• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.15 no.2
• /
• pp.123-135
• /
• 2011

In this paper, we present arc-length estimations for quadratic rational B$\acute{e}$zier curves using the length of polygon and distance between both end points. Our arc-length estimations coincide with the arc-length of the quadratic rational B$\acute{e}$zier curve exactly when the weight ${\omega}$ is 0, 1 and ${\infty}$. We show that for all ${\omega}$ > 0 our estimations are strictly increasing with respect to ${\omega}$. Moreover, we find the parameter ${\mu}^*$ which makes our estimation coincide with the arc-length of the quadratic rational B$\acute{e}$zier curve when it is a circular arc too. We also show that ${\mu}^*$ has a special limit, which is used for optimal estimation. We present some numerical examples, and the numerical results illustrates that the estimation with the limit value of ${\mu}^*$ is an optimal estimation.

• Structural Engineering and Mechanics
• /
• v.65 no.5
• /
• pp.573-585
• /
• 2018

This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to produce numerical results in accordance with Kirchhoff, Mindlin, and third order shear deformation theories. All material properties, including the length scale parameters, are assumed to be functions of the plate thickness coordinate in the derivations. Developed equations are solved numerically by means of differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature for certain limiting cases. Further numerical results are provided to illustrate the effects of material and geometric parameters on bending, free vibrations, and buckling. The results generated by Kirchhoff and third order shear deformation theories are in very good agreement, whereas Mindlin plate theory slightly overestimates static deflection and underestimates natural frequency. A rise in the length scale parameter ratio, which identifies the degree of spatial variations, leads to a drop in dimensionless maximum deflection, and increases in dimensionless vibration frequency and buckling load. Size effect is shown to play a more significant role as the plate thickness becomes smaller compared to the length scale parameter. Numerical results indicate that consideration of length scale parameter variation is required for accurate modelling of graded rectangular micro-plates.

• The Journal of the Acoustical Society of Korea
• /
• v.9 no.2
• /
• pp.34-41
• /
• 1990

The energy parameter is widely used in pre-processing of speech signals, because it represent the phoneme characteristics of well But, the energy parameter is affected by the window length during the extracting. Thus, in this paper, the window length effects are studied in detail, and we proposed a new energy extraction algorithm that reduces the length effects. The energy contours with this algorithm are well representing for the characteristics of speech phonemes. And the computations to implement the algorithm are only required one subtraction, one addition, and two comparison aperation per speech sample.

• Structural Engineering and Mechanics
• /
• v.6 no.4
• /
• pp.411-425
• /
• 1998

The effective length factor of a framed column may be determined by means of the alignment chart procedure. This method is based on many unrealistic assumptions, among which is that all columns have the same stiffness parameter, which is dependent on the length, axial load, and moment of inertia of the column. A new approximate method is developed for the determination of effective length factors for columns in unbraced frames. This method takes into account the effects of inelastic column behaviour, far end conditions of the restraining beams and columns, semi-rigid beam-to-column connections, and differentiated stiffness parameters of columns. This method may be implemented on a microcomputer. A numerical study was carried out to demonstrate the extent to which the involved parameters affect the K factor. The beam-to-column connection stiffness, the stiffness parameter of columns, and the far end conditions of restraining members have a significant effect on the K factor of the column under investigation. The developed method is recommended for design purposes.

• Journal of Biomedical Engineering Research
• /
• v.29 no.3
• /
• pp.222-230
• /
• 2008

This paper introduces a method of estimating the knee joint moment developed during MVC. By combining the Hill-type muscle model and analytic results on moment arm and musculotendon length change as a function of hip and knee joint angle, the knee joint moment at a specific knee joint angle during MVC is determined. Many differences between the estimated results and the experimental data are noted. It is believed that these differences originate from inaccurate information on the muscle-tendon parameters. The establishment of exact values for the subject's muscle parameters is almost impossible task. However, sensitivity analysis shows that the tendon slack length is the most critical parameter when applying the Hill-type muscle model. The effect of a change of this parameter on the muscle length force relationship is analyzed in detail.

• Journal of the Korean Society of Fisheries and Ocean Technology
• /
• v.29 no.2
• /
• pp.152-161
• /
• 1993

This paper deals with the effect of spatial distribution of material properties on its statistical characteristics and numerical estimation method of reliability of fatigue sensitive structures with respect to the fatigue crack growth. A method is proposed to determine experimentally the probability distribution functions of material parameters of Paris law. da/dN=C(ΔK/K sub(0) ) super(m), using stress intensity factor controlled fatigue tests. The result with a high tensile strength steel shows that the distribution of the parameter m is approximately normal and that of 1/C, is a 3-parameter Weibull. The main result obtained are : (1) The theoretical autocorrelation of the resistance, 1/C, to fatigue crack growth are almost same for different lengths. (2) The variance decreases with the increasing a averaging length. When spatial correlation length is very small. the variane decreases significantly were the averaging length. (3) The probability distribution of load cycles or the number for a crack to reach a certain length can be estimated using these functions by simulation of non-Gaussian(expecially Weibull) Stochastic Process.

• Earthquakes and Structures
• /
• v.26 no.4
• /
• pp.299-309
• /
• 2024

The present paper develops application of third-order shear deformation theory (TSDT) and modified couple stress theory (MCST) to size-dependent bending analysis of a functionally graded cylindrical micro-shell. The radial and axial displacement components are described based on TSDT for more accurate analysis. The effect of small scales is accounted based on MCST. The principle of virtual work is used for derivation of bending governing equations. The solution is presented for a simply-supported boundary condition to account the influence of various important parameters such as micro length scale parameter, in-homogeneous index and some dimensionless geometric parameters such as length to radius and length to thickness ratios on the bending results. A comparative analysis is presented to examine the effect of order of employed shear deformation theory on the axial and radial displacements.

• Structural Engineering and Mechanics
• /
• v.53 no.6
• /
• pp.1201-1214
• /
• 2015

This paper introduces the combined effect of electric field, magnetic field and thermal field on edge wave propagating in a homogeneous isotropic prestressed plate of finite thickness and infinite length. The dispersion relation of edge wave has been obtained by using classical dynamical theory of thermoelasticity. The phase velocity has been computed and shown graphically for various initial stress parameter, electro-magneto parameter, electric parameter and thermoelastic coupling parameter.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.18 no.6
• /
• pp.681-689
• /
• 2009

Disk grinding was often applied to deburring process in order to enhance the final product quality. Inherent chamfering capability of the flexible disk grinding process in the early stage was analyzed with respect to various process parameters including workpiece length, wheel speed, depth of cut and feed. Initial chamfered edge defined as arc zone was characterized with local radius of curvature. Averaged radius and arc zone ratio was well evaluated using neural network system. Additional neural network analysis adding workpiece length showed enhance performance in predicting arc zone ratio and curvature radius with reduced error rate. A process condition design parameter was estimated using remaining input and output parameters with the prediction error rate lower than 2.0% depending on the relevant input parameter combination and neural network structure composition.

• Structural Engineering and Mechanics
• /
• v.68 no.1
• /
• pp.103-119
• /
• 2018

In the present research, an attempt is made to obtain a semi analytical solution for both nonlinear natural frequency and forced vibration of embedded functionally graded double layered nanoplates with all edges simply supported based on nonlocal strain gradient elasticity theory. The interaction of van der Waals forces between adjacent layers is included. For modeling surrounding elastic medium, the nonlinear Winkler-Pasternak foundation model is employed. The governing partial differential equations have been derived based on the Mindlin plate theory utilizing the von Karman strain-displacement relations. Subsequently, using the Galerkin method, the governing equations sets are reduced to nonlinear ordinary differential equations. The semi analytical solution of the nonlinear natural frequencies using the homotopy analysis method and the exact solution of the nonlinear forced vibration through the Harmonic Balance method are then established. The results show that the length scale parameters give nonlinearity of the hardening type in frequency response curve and the increase in material length scale parameter causes to increase in maximum response amplitude, whereas the increase in nonlocal parameter causes to decrease in maximum response amplitude. Increasing the material length scale parameter increases the width of unstable region in the frequency response curve.