• Journal of Astronomy and Space Sciences
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• v.28 no.1
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• pp.37-54
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• 2011

Two semi-analytic solutions for a perturbed two-body problem known as Lagrange planetary equations (LPE) were compared to a numerical integration of the equation of motion with same perturbation force. To avoid the critical conditions inherited from the configuration of LPE, non-singular orbital elements (EOE) had been introduced. In this study, two types of orbital elements, classical Keplerian orbital elements (COE) and EOE were used for the solution of the LPE. The effectiveness of EOE and the discrepancy between EOE and COE were investigated by using several near critical conditions. The near one revolution, one day, and seven days evolutions of each orbital element described in LPE with COE and EOE were analyzed by comparing it with the directly converted orbital elements from the numerically integrated state vector in Cartesian coordinate. As a result, LPE with EOE has an advantage in long term calculation over LPE with COE in case of relatively small eccentricity.

• Interaction and multiscale mechanics
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• v.2 no.3
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• pp.223-233
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• 2009

This paper presents a new nonlocal stress variational principle approach for the transverse free vibration of an Euler-Bernoulli cantilever nanobeam with an initial axial tension at its free end. The effects of a nanoscale at molecular level unavailable in classical mechanics are investigated and discussed. A sixth-order partial differential governing equation for transverse free vibration is derived via variational principle with nonlocal elastic stress field theory. Analytical solutions for natural frequencies and transverse vibration modes are determined by applying a numerical analysis. Examples conclude that nonlocal stress effect tends to significantly increase stiffness and natural frequencies of a nanobeam. The relationship between natural frequency and nanoscale is also presented and its significance on stiffness enhancement with respect to the classical elasticity theory is discussed in detail. The effect of an initial axial tension, which also tends to enhance the nanobeam stiffness, is also concluded. The model and approach show potential extension to studies in carbon nanotube and the new result is useful for future comparison.

• Structural Engineering and Mechanics
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• v.60 no.4
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• pp.547-565
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• 2016

In this work a new 3-unknown non-polynomial shear deformation theory for the buckling and vibration analyses of functionally graded material (FGM) sandwich plates is presented. The present theory accounts for non-linear in plane displacement and constant transverse displacement through the plate thickness, complies with plate surface boundary conditions, and in this manner a shear correction factor is not required. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only 3 unknowns as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT). The plate properties are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton's principle. Analytical solutions of natural frequency and critical buckling load for functionally graded sandwich plates are obtained using the Navier solution. The results obtained for plate with various thickness ratios using the present non-polynomial plate theory are not only substantially more accurate than those obtained using the classical plate theory, but are almost comparable to those obtained using higher order theories with more number of unknown functions.

• Journal of Korea Water Resources Association
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• v.37 no.11
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• pp.889-896
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• 2004

The fractal advection-diffusion equation (ADE) is a generalization of the classical AdE in which the second-order derivative is replaced with a fractal order derivative. While the fractal ADE have been analyzed with a stochastic process In the Fourier and Laplace space so far, in this study a fractal ADE for describing solute transport in rivers is derived with a finite difference scheme in the real space. This derivation with a finite difference scheme gives the hint how the fractal derivative order and fractal diffusion coefficient can be estimated physically In contrast to the classical ADE, the fractal ADE is expected to be able to provide solutions that resemble the highly skewed and heavy-tailed time-concentration distribution curves of contaminant plumes observed in rivers.

• Structural Engineering and Mechanics
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• v.59 no.3
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• pp.579-599
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• 2016

In this study, static bending of edge cracked micro beams is studied analytically under uniformly distributed transverse loading based on modified couple stress theory. The cracked beam is modelled using a proper modification of the classical cracked-beam theory consisting of two sub-beams connected through a massless elastic rotational spring. The deflection curve expressions of the edge cracked microbeam segments separated by the rotational spring are determined by the Integration method. The elastic curve functions of the edge cracked micro beams are obtained in explicit form for cantilever and simply supported beams. In order to establish the accuracy of the present formulation and results, the deflections are obtained, and compared with the published results available in the literature. Good agreement is observed. In the numerical study, the elastic deflections of the edge cracked micro beams are calculated and discussed for different crack positions, different lengths of the beam, different length scale parameter, different crack depths, and some typical boundary conditions. Also, the difference between the classical beam theory and modified couple stress theory is investigated for static bending of edge cracked microbeams. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.179-184
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• 2002

We consider the heterogeneous fleet vehicle routing problem (HVRP), a variant of the classical vehicle routing problem (VRP). The HVRP differs from the classical VRP in that it deals with a heterogeneous fleet of vehicles having various capacities, fixed costs, and variables costs. Therefore the HVRP is to find the fleet composition and a set of routes with minimum total cost. We give an integer programming formulation of the problem and propose an algorithm to solve it. Although the formulation has exponentially many variables, we can efficiently solve the linear programming relaxation of it by using the column generation technique. To generate profitable columns we solve a shortest path problem with capacity constraints using dynamic programming. After solving the linear programming relaxation, we apply a branch-and-bound procedure. We test the proposed algorithm on a set of benchmark instances. Test results show that the algorithm gives best-known solutions to almost all instances.

• Advances in nano research
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• v.3 no.4
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• pp.177-191
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• 2015

In this article, various higher-order shear deformation theories (HSDTs) are developed for bending and buckling behaviors of nanowires including surface stress effects. The most important assumption used in different proposed beam theories is that the deflection consists of bending and shear components and thus the theories have the potential to be utilized for modeling of the surface stress influences on nanowires problems. Numerical results are illustrated to prove the difference between the response of the nanowires predicted by the classical and non-classical solutions which depends on the magnitudes of the surface elastic constants.

• Geomechanics and Engineering
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• v.19 no.2
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• pp.179-191
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• 2019

Based on the effective stress principle, a new formula for shear strength of unsaturated soil is derived under the general nonlinear Mohr-Coulomb (M-C) strength criterion to improve the classical strength criterion of unsaturated soil. Meanwhile, the simple irrigation model under steady seepage is adopted to obtain the distribution of the matrix suction or the degree of saturation (DOS) above the groundwater table in the slope. Then, combined with the improved strength criterion of unsaturated soil and the simple irrigation model under steady seepage, the limit equilibrium (LE) solutions for the unsaturated slope stability are established according to the global LE conditions of the entire sliding body with assumption of the stresses on the slip surface. Compared to the classical strength criterion of unsaturated soil, not only the cohesion soil but also the internal friction angle is affected by the matric suction or the DOS in the improved strength criterion. Moreover, the internal friction angle related to the matric suction has the nonlinear characteristics, particularly for a small of the matric suction. Thereafter, the feasibility of the present method is verified by comparison and analysis on some slope examples. Furthermore, stability charts are also drawn to quickly analyze the unsaturated slope stability.

• Steel and Composite Structures
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• v.43 no.6
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• pp.707-723
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• 2022

This article aims to investigate the size dependent bending behavior of perforated nanobeams incorporating the nonlocal and the microstructure effects based on the nonlocal strain gradient elasticity theory (NSGET). Shear deformation effect due to cutout process is studied by using Timoshenko beams theory. Closed formulas for the equivalent geometrical characteristics of regularly squared cutout shape are derived. The governing equations of motion considering the nonlocal and microstructure effects are derived in comprehensive procedure and nonclassical boundary conditions are presented. Analytical solution for the governing equations of motion is derived. The derived non-classical analytical solutions are verified by comparing the obtained results with the available results in the literature and good agreement is observed. Numerical results are obtained and discussed. Parametric studies are conducted to explore effects of perforation characteristics, the nonclassical material parameters, beam slenderness ratio as well as the boundary and loading conditions on the non-classical transverse bending behavior of cutout nanobeams. Results obtained are supportive for the design, analysis and manufacturing of such nanosized structural system.

• Steel and Composite Structures
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• v.45 no.5
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• pp.697-713
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• 2022

In the context of the finite elements method, the dynamic behavior of porous functionally graded double wishbone vehicle suspension structural system incorporating joints flexibility constraints under road bump excitation is studied and analyzed. The functionally graded material properties distribution through the thickness direction is simulated by the power law including the porosity effect. To explore the porosity effects, both classical and adopted porosity models are considered based on even porosity distribution pattern. The dynamic equations of motion are derived based on the Hamiltonian principle. Closed forms of the inertia and material stiffness components are derived. Based on the plane frame isoparametric Timoshenko beam element, the dynamic finite elements equations are developed incorporating joint flexibilities constraints. The Newmark's implicit direct integration methodology is utilized to obtain the transient vibration time response under road bump excitation. The presented procedure is validated by comparing the computational model results with the available numerical solutions and an excellent agreement is observed. Obtained results show that the decrease of porosity percentage and material graduation tends to decrease the deflection as well as the resulting stresses of the control arms thus improving the dynamic performance and increasing the service lifetime of the control arms.