• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.28 no.10
• /
• pp.1566-1573
• /
• 2004

When a projectile travels at high speed underwater, supercavitating flow arises, in which a huge cavity is generated behind the projectile so that only the nose, i.e., the cavitator, of the projectile is wetted, while the rest of it should be surrounded by the cavity. In that case, the projectile can achieve very high speed due to the reduced drag. Furthermore if the nose of the body is shaped properly, the attendant pressure drag can be maintained at a very low value, so that the overall drag is also reduced dramatically. In this study, shape optimization technique is employed to determine the optimum cavitator shape for minimum drag, given certain operating conditions. Shape optimization technique is also used to solve the potential flow problem fur any given cavitator, which is a free boundary value problem having the cavity shape as unknown a priori. Analytical sensitivities are derived for various shape parameters in order to implement a gradient-based optimization algorithm. Simultaneous optimization technique is proposed for efficient cavitator shape optimization, in which the cavity and cavitator shape are determined in a single optimization routine.

• Proceedings of the KSME Conference
• /
• 2003.11a
• /
• pp.1876-1881
• /
• 2003

When a projectile travels at high speed underwater, supercavitating flow arises, in which a huge cavity is generated behind the projectile so that only the nose, i.e., the cavitator, of the projectile is wetted, while the rest of it should be surrounded by the cavity. In that case, the projectile can achieve very high speed due to the reduced drag. Furthermore if the nose of the body is shaped properly, the attendant pressure drag can be maintained at a very low value, so that the overall drag is also reduced dramatically. In this study, shape optimization technique is employed to determine the optimum cavitator shape for minimum drag, given certain operating conditions. Shape optimization technique is also used to solve the potential flow problem for any given cavitator, which is a free boundary value problem having the cavity shape as unknown a priori. Analytical sensitivities are derived for various shape parameters in order to implement a gradient-based optimization algorithm. Simultaneous optimization technique is proposed for efficient cavitator shape optimization, in which the cavity and cavitator shape are determined in a single optimization routine.

• Journal of the Korean Mathematical Society
• /
• v.52 no.5
• /
• pp.1069-1096
• /
• 2015

In this article we introduce a numerical method, named Gegenbauer wavelets method, which is derived from conventional Gegenbauer polynomials, for solving fractional initial and boundary value problems. The operational matrices are derived and utilized to reduce the linear fractional differential equation to a system of algebraic equations. We perform the convergence analysis for the Gegenbauer wavelets method. We also combine Gegenbauer wavelets operational matrix method with quasilinearization technique for solving fractional nonlinear differential equation. Quasilinearization technique is used to discretize the nonlinear fractional ordinary differential equation and then the Gegenbauer wavelet method is applied to discretized fractional ordinary differential equations. In each iteration of quasilinearization technique, solution is updated by the Gegenbauer wavelet method. Numerical examples are provided to illustrate the efficiency and accuracy of the methods.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.10 s.181
• /
• pp.2469-2476
• /
• 2000

The meshing of the domain has long been the major bottleneck in performing the finite element analysis. Research efforts which are so-called meshfree methods have recently been directed towards eliminating or at least easing the requirement for meshing of the domain. In this paper, a new meshfree method for solving nonlinear boundary value problem, based on the bubble packing technique and Delaunay triangle is proposed. The method can be efficiently implemented to the problems with singularity by using formly distributed nodes.

• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.329-337
• /
• 2007

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for BVPs $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u(0)\;-\;B(u'({\eta}))\;=\;0,\;u'(1)\;=\;0}$$ and $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u'(0)\;=\;0,\;u(1)+B(u'(\eta))\;=\;0.}$$. The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0, 1.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.4 no.2
• /
• pp.111-133
• /
• 2000

A Legendre spectral tau approximation scheme for solving the two-dimensional stationary incompressible Stokes equations is considered. Based on the vorticity-stream function formulation and variational forms, boundary value and normal derivative of vorticity are computed. A factorization technique for matrix stems based on the Schur decomposition is derived. Several numerical experiments are performed.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.6
• /
• pp.1495-1510
• /
• 2022

This paper aims to investigate the initial boundary value problem of the nonlinear viscoelastic Petrovsky type equation with nonlinear damping and logarithmic source term. We derive the blow-up results by the combination of the perturbation energy method, concavity method, and differential-integral inequality technique.

• Smart Structures and Systems
• /
• v.2 no.3
• /
• pp.209-224
• /
• 2006

The use of smart dampers to optimally control the response of structures is on the increase. To maximize the potential use of such damper systems, their accurate modeling and assessment of their performance is of vital interest. In this study, the performance of a controllable fluid dashpot damper, in terms of damper forces, damper dynamic range and damping force hysteretic loops, respectively, is studied mathematically. The study employs a damper Bingham-Maxwell (BingMax) model whose mathematical formulation is developed using a Fourier series technique. The technique treats this one-dimensional Navier-Stokes's momentum equation as a linear superposition of initial-boundary value problems (IBVPs): boundary conditions, viscous term, constant Direct Current (DC) induced fluid plug and fluid inertial term. To hold the formulation applicable, the DC current level to the damper is supplied as discrete constants. The formulation and subsequent simulation are validated with experimental results of a commercially available magneto rheological (MR) dashpot damper (Lord model No's RD-1005-3) subjected to a sinusoidal stroke motion using a 'SCHENK' material testing machine in the Materials Laboratory at the University of Technology, Sydney.

• Coupled systems mechanics
• /
• v.4 no.3
• /
• pp.263-277
• /
• 2015

This paper presents a coupled FEM-BEM strategy for the numerical analysis of elastodynamic problems where infinite-domain models and complex heterogeneous media are involved, rendering a configuration in which neither the Finite Element Method (FEM) nor the Boundary Element Method (BEM) is most appropriate for the numerical analysis. In this case, the coupling of these methodologies is recommended, allowing exploring their respective advantages. Here, frequency domain analyses are focused and an iterative FEM-BEM coupling technique is considered. In this iterative coupling, each sub-domain of the model is solved separately, and the variables at the common interfaces are iteratively updated, until convergence is achieved. A relaxation parameter is introduced into the coupling algorithm and an expression for its optimal value is deduced. The iterative FEM-BEM coupling technique allows independent discretizations to be efficiently employed for both finite and boundary element methods, without any requirement of matching nodes at the common interfaces. In addition, it leads to smaller and better-conditioned systems of equations (different solvers, suitable for each sub-domain, may be employed), which do not need to be treated (inverted, triangularized etc.) at each iterative step, providing an accurate and efficient methodology.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.50 no.11
• /
• pp.505-513
• /
• 2001

This paper presents the new three-level optimal control scheme for the large scale nonlinear systems, which is based on fast walsh transform. It is well known that optimization for nonlinear systems leads to the resolution of a nonlinear two point boundary value problem which always requires a numerical iterative technique for their solution. However, Three-level costate coordination can avoid two point boundary condition in subsystem. But this method also has the defect that must solve high order differential equation in intermediate level. The proposed method makes use of fast walsh transform, therefore, is simple in computation because of solving algebra equation instead of differential equation.