• 대한수학회논문집
• /
• 제10권4호
• /
• pp.925-929
• /
• 1995

Consider the problem $-div($\mid$\bigtriangledown_u$\mid$^{p-2}\bigtriangledown_u) = $\mid$u$\mid$^{p^*-2}u + \lambda$\mid$u$\mid$^{q-2}u$ in B, u = 0 on $\partial B$; where $B \subset R^n$ is a ball, $\lambda < 0, 1 < p < n$ and $p^* = \frac{np}{n-p}$ is the critical Sobolev exponent. For given $\lambda > 0$, we show that there exists $k = k(\lambda) \in N$ such that any radial solutions to this problem have at most k noda curves when $p \leq q \leq p^* - 1$.

• Structural Engineering and Mechanics
• /
• 제20권3호
• /
• pp.335-346
• /
• 2005

The T-stress of cracks in elastic sheets is solved by using the fractal finite element method (FFEM). The FFEM, which had been developed to determine the stress intensity factors of cracks, is re-applied to evaluate the T-stress which is one of the important fracture parameters. The FFEM combines an exterior finite element model with a localized inner model near the crack tip. The mesh geometry of the latter is self-similar in radial layers around the tip. The higher order Williams series is used to condense the large numbers of nodal displacements at the inner model near the crack tip to a small set of unknown coefficients. Numerical examples revealed that the present approach is simple and accurate for calculating the T-stresses and the stress intensity factors. Some errors of the T-stress solutions shown in the previous literature are identified and the new solutions for the T-stress calculations are presented.

• Journal of Mechanical Science and Technology
• /
• 제17권12호
• /
• pp.1938-1948
• /
• 2003

This paper represents that an enhanced genetic algorithm (EGA) is applied to optimal design of a squeeze film damper (SFD) to minimize the maximum transmitted load between the bearing and foundation in the operational speed range. A general genetic algorithm (GA) is well known as a useful global optimization technique for complex and nonlinear optimization problems. The EGA consists of the GA to optimize multi-modal functions and the simplex method to search intensively the candidate solutions by the GA for optimal solutions. The performance of the EGA with a benchmark function is compared to them by the IGA (Immune-Genetic Algorithm) and SQP (Sequential Quadratic Programming). The radius, length and radial clearance of the SFD are defined as the design parameters. The objective function is the minimization of a maximum transmitted load of a flexible rotor system with the nonlinear SFDs in the operating speed range. The effectiveness of the EGA for the optimal design of the SFD is discussed from a numerical example.

• Membrane and Water Treatment
• /
• 제11권4호
• /
• pp.295-302
• /
• 2020

In this paper, theoretical approach with applications of the periodic wave solutions in an elastic material is applied by study the effect of initial stress, and rotation, on the radial displacement and the corresponding stresses in non-homogeneous orthotropic material. An Analytical solution for the elastodynamic equation has obtained concerning the component of displacement. The variations of stresses and displacements have shown graphically. Comparisons with previously published results in the absence of initial stress, rotation and non-homogeneity have made. Finally, numerical results have given and illustrated graphically for each case considered.

• Steel and Composite Structures
• /
• 제22권1호
• /
• pp.161-182
• /
• 2016

A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) analysis of functionally graded material (FGM) axisymmetric circular plates with simply-supported and clamped edges. The strong formulation of this 3D elasticity axisymmetric problem is derived on the basis of the Reissner mixed variational theorem (RMVT), which consists of the Euler-Lagrange equations of this problem and its associated boundary conditions. The primary field variables are naturally independent of the circumferential coordinate, then interpolated in the radial coordinate using the early proposed DRK interpolation functions, and finally the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The state space DRK solutions can then be obtained by means of the transfer matrix method. The accuracy and convergence of this method are examined by comparing their solutions with the accurate ones available in the literature.

• Steel and Composite Structures
• /
• 제27권6호
• /
• pp.789-801
• /
• 2018

A weak-form formulation of finite annular prism methods (FAPM) based on Reissner's mixed variational theorem (RMVT), is developed for the quasi three-dimensional (3D) static analysis of two-directional functionally graded (FG) circular plates with various boundary conditions and under mechanical loads. The material properties of the circular plate are assumed to obey either a two-directional power-law distribution of the volume fractions of the constituents through the radial-thickness surface or an exponential function distribution varying doubly exponentially through it. These FAPM solutions of the loaded FG circular plates with both simply-supported and clamped edges are in excellent agreement with the solutions obtained using the 3D analytical approach and two-dimensional advanced plate theories available in the literature.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2003년도 하계학술대회 논문집 B
• /
• pp.1048-1050
• /
• 2003

Recently, many linear motion generators and motors are rapidly finding applications that ranges from short stroke linear motion vibrators, such as dynamic con type loud speakers to stilting engine driven linear reciprocating alternators, compressors, textile machines etc. In this paper, we analyze the characteristics of tubular linear motor with Halbach and radial magnet array respectively. We already derived magnetic field solutions due to the PMs and to the currents and Motor thrust. On the basis of analytical field solutions, this paper deals with flux linkages and back emf. The results are validated extensively by comparison with finite element analyses. Then, this parer also presents thrust characteristics according to design parameters for each model.

• 대한수학회지
• /
• 제58권6호
• /
• pp.1449-1460
• /
• 2021

In this paper, we consider the following nonlocal fractional Laplacian equation with a singular nonlinearity (-∆)^su(x) = λu^β (x) + a₀u^-γ (x), x ∈ ℝⁿ, where 0 < s < 1, γ > 0, $1<{\beta}{\leq}\frac{n+2s}{n-2s}$, λ > 0 are constants and a₀ ≥ 0. We use a direct method of moving planes which introduced by Chen-Li-Li to prove that positive solutions u(x) must be radially symmetric and monotone increasing about some point in ℝⁿ.

• Korean Chemical Engineering Research
• /
• 제57권5호
• /
• pp.652-665
• /
• 2019

Analytical solutions of the reactant concentration inside porous spherical catalytic particles were obtained from unsteady reaction-diffusion equation by applying eigenfunction expansion method. Various surface concentrations as exponentially decaying or oscillating function were considered as boundary conditions to solve the unsteady partial differential equation as a function of radial distance and time. Dirac delta function was also used for the instantaneous injection of the reactant as the surface boundary condition to calculate average reactant concentration inside the particles as a function of time by Laplace transform. Besides spherical morphology, other geometries of particles, such as cylinder or slab, were considered to obtain the solution of the reaction-diffusion equation, and the results were compared with the solution in spherical coordinate. The concentration inside the particles based on calculation was compared with the bulk concentration of the reactant molecules measured by photocatalytic decomposition as a function of time.

• Geomechanics and Engineering
• /
• 제16권6호
• /
• pp.619-626
• /
• 2018

A simple prediction procedure was investigated for calculating the stresses and displacements of a circular opening. Unlike existed approaches, the proposed approach starts each step with a radius increment. The stress for each annulus could be obtained analytically, while strain increments for each step can be determinate numerically from the compatility equation by finite difference approximation, flow rule and Hooke's law. In the successive manner, the distributions of stresses and displacements could be found. It should be noted that the finial radial stress and displacement were equal to the internal supporting pressure and deformation at the tunnel wall, respectively. By assuming different plastic radii, GRC and the evolution curve of plastic radii and internal supporting pressures could be obtained conveniently. Then the real plastic radius can be calculated by using linear interpolation in the evolution curve. Some numerical and engineering examples were performed to demonstrate the accuracy and validity for the proposed procedure. The comparisons results show that the proposed procedure was faster than that in Lee and Pietrucszczak (2008). The influence of annulus number and dilation on the accuracy of solutions was also investigated. Results show that the larger the annulus number was, the more accurate the solutions were. Solutions in Park et al. (2008) were significantly influenced by dilation.