• Advances in nano research
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• v.6 no.3
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• pp.257-278
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• 2018

Vibration of axially functionally graded nano-rods and beams is investigated. It is assumed that the material properties change along the rod and beam length. The Ritz method with algebraic polynomials is used in the formulation of the problems. Stress gradient elasticity theory is utilized in order to include the nonlocal effects. Frequencies are obtained for different boundary conditions, geometrical and material properties. Nonlocal parameter is assumed as changing linearly or quadratically along the length of the nanostructure. Frequencies are compared to constant nonlocal parameter cases and considerable differences are observed between constant and variable nonlocal parameter cases. Mode shapes in various cases are depicted in order to explain the effects of axial grading.

• Steel and Composite Structures
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• v.2 no.3
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• pp.195-208
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• 2002

Elasticity solutions to the boundary-value problems of dynamic response under transverse asymmetric load of cross-ply shallow cylindrical panels are presented. The shell panel is simply supported along all four sides and has finite length. The highly coupled partial differential equations are reduced to ordinary differential equations with constant coefficients by means of trigonometric function expansion in the circumferential and axial directions. The resulting ordinary differential equations are solved by Galerkin finite element method. Numerical examples are presented for two (0/90 deg.) and three (0/90/0 deg.) laminations under dynamic loading.

• Interaction and multiscale mechanics
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• v.4 no.2
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• pp.123-137
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• 2011

We review a series of crack problems arising in the general deformations of a linearly elastic solid (Mode-I, Mode-II and Mode-III crack) and, perhaps more significantly, when the contribution of surface effects are taken into account. The surface mechanics are incorporated using the continuum based surface/interface model of Gurtin and Murdoch. We show that the deformations of an elastic solid containing a single crack can be decoupled into in-plane (Mode-I and Mode-II crack) and anti-plane (Mode-III crack) parts, even when the surface mechanics is introduced. In particular, it is shown that, in contrast to classical fracture mechanics (where surface effects are neglected), the incorporation of surface elasticity leads to the more accurate description of a finite stress at the crack tip. In addition, the corresponding stress fields exhibit strong dependency on the size of crack.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.4
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• pp.574-581
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• 2001

Transient linear elastodynamic problems are numerically analyzed in a time-domain by the Finite Element Method, for which the variational formulation based upon the equations of motion in convolution integral is newly derived. This formulation is implicit and does not include the time derivative terms so that the computation procedure is simple and less assumptions are required comparing to the conventional time-domain dynamic numerical algorithms, being able to get the improved numerical accuracy and stability. That formulation is expanded using the semi-discrete approximation to obtain the finite element equations. In the temporal approximation, the time axis is divided equally and constant and linear time variations are assumed in those intervals. It is found that unconditionally stable numerical results are obtained in case of the constant time variation. Some numerical examples are given to show the versatility of the presented formulation.

• Interaction and multiscale mechanics
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• v.3 no.3
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• pp.267-276
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• 2010

A nonlocal finite element model is developed for solving elasto-static frictional contact problems of nanostructures and nanoscale devices. A two dimensional Eringen-type nonlocal elasticity model is adopted. The material is characterized by a stress-strain constitutive relation of a convolution integral form whose kernel is capable to take into account both the diffusion process of nonlocal elasticity and the scale ratio effects. The incremental convex programming procedure is exploited as a solver. Two examples of different nature are presented, the first one presents the behavior of a nanoscale contacting system and the second example discusses the nano-indentation problem.

• Journal of the Korean Society of Safety
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• v.16 no.4
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• pp.208-212
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• 2001

DQM(differential quadrature method) is applied to computation of two dimensional elasticity problems in helical spring. Elastic shear stresses in an axially loaded helical spring having rectangular and square cross sections are calculated. The results are compared with those obtained using the method of successive approximations. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.

• Structural Engineering and Mechanics
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• v.15 no.4
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• pp.395-414
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• 2003

In this paper we recall briefly the constitutive equations for solids subjected to thermal strain taking in account the bounded tensile stress of the material. In view to solve the equilibrium problem via the finite element method using the Newton Raphson procedure, we show that the tangent elasticity tensor is semi-definite positive. Therefore, in order to obtain a convergent numerical method, the constitutive equation needs to be modified. Specifically, the dependency of the stress by the anelastic deformation is made explicit by means of a parameter ${\delta}$, varying from 0 to 1, that factorizes the elastic tensor. This parameterization, for ${\delta}$ near to 0, assures the positiveness of the tangent elasticity tensor and enforces the convergence of the numerical method. Some numerical examples are illustrated.

• Proceedings of the Korean Institute of Building Construction Conference
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• 2009.05b
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• pp.225-229
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• 2009

It has been found that existing detects at the junction between waterproofing layer as well as the material and the surfaces of the construction when waterproofing sheet is employed in the currently used unground structures waterproofing technology, causing a series of problems such as the high cost to the maintenance for leakage and the durability. The purpose of this study is about reducing the waterpoofing defects in underground structures. consequently, the homogeneous sheet which has some quality such as the unvulcanizate, high-adhesion and high-elastic was examined on physical properties. As a test result, it was confirmed to have satisfied performance about the ks. However, it must be continued to study through mock-up test for confirming of site application.

• Advances in Computational Design
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• v.9 no.1
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• pp.73-80
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• 2024

The aim of this paper is to remove the rigid body motion in the interior boundary value problem (BVP) of plane elasticity by solving the interior and exterior BVPs simultaneously. First, we formulate the interior and exterior BVPs simultaneously. The tractions applied on the contour in two problems are the same. After adding and subtracting the two boundary integral equations (BIEs), we will obtain a couple of BIEs. In the coupled BIEs, the properties of relevant integral operators are modified, and those integral operators are generally invertible. Finally, a unique solution for boundary displacement of interior region can be obtained.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.5
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• pp.939-951
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• 2002

We propose a new multiscale Galerkin method based on interpolation wavelets for two-dimensional Poisson's and plane elasticity problems. The major contributions of the present work are: 1) full multiresolution numerical analysis is carried out, 2) general boundaries are handled by a fictitious domain method without using a penalty term or the Lagrange multiplier, 3) no special integration rule is necessary unlike in the (bi-)orthogonal wavelet-based methods, and 4) an efficient adaptive scheme is easy to incorporate. Several benchmark-type problems are considered to show the effectiveness and the potentials of the present approach. is 1-2m/s and impact deformation of the electrode depends on the strain rate at that velocity, the dynamic behavior of the sinter-forged Cu-Cr is a key to investigate the impact characteristics of the electrodes. The dynamic response of the material at the high strain rate is obtained from the split Hopkinson pressure bar test using disc-type specimens. Experimental results from both quasi-static and dynamic compressive tests are Interpolated to construct the Johnson-Cook model as the constitutive relation that should be applied to simulation of the dynamic behavior of the electrodes. The impact characteristics of a vacuum interrupter are investigated with computer simulations by changing the value of five parameters such as the initial velocity of a movable electrode, the added mass of a movable electrode, the wipe spring constant, initial offset of a wipe spring and the virtual fixed spring constant.