• International Journal of Precision Engineering and Manufacturing
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• 제4권4호
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• pp.25-31
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• 2003

A computer simulation model for investigating a two-dimensional (2-D) rounding mechanism in a centerless grinding process is described. This model includes the interference phenomena and the concept of machining elasticity. Since initial contact points are used as a reference, the result of this simulation is not affected by the location of the reference circle center and the radius of the reference circle. Also, details of the machining factor are studied by using process variables (grinding wheel speed, wheel specification, workpiece speed, dressing condition, etc.). The effect of the threshold grinding force on the size of ground workpiece is investigated. For the verification of this method, simulation results are compared with the experimental work.

• 한국가구학회지
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• 제11권2호
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• pp.1-6
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• 2000

This study was carried out to investigate the effect of steaming on mechanical properties of heat-compressed wood specimens. The specimens for this mechanical strength tests were prepared to super-heated steam treatment after compression to the radial direction of sonamu (Pinus densiflora). The specimen's size is $50(L)mm{\times}20(R)mm{\times}17(T)mm$. Steaming temperature and treatment time is $120^{\circ}C$ and 20, 40, 60, 80, 100 minutes, respectively. Modulus of elasticity(MOE) in compressive test is directly proportional to steaming time. On the other hand, modulus of elasticity in bending test between steaming and not steaming after heat-compressed wood is similar irrespective of steaming time. The reason for this phenomenon is not clear yet.

• Structural Engineering and Mechanics
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• 제15권6호
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• pp.705-716
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• 2003

Gradient elastic flexural beams are dynamically analysed by analytic means. The governing equation of flexural beam motion is obtained by combining the Bernoulli-Euler beam theory and the simple gradient elasticity theory due to Aifantis. All possible boundary conditions (classical and non-classical or gradient type) are obtained with the aid of a variational statement. A wave propagation analysis reveals the existence of wave dispersion in gradient elastic beams. Free vibrations of gradient elastic beams are analysed and natural frequencies and modal shapes are obtained. Forced vibrations of these beams are also analysed with the aid of the Laplace transform with respect to time and their response to loads with any time variation is obtained. Numerical examples are presented for both free and forced vibrations of a simply supported and a cantilever beam, respectively, in order to assess the gradient effect on the natural frequencies, modal shapes and beam response.

• Structural Engineering and Mechanics
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• 제59권3호
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• pp.475-502
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• 2016

Nanobeams are widely used as a structural element for nanodevices and nanomachines. The development of nano-sized machines depends on proper understanding of mechanical behavior of these nano-sized beam elements. Small length scales such as lattice spacing between atoms, surface properties, grain size etc. are need to be considered when applying any classical continuum model. In this study, Eringen's nonlocal elasticity theory is incorporated into classical beam model considering the effects of axial extension and the shear deformation to capture unique static behavior of the nanobeams under continuum mechanics theory. The governing differential equations are obtained for curved beams and solved exactly by using the initial value method. Circular uniform beam with concentrated loads are considered. The displacements, slopes and the stress resultants are obtained analytically. A detailed parametric study is conducted to examine the effect of the nonlocal parameter, mechanical loadings, opening angle, boundary conditions, and slenderness ratio on the static behavior of the nanobeam.

• Structural Engineering and Mechanics
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• 제66권3호
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• pp.369-377
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• 2018

In this article, buckling and free vibration of functionally graded (FG) nanobeams resting on elastic foundation are investigated by developing various higher order beam theories which capture shear deformation influences through the thickness of the beam without the need for shear correction factors. The elastic foundation is modeled as linear Winkler springs as well as Pasternak shear layer. The material properties of FG nanobeam are supposed to change gradually along the thickness through the Mori-Tanaka model. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. From Hamilton's principle, the nonlocal governing equations of motion are derived and then solved applying analytical solution. To verify the validity of the developed theories, the results of the present work are compared with those available in literature. The effects of shear deformation, elastic foundation, gradient index, nonlocal parameter and slenderness ratio on the buckling and free vibration behavior of FG nanobeams are studied.

• 대한기계학회논문집
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• 제18권1호
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• pp.65-76
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• 1994

A higher-oder laminated plate theory including the effect of transverse shear deformation is developed to calculate the gross response and the detailed stress distribution. The theory satisfies the continuity condition of transverse shear stress, and accounts for parabolic variation of the transverse shear stresses through the thickness of each layer. Exact closed-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and a simple higher-order theory solutions. The results of the present work exhibit acceptable accuracy when compared to the three-dimensional elasticity solutions.

• East Asian mathematical journal
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• 제37권5호
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• pp.553-566
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• 2021

In the over-the-counter market, option's buyers could have a problem for default risk caused by option's writers. In addition, many participants try to maximize their benefits obviously in investing the financial derivatives. Taking all these circumstances into consideration, we deal with the vulnerable power options under a constant elasticity variance (CEV) model. We derive an analytic pricing formula for the vulnerable power option by using the asymptotic analysis, and then we verify that the analytic formula can be obtained accurately by comparing our solution with Monte-Carlo price. Finally, we examine the effect of CEV on the option price based on the derived solution.

• Advances in nano research
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• 제7권4호
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• pp.265-275
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• 2019

In this work, the effect of size on the axial buckling behavior of single-layered graphene sheets embedded in elastic media is studied. We incorporate Eringen's nonlocal elasticity equations into three plate theories of first order shear deformation theory, higher order shear deformation theory, and classical plate theory. The surrounding elastic media are simulated using Pasternak and Winkler foundation models and their differences are evaluated. The results obtained from different nonlocal plate theories include the values of Winkler and Pasternak modulus parameters, mode numbers, nonlocal parameter, and side lengths of square SLGSs. We show here that axial buckling behavior strongly depends on modulus and nonlocal parameters, which have different values for different mode numbers and side lengths. In addition, we show that in different nonlocal plate theories, nonlocality is more influential in first order shear deformation theory, especially in certain range of nonlocal parameters.

• Steel and Composite Structures
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• 제32권2호
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• pp.281-292
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• 2019

Nonlocal elasticity and Reddy plant theory are used to study the vibration response of functionally graded (FG) nanoplates resting on two parameters elastic medium called Pasternak foundation. Nonlocal higher order theory accounts for the effects of both scale and the effect of transverse shear deformation, which becomes significant where stocky and short nanoplates are concerned. It is assumed that the properties of FG nanoplate follow a power law through the thickness. In addition, Poisson's ratio is assumed to be constant in this model. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of nanoplate with surrounding elastic medium. Using Hamilton's principle, size-dependent governing differential equations of motion and corresponding boundary conditions are derived. A differential quadrature approach is being utilized to discretize the model and obtain numerical solutions for various boundary conditions. The model is validated by comparing the results with other published results.

• Steel and Composite Structures
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• 제32권3호
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• pp.293-304
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• 2019

In the present paper, the element free Galerkin (EFG) method is developed for geometrically nonlinear analysis of deep beams considering small scale effect. To interpret the behavior of structure at the nano scale, the higher-order gradient elasticity nonlocal theory is taken into account. The radial point interpolation method with high order of continuity is used to construct the shape functions. The nonlinear equation of motion is derived using the principle of the minimization of total potential energy based on total Lagrangian approach. The Newmark method with the small time steps is used to solve the time dependent equations. At each time step, the iterative Newton-Raphson technique is applied to minimize the residential forces caused by the nonlinearity of the equations. The effects of nonlocal parameter and aspect ratio on stiffness and dynamic parameters are discussed by numerical examples. This paper furnishes a ground to develop the EFG method for large deformation analysis of structures considering small scale effects.