp.472-478
• /
• 2004

This paper describes the characteristics of the unsteady pressure on the stator surface induced by rotor viscous wakes. The primary object of this study is to investigate the effects of axial spacing between the rotor and the stator and three-dimensional vane geometries such as stator sweep and stator lean on the unsteady pressure fluctuations on the stator vane. To predict these fluctuations, unsteady three-dimensional Navier-Stokes analyses are performed. Furthermore, a three-dimensional analytical method using unsteady lifting-surface theory is also used to elucidate the mechanism of interaction of passing rotor wakes with downstream stator. Five different fan configurations with three sets of stator geometries, which are three radial stator configurations with different axial spacing, the swept stator and the swept and leaned stator, are used for this study. It is found that, in axial spacing between rotor and stator, the effect of radial phase skew of incoming rotor wake is important for the reduction of the induced unsteady pressure in addition to the rotor wake decay. It is also shown that incorporation of stator sweep and lean is effective to reduce this unsteady pressure.

• Steel and Composite Structures
• /
• v.38 no.5
• /
• pp.477-496
• /
• 2021

The main objective of this paper is to study vibration of sandwich open cylindrical panel with damaged core and FG face sheets based on three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. Three complicated equations of motion for the panel under consideration are semi-analytically solved by using 2-D differential quadrature method. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution and boundary conditions. It is seen that for the large amount of power-law index "P", increasing this parameter does not have significant effect on the non-dimensional natural frequency parameters of the FG sandwich curved panel. Results indicate that by increasing the value of isotropic damage parameter "D" up to the unity (fully damaged core) the frequency would tend to become zero. One can dictate the fiber variation profile through the radial direction of the sandwich panel via the amount of "P", "b" and "c" parameters. It should be noticed that with increase of volume fraction of fibers, the frequency parameter of the panels does not increase necessarily, so by considering suitable amounts of power-law index "P" and the parameters "b" and "c", one can get dynamic characteristics similar or better than the isotropic limit case for laminated FG curved panels.

• Journal of the Korean Institute of Telematics and Electronics C
• /
• v.35C no.2
• /
• pp.71-79
• /
• 1998

In this paper, we propose a new mART(modified ART) neural network by combining the winner neuron definition method of SOM(self-organizing map) and the real-time adaptive clustering function of ART(adaptive resonance theory) and construct it in a modular structure, for the purpose of organizing the feature maps of three dimensional targets. Being constructed in a modular structure, the proposed modular mART can effectively prevent the clusters from representing multiple classes and can be trained to organze two dimensional distortion invariant feature maps so as to recognize targets with three dimensional distortion. We also present the recognition result and self-organization perfdormance of the proposed modular mART neural network after carried out some experiments with 14 tank and fighter target models.

• Structural Engineering and Mechanics
• /
• v.16 no.2
• /
• pp.115-126
• /
• 2003

A novel finite element model based on the incremental endochronic theory with the effect of temperature was developed in this study to explore the deformed behaviors of a flexible pavement material. Three mesh systems and two loading steps were used in the calculation process for a specimen of three-dimensional circular cylinder. Computational results in the case of an uni-axial compression test for temperatures at $20^{\circ}C$ and at $40^{\circ}C$ were compared with available experimental measurements to verify the ability of developing numerical scheme. The isotropic response and the deviatoric response due to the thermal effect were presented from deformations in different profiles and displacement plots for the entire specimen. The characteristics of changing asphalt concrete material under a specified loading condition might be seen clearly from the numerical results, and might provide an useful information in the field of road engineering.

• 한국기계연구소 소보
• /
• s.14
• /
• pp.111-119
• /
• 1985

A review on the design analysis of an axial-flow turbine is presented. Followed by a brief introduction to the fundamentals on an axial-flow turbine, a design procedure is described with a sample design of one for a small turbo-jet engine. Design procedure is composed of two parts: one-dimensional analysis of three-dimensional effects based on radial equilibrium theory. The method described herein is so simple and rapid that it can be applied to the preliminary design analysis of turbo-machinery equipped with axial-flow turbines.