• Computers and Concrete
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• 제25권4호
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• pp.283-291
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• 2020

The present paper researches post-buckling behaviors of geometrically imperfect concrete beam resting on elastic foundation reinforced with graphene oxide powders (GOPs) based on finite element method (FEM). Distribution of GOPs are considered as uniform and linearly graded through the thickness. Geometric imperfection is considered as first buckling mode shape of the beam, the GOP reinforced beam is rested in initial position. The material properties of GOP reinforced composite have been calculated via employment of Halpin-Tsai micromechanical scheme. The provided refined beam element verifies the shear deformation impacts needless of any shear correction coefficient. The post-buckling load-deflections relations have been calculated via solving the governing equations having cubic non-linearity implementing FEM. Obtained findings indicate the importance of GOP distributions, GOP weight fraction, matrix material, geometric imperfection, shear deformation and foundation parameters on nonlinear buckling behavior of GOP reinforced beam.

• Steel and Composite Structures
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• 제33권2호
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• pp.261-275
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• 2019

The main objective of this paper is to study the axial buckling and post-buckling of geometrically imperfect single-layer graphene sheets (GSs) under in-plane loading in the theoretical framework of the nonlocal strain gradient theory. To begin with, a graphene sheet is modeled by a two-dimensional plate subjected to simply supported ends, and supposed to have a small initial curvature. Then according to the Hamilton's principle, the nonlinear governing equations are derived with the aid of the classical plate theory and the von-karman nonlinearity theory. Subsequently, for providing a more accurate physical assessment with respect to the influence of respective parameters on the mechanical performances, the approximate analytical solutions are acquired via using a two-step perturbation method. Finally, the authors perform a detailed parametric study based on the solutions, including geometric imperfection, nonlocal parameters, strain gradient parameters and wave mode numbers, and then reaching a significant conclusion that both the size-dependent effect and a geometrical imperfection can't be ignored in analyzing GSs.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 추계학술대회논문집
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• pp.369-374
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• 2002

This paper presents theoretical analysis of the NRRO(non-repeatable run-out) for a ball bearing with geometric imperfection. The 3DOF dynamic analysis of a ball bearing using the Newton-Raphson method is performed to calculate the displacement of shaft center. Frequency and magnitude characteristics of radial and axial vibrations are investigated. The ball form errors of the ball, the inner race, and the outer race in a HDD spindle ball bearing are precisely measured. NRRO of a ball bearing is analyzed by using the measured waviness data. It is concluded that dominant components of radial vibrations are ${\Large}f_c\;and\;2{\Larg}f_b{\pm}{\Large}f_c$, and dominant component of axial vibrations is $2{\Large}f_b$. These are generated by the size error and the second waviness of the balls.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 추계학술대회논문초록집
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• pp.341.1-341
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• 2002

This paper presents theoretical analysis of the NRRO(the non-repeatable run-out) for a ball bearing with geometric imperfection. The 3DOF dynamic analysis of a ball bearing using the Runge-Kutta method is performed to calculate the displacement of shaft center. Frequency and magnitude characteristics of radial and axial vibrations are investigated. The ball form errors of the ball, the inner race, and the outer race in a HDD spindle ball bearing are precisely measured. (omitted)

• 한국윤활학회:학술대회논문집
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• 한국윤활학회 2001년도 제34회 추계학술대회 개최
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• pp.237-242
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• 2001

In this paper, we theoretically analyzed the NRRO(the non-repeatable run-out) of a ball bearing with ball geometric imperfection. The quasi-static and dynamic analysis of a ball bearing was performed to calculate the displacement of shaft center caused by the ball form errors while the shaft is rotating. From consideration of the generating mechanism of NRRO, it is found that the size and form errors of ball generate vibrations with (equation omitted)$\_$c/ and n(equation omitted)$\_$b/${\pm}$(equation omitted)$\_$c/(where n is even) components, respectively. The ball form errors of a ball bearing were precisely measured and NRRO of a ball bearing was calculated using the measured data. A statistical approach was peformed to analyze NRRO of ball bearings with radial errors.

• Advances in materials Research
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• 제8권3호
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• pp.237-257
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• 2019

The present article researches large-amplitude thermal free vibration characteristics of nonlocal two-phase piezo-magnetic nano-size beams having geometric imperfections by considering piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. All previous studies on vibrations of piezoelectric-magnetic nano-size beams ignore the influences of geometric imperfections which are crucial since a nanobeam is not always ideal or perfect. Nonlinear governing equations of a smart nanobeam are derived based on classical beam theory and an analytical trend is provided to obtain nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric phase in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behaviors of smart nanobeam is dependent on the magnitude of exerted electric voltage, magnetic imperfection amplitude and substrate constants.

• Smart Structures and Systems
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• 제25권6호
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• pp.707-717
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• 2020

In this paper, analysis of thermal post-buckling behaviors of sandwich nanobeams with two layers of multi-phase magneto-electro-thermo-elastic (METE) composites have been presented considering geometric imperfection effects. Multi-phase METE material is composed form piezoelectric and piezo-magnetic constituents for which the material properties can be controlled based on the percentages of the constituents. Nonlinear governing equations of sandwich nanobeam are derived based on nonlocal elasticity theory together with classic thin beam model and an analytical solution is provided. It will be shown that post-buckling behaviors of sandwich nanobeam in thermo-electro-magnetic field depend on the constituent's percentages. Buckling temperature of sandwich nanobeam is also affected by nonlocal scale factor, magnetic field intensity and electrical voltage.

• 한국공간구조학회:학술대회논문집
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• 한국공간구조학회 2006년도 춘계 학술발표회 논문집 제3권1호(통권3호)
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• pp.191-204
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• 2006

This paper investigate the optimum thickness distribution of plate structure with different essential boundary conditions in the fundamental natural frequency maximization problem. In this study, the fundamental natural frequency is considered as the objective function to be maximized and the initial volume of structures is used as the constraint function. The computer-aided geometric design (CAGD) such as Coon's patch representation is used to represent the thickness distribution of plates. A reliable degenerated shell finite element is adopted calculate the accurate fundamental natural frequency of the plates. Robust optimization algorithms implemented in the optimizer DoT are adopted to search optimum thickness values during the optimization iteration. Finally, the optimum thickness distribution with respect to different boundary condition

• Structural Engineering and Mechanics
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• 제86권3호
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• pp.361-371
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• 2023

Boundary condition is an important factor affecting the vibration characteristics of structures, under different boundary conditions, structures will exhibit different vibration behaviors. On the basis of the previous work, this paper extends to the nonlinear resonance behavior of axially moving graphene platelets reinforced metal foams (GPLRMF) plates with geometric imperfection under different boundary conditions. Based on nonlinear Kirchhoff plate theory, the motion equations are derived. Considering three boundary conditions, including four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS), the nonlinear ordinary differential equation system is obtained by Galerkin method, and then the equation system is solved to obtain the nonlinear ordinary differential control equation which only including transverse displacement. Subsequently, the resonance response of GPLRMF plates is obtained by perturbation method. Finally, the effects of different boundary conditions, material properties (including the GPLs patterns, foams distribution, porosity coefficient and GPLs weight fraction), geometric imperfection, and axial velocity on the resonance of GPLRMF plates are investigated.

• 한국농공학회지
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• 제42권5호
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• pp.151-159
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• 2000

Dynamic loading of structures often causes excursions of stresses will into the inelastic range and the influence of geometry changes on the response is also significant in may cases. In general , the shell structures designed according to quasi-Static analysis may collapse under condition of dynamic loading. Therefore, for a more realistic prediction on the lad carrying capacity of these shell. both material and geometric nonlinear effects should be considered. In this study , the material nonlinearity effect on the dynamic response is formulated by the elasto-viscoplastic model highly corresponding to the real behavior of the material. Also, the geometrically nonlinear behavior is taken into account using a Total Lagrangian formulation. the reinforcing bars are modeled by the equivalent steel layer at the location of reinforcements, and Von Mises yield criteria is adopted for the steel layer behavior. Also, Drucker-Prager yield criteria is applied for the behavior of concrete. the shape imperfection of dome is assumed as 'dimple type' which can be expressed Wd1=Wd0(1-(r-a)m)n while the shape imperfection of wall is assumed as sinusoidal curve which is Wwi =Wwo sin(n $\pi$y/l). In numerical test, three cases of shape imperfection of 0.0 -5.0cm(opposite direction to loading ; inner shape imperfection)and 5cm (direction to loading : outward shape imperfection) and thickness of steel layer determined by steel ratio of 0,3, and 5% were analyzed. The effect of shape imperfection and steel ratio and behavior characteristics of perfect shape shell and imperfect shape shell are identified through analysis of above mentioned numerical test. Dynamic behaviors of dome and wall according toe combination of shape imperfection and steel ratio are also discussed in this paper.