• Steel and Composite Structures
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• v.45 no.4
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• pp.547-554
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• 2022

This paper studies the static stability of an axially graded column with the power-law gradient varying along the axial direction. For a nonhomogeneous column with one end linked to a rotational spring and loaded by a compressive force, respectively, an Euler problem is analyzed by solving a boundary value problem of an ordinary differential equation with varying coefficients. Buckling loads through the characteristic equation with the aid of the Bessel functions are exactly given. An alternative way to approximately determine buckling loads through the integral equation method is also presented. By comparing approximate buckling loads with the exact ones, the approximate solution is simple in form and enough accurate for varying power-law gradients. The influences of the gradient index and the rotational spring stiffness on the critical forces are elucidated. The critical force and mode shapes at buckling are presented in graph. The critical force given here may be used as a benchmark to check the accuracy and effectiveness of numerical solutions. The approximate solution provides a feasible approach to calculating the buckling loads and to assessing the loss of stability of columns in engineering.

• Journal of the Optical Society of Korea
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• v.16 no.4
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• pp.372-380
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• 2012

The optical method Digital Speckle Correlation Measurement (DSCM) has been extensively applied due its capability to measure the entire displacement field over a body surface. A formula of displacement measurement errors by the gradient-based DSCM method was derived. The errors were found to explicitly relate to the image grayscale errors consisting of sub-pixel interpolation algorithm errors, image noise, and subset deformation mismatch at each point of the subset. A power-law dependence of the standard deviation of displacement measurement errors on the subset size was established when the subset deformation was rigid body translation and random image noise was dominant and it was confirmed by both the numerical and experimental results. In a gradient-based algorithm the basic assumption is rigid body translation of the interrogated subsets, however, this is in contradiction to the real circumstances where strains exist. Numerical and experimental results also indicated that, subset shape function mismatch was dominant when the order of the assumed subset shape function was lower than that of the actual subset deformation field and the power-law dependence clearly broke down. The power-law relationship further leads to a simple criterion for choosing a suitable subset size, image quality, sub-pixel algorithm, and subset shape function for DSCM.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.10a
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• pp.706-709
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• 1997

Extruders are the heart of the polymer processing industry. The single most important mechanical element of a screw extruder is the screw. The proper design of the geometriy of the extruder screw is of crucial importance to the proper functioning of the extruder. If material transport instabilities occur as a result of improper screw geometry, even the most sophisticated computerized control system cannot solve the problem. For this purpose, characteristics design on helix angle of the extruder screw. This paper presents strength of the screw flight, optimum helix angle versus dimensionless down channel pressure gradient, optimum helix angle versus the power law index in simultaneous optimization, volumetric efficiency versus helix angle at various number of flights and power consumption versus helix angle in the barrel of screw extruder.

• Structural Engineering and Mechanics
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• v.77 no.6
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• pp.797-807
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• 2021

A new simple solution for critical buckling of FG sandwich plates under axial and biaxial loads is presented using new modified power-law formulations. Both even and uneven distributions of porosity are taken into account in this study. Material properties of the sandwich plate faces are assumed to be graded in the thickness direction according to a modified power-law distribution in terms of the volume fractions of the constituents. Equilibrium and stability equations of FG sandwich plate with various boundary conditions are derived using the higher-order shear deformation plate theory. The results reveal that the distribution shape of the porosity, the gradient index, loading type and functionally graded layers thickness have significant influence on the buckling response of functionally graded sandwich plates.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2003.05a
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• pp.461-464
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• 2003

A new control volume finite element method is proposed for three dimensional analysis of polymer flow. Tetrahedral finite element is employed and co-located interpolation procedure for pressure and velocity is implemented. Inclusion of pressure gradient term in the velocity shape functions prevents the checkerboard pressure field from being developed. Vectorial nature of pressure gradient is considered in the velocity shape function so that velocity profile in the limit of very small Reynolds number becomes physically meaningful. The proposed method was verified through three dimensional simulation of pipe flow problem for Newtonian and power-law fluid. Calculated pressure and velocity field showed an excellent agreement with analytic solutions for pressure and velocity. Driven-cavity problem, which is reported to yield checkerboard pressure filed when conventional finite element method is applied, could be solved without yielding checkerboard pressure field when the proposed control volume finite element method was applied. The proposed method could be successfully applied to the three dimensional mold filling problem.

• The Korean Journal of Ecology
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• v.27 no.1
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• pp.27-33
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• 2004

Cryptomeria japonica plantation was monitored every year during 15 years from 1983 to 1997 for stem diameter and volume. The reciprocal equation, 1/Y = A + B/N, was applied to the relationship between cumulative volume Y and cumulative number N from the largest tree in the stand each year. The parameters A and B, which means respectively the reciprocal of an asymptotic value of total stand stem volume and the reciprocal of the maximum stem volume, are related by a power function. The power functional relationship between A and B derived a linear relationship of B-points ( $N_{B}$, $V_{B}$; $N_{B}$ = B/A, $Y_{B}$ = 1/2A) of each Y-N curve on log-log coordinates. The gradient of B-point line was so steep that the Y-N curve moved parallel upward year by year. The time trajectory of mean stem volume (W) and density ($\rho$) provided evidence in favor of the 3/2 power law of self-thinning, because the gradient of W - $\rho$ trajectory on log-log coordinates approximated to -3/2 at the final stage of stand development. On the basis of the results of Y-N curves and W - $\rho$ trajectory, the time trajectory of maximum stem volume $W_{max obs}$ and $\rho$ was derived theoretically. The gradient of $W_{max obs}$ - $\rho$ trajectory on log-log coordinates is calculated to be -0.6105 at the final stage. The gradient of $W_{max obs}$ - $\rho$ trajectory was steeper than that of W - $\rho$ trajectory at the early stage, while the former is gentler than the latter at the later stage.stage.e.age.e.

• Structural Engineering and Mechanics
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• v.64 no.6
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• pp.683-693
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• 2017

According to a generalized nonlocal strain gradient theory (NSGT), dynamic modeling and free vibrational analysis of nanoporous inhomogeneous nanoplates is presented. The present model incorporates two scale coefficients to examine vibration behavior of nanoplates much accurately. Porosity-dependent material properties of the nanoplate are defined via a modified power-law function. The nanoplate is resting on a viscoelastic substrate and is subjected to hygro-thermal environment and in-plane linearly varying mechanical loads. The governing equations and related classical and non-classical boundary conditions are derived based on Hamilton's principle. These equations are solved for hinged nanoplates via Galerkin's method. Obtained results show the importance of hygro-thermal loading, viscoelastic medium, in-plane bending load, gradient index, nonlocal parameter, strain gradient parameter and porosities on vibrational characteristics of size-dependent FG nanoplates.

• Wind and Structures
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• v.19 no.5
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• pp.505-522
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• 2014

While effects of the atmospheric boundary layer flow on engineering infrastructure are more or less known, some local transient winds create difficulties for structures, traffic and human activities. Hence, further research is required to fully elucidate flow characteristics of some of those very unique local winds. In this study, important characteristics of observed vertical velocity profiles along the main wind direction for the gusty Bora wind blowing along the eastern Adriatic coast are presented. Commonly used empirical power-law and the logarithmic-law profiles are compared against unique 3-level high-frequency Bora measurements. The experimental data agree well with the power-law and logarithmic-law approximations. An interesting feature observed is a decrease in the power-law exponent and aerodynamic surface roughness length, and an increase in friction velocity with increasing Bora wind velocity. This indicates an urban-like velocity profile for smaller wind velocities and rural-like velocity profile for larger wind velocities, which is due to a stronger increase in absolute velocity at each of the heights observed as compared to the respective velocity gradient (difference in average velocity among two different heights). The trends observed are similar during both the day and night. The thermal stratification is near neutral due to a strong mechanical mixing. The differences in aerodynamic surface roughness length are negligible for different time averaging periods when using the median. For the friction velocity, the arithmetic mean proved to be independent of the time record length, while for the power-law exponent both the arithmetic mean and the median are not influenced by the time averaging period. Another issue is a large difference in aerodynamic surface roughness length when calculating using the arithmetic mean and the median. This indicates that the more robust median is a more suitable parameter to determine the aerodynamic surface roughness length than the arithmetic mean value. Variations in velocity profiles at the same site during different wind periods are interesting because, in the engineering community, it has been commonly accepted that the aerodynamic characteristics at a particular site remain the same during various wind regimes.

• Structural Monitoring and Maintenance
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• v.7 no.2
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• pp.69-84
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• 2020

Based on differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT), forced vibrations of a porous functionally graded (FG) scale-dependent beam in thermal environments have been investigated in this study. The nanobeam is assumed to be in contact with a moving point load. NSGT contains nonlocal stress field impacts together with the microstructure-dependent strains gradient impacts. The nano-size beam is constructed by functionally graded materials (FGMs) containing even and un-even pore dispersions within the material texture. The gradual material characteristics based upon pore effects have been characterized using refined power-law functions. Dynamical deflections of the nano-size beam have been calculated using DQM and Laplace transform technique. The prominence of temperature rise, nonlocal factor, strain gradient factor, travelling load speed, pore factor/distribution and elastic substrate on forced vibrational behaviors of nano-size beams have been explored.

• Advances in nano research
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• v.8 no.1
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• pp.49-58
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• 2020

This paper investigates the vibration characteristics of flexoelectric nanobeams resting on viscoelastic foundation and subjected to magneto-electro-viscoelastic-hygro-thermal (MEVHT) loading. In this regard, the Nonlocal strain gradient elasticity theory (NSGET) is employed. The proposed formulation accommodates the nonlocal stress and strain gradient parameter along with the flexoelectric coefficient to accurately predict the frequencies. Further, with the aid of Hamilton's principle the governing differential equations are derived which are then solved through Galerkin-based approach. The variation of the natural frequency of MEVHT nanobeams under the influence of various parameters such as the nonlocal strain gradient parameter, different field loads, power-law exponent and slenderness ratio are also investigated.