• Structural Engineering and Mechanics
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• v.70 no.6
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• pp.737-750
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• 2019

This paper investigates the static and dynamic behaviors of imperfect single walled carbon nanotube (SWCNT) modeled as a beam structure by using energy-equivalent model (EEM), for the first time. Based on EEM Young's modulus and Poisson's ratio for zigzag (n, 0), and armchair (n, n) carbon nanotubes (CNTs) are presented as functions of orientation and force constants. Nonlinear Euler-Bernoulli assumptions are proposed considering mid-plane stretching to exhibit a large deformation and a small strain. To simulate the interaction of CNTs with the surrounding elastic medium, nonlinear elastic foundation with cubic nonlinearity and shearing layer are employed. The equation governed the motion of curved CNTs is a nonlinear integropartial-differential equation. It is derived in terms of only the lateral displacement. The nonlinear integro-differential equation that governs the buckling of CNT is numerically solved using the differential integral quadrature method (DIQM) and Newton's method. The linear vibration problem around the static configurations is discretized using DIQM and then is solved as a linear eigenvalue problem. Numerical results are depicted to illustrate the influence of chirality angle and imperfection amplitude on static response, buckling load and dynamic behaviors of armchair and zigzag CNTs. Both, clamped-clamped (C-C) and simply supported (SS-SS) boundary conditions are examined. This model is helpful especially in mechanical design of NEMS manufactured from CNTs.

• Journal of the Korean Society for Precision Engineering
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• v.27 no.6
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• pp.90-97
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• 2010

In order to understand the biomaterial like the blood vessel of artery, there is a need to quantify the biomechanical behavior of the vessel. Using computer-controlled experimental system, the experiment can acquire data such as inner pressure, axial load, diameter and axial gauge length without contacting the specimen. Rubber-liked material which is similar to passive artery was selected as pseudo-biomaterial. Deformations are measured for pressure-diameter curves. The data were collected and stored online to be used in the feedback control of experimental protocols. Finally, the illustrative data obtained from the experimental system were presented and the system shows that strain invariants are controlled to understand the nonlinear elastic behavior of biomaterial which is involved with strain energy function.

• Transactions of the Korean Society of Mechanical Engineers
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• v.2 no.3
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• pp.62-68
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• 1978

The influences of the large amplitude free vibrations of simply supported Timoshenko beams with ends restrained to remain a fixed distance apart and with no axial restraints, which cause a longitudinal elastic force and a longitudinal inertia force, respectively, are investigated. The equations of motion derived by an appropriate linearizarion of the nonlinear strain- displacement relation have nonlinear terms arising from large curvature, longitudinal elastic force and longitudinal inertia force. The fourth order nonlinear partial differential equations for the deflection, can be reduced to the nonlinear ordinary differential equations by means of Galerkin procedure and a modal expansion. The general response and frequensy-amplitude relations are derived by the perturbation method of strained parameters. Comparison with previously published results is made.

• Geomechanics and Engineering
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• v.22 no.4
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• pp.277-290
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• 2020

This paper presents an elastic-plastic solution for the circular tunnel of elastic-strain softening behavior considering the pressure-dependent Young's modulus and the nonlinear dilatancy. The proposed solution is verified by the results of the field measuring and numerical simulation from a practical project, and a published closed-form analysis solution. The influence of each factor is discussed in detail, and the ability of Young's modulus and dilatancy characterizing the mechanical response of surrounding rock is investigated. It is found that, in low levels of support pressure, adopting the constant Young's modulus model will seriously misestimate the surrounding rock deformation. Using the constant dilatancy model will underestimate the surrounding rock deformation. When adopting the constant dilatancy model, as the dilation angle increases, the range of the plastic region increases, and the surrounding rock deformation weakens. When adopting the nonlinear dilatancy, the plastic region range and the surrounding rock deformation are the largest. The surrounding rock deformation using pressure-dependent Young's modulus model is between those resulted from two constant Young's modulus models. The constant α of pressuredependent Young's modulus model is the main factor affecting the tunnel displacement. The influence of α using a constant dilatancy model is much more apparent than that using a nonlinear dilatancy model.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.335-342
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• 2002

A continuum-based design sensitivity analysis (DSA) method fur non-shape problems is developed for geometrically nonlinear elastic structures. The non-shape problem is characterized by the design variables that are not associated with the domain of system like sizing, material property, loading, and so on. Total Lagrangian formulation with the Green-Lagrange strain and the second Piola-Kirchhoff stress is employed to describe the geometrically nonlinear structures. The spatial domain is discretized using the 4-node isoparametric plane stress/strain elements. The resulting nonlinear system is solved using the Newton-Raphson iterative method. To take advantage of the derived analytical sensitivity In topology optimization, a fast and efficient design sensitivity analysis method, adjoint variable method, is employed and the material property of each element is selected as non-shape design variable. Combining the design sensitivity analysis method and a gradient-based design optimization algorithm, an automated design optimization method is developed. The comparison of the analytical sensitivity with the finite difference results shows excellent agreement. Also application to the topology design optimization problem suggests a very good insight for the layout design.

• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.279-292
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• 2006

A new approach using the differential quadrature method (DQM) is derived for analysis of non-uniform beams resting on nonlinear media in this study. The influence of velocity dependent viscous damping and strain rate dependent viscous damping is investigated. The results solved using the DQM have excellent agreement with the results solved using the FEM. Numerical results indicated that the DQM is valid and efficient for non-uniform beams resting on non-linear media.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1992.10a
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• pp.52-57
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• 1992

The purpose of this study is that to develop computer program, which is about to analy size nonlinear behaviour of elastic framed structures include to geometric & material nonlineality, and to formulate between stress-strain relationship. In order to examplity the efficiency of this program, a few analytical results have been obtained on : (1) nonlinear behaviour of beam which is subject to vertical force (2) nonlinear behaviour of portal frame which is subject to vertical & horizontal force.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.6
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• pp.848-859
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• 2004

Mechanical testing methods to determine the material constants for large deformation nonlinear finite element analysis were demonstrated for natural rubber. Uniaxial tension, uniaxial compression, equi-biaxial tension and pure shear tests of rubber specimens are performed to achieve the stress-strain curves. The stress-strain curves are obtained after between 5 and 10 cycles to consider the Mullins effect. Mooney and Ogden strain-energy density functions, which are typical form of the hyperelastic material, are determined and compared with each other. The material constants using only uniaxial tension data are about 20% higher than those obtained by any other test data set. The experimental equations of shear elastic modulus on the hardness and maximum strain are presented using multiple regression method. Large deformation finite element analysis of automotive transmission mount using different material constants is performed and the load-displacement curves are compared with experiments. The selection of material constant in large deformation finite element analysis depend on the strain level of component in service.

• Magazine of the Korea Concrete Institute
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• v.8 no.2
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• pp.119-127
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• 1996

Objection of this study is to present the three-dimensional material nonlinear analysis of reinforced concrete. A concrete is idealized with three-dimensional 16-node solid element including triaxial nonlinear stress-strain behavior, cracking, crushing and strain softening: a steel with three-dimensional 3 node truss element including elastic-plastic behavior with strain hardening. The cracked shear retention factor is introduced to estimate the effective shear modulus con sidering aggregate interlock after c:racking and a modified newton method is used to obtain a nu merical solution. Numerical results in a gauss point is displayed graphically. Numerical examples of Krahl's reinforced concrete beam and Hedgreds shell are selected to compare with the experimental and numerical results.

• Structural Engineering and Mechanics
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• v.71 no.6
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• pp.669-682
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• 2019

We in this article study nonlinear thermal buckling of bi-directional functionally graded beams in the theoretical frameworks of nonlocal strain graded theory. To begin with, it is assumed that the effective material properties of beams vary continuously in both the thickness and width directions. Then, we utilize a higher-order shear deformation theory that includes a physical neutral surface to derive the size-dependent governing equations combining with the Hamilton's principle and the von $K{\acute{a}}rm{\acute{a}}n$ geometric nonlinearity. It should be pointed out that the established model, containing a nonlocal parameter and a strain gradient length scale parameter, can availably account for both the influence of nonlocal elastic stress field and the influence of strain gradient stress field. Subsequently, via using a easier group of initial asymptotic solutions, the corresponding analytical solution of thermal buckling of beams is obtained with the help of perturbation method. Finally, a parametric study is carried out in detail after validating the present analysis, especially for the effects of a nonlocal parameter, a strain gradient length scale parameter and the ratio of the two on the critical thermal buckling temperature of beams.