• Structural Engineering and Mechanics
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• v.66 no.5
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• pp.557-568
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• 2018

An investigation is made in the present work on the post-buckling and geometrically nonlinear behaviors of moderately thick perfect and imperfect rectangular plates made-up of functionally graded materials. Spectral collocation approach based on Legendre basis functions is developed to analyze the functionally graded plates while they are subjected to end-shortening strain. The material properties in this study are varied through the thickness according to the simple power law distribution. The fundamental equations for moderately thick rectangular plates are derived using first order shear deformation plate theory and taking into account both geometric nonlinearity and initial geometric imperfections. In the current study, the domain of interest is discretized with Legendre-Gauss-Lobatto nodes. The equilibrium equations will be obtained by discretizing the Von-Karman's equilibrium equations and also boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Due to effect of geometric nonlinearity, the final set of equilibrium equations is nonlinear and therefore the quadratic extrapolation technique is used to solve them. Since the number of equations in this approach will always be more than the number of unknown coefficients, the least squares technique will be used. Finally, the effects of boundary conditions, initial geometric imperfection and material properties are investigated and discussed to demonstrate the validity and capability of proposed method.

• ETRI Journal
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• v.35 no.6
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• pp.1115-1125
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• 2013

This paper presents a scheme for geometric correction of projected content for planar and quadratic projection surfaces. The scheme does not require the projection surface to be perfectly quadratic or planar and is therefore suitable for uneven low-cost commercial and home projection surfaces. An approach based on the recursive subdivision of second-order B$\acute{e}$zier patches is proposed for the estimation of projection distortion owing to surface imperfections. Unlike existing schemes, the proposed scheme is completely automatic, requires no prior knowledge of the projection surface, and uses a single uncalibrated camera without requiring any physical markers on the projection surface. Furthermore, the scheme is scalable for geometric calibration of multi-projector setups. The efficacy of the proposed scheme is demonstrated using simulations and via practical experiments on various surfaces. A relative distortion error metric is also introduced that provides a quantitative measure of the suppression of geometric distortions, which occurs as the result of an imperfect projection surface.

• Structural Engineering and Mechanics
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• v.90 no.4
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• pp.357-370
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• 2024

Due to the fact that the mechanism of the effects of temperature and initial geometric imperfection on low-velocity impact problem of axially moving plates is not yet clear, the present paper is to fill the gap. In the present paper, the nonlinear dynamic behavior of axially moving imperfect graphene platelet reinforced metal foams (GPLRMF) plates subjected to lowvelocity impact in thermal environment is analyzed. The equivalent physical parameters of GPLRMF plates are estimated based on the Halpin-Tsai equation and the mixing rule. Combining Kirchhoff plate theory and the modified nonlinear Hertz contact theory, the nonlinear governing equations of GPLRMF plates are derived. Under the condition of simply supported boundary, the nonlinear control equation is discretized with the help of Gallekin method. The correctness of the proposed model is verified by comparison with the existing results. Finally, the time history curves of contact force and transverse center displacement are obtained by using the fourth order Runge-Kutta method. Through detailed parameter research, the effects of graphene platelet (GPL) distribution mode, foam distribution mode, GPL weight fraction, foam coefficient, axial moving speed, prestressing force, temperature changes, damping coefficient, initial geometric defect, radius and initial velocity of the impactor on the nonlinear impact problem are explored. The results indicate that temperature changes and initial geometric imperfections have significant impacts.

• Steel and Composite Structures
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• v.21 no.5
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• pp.1121-1144
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• 2016

This paper presents a displacement-based finite element procedure for second-order distributed plasticity analysis of planar steel frames with semi-rigid beam-to-column connections under static loadings. A partially strain-hardening elastic-plastic beam-column element, which directly takes into account geometric nonlinearity, gradual yielding of material, and flexibility of semi-rigid connections, is proposed. The second-order effects and distributed plasticity are considered by dividing the member into several sub-elements and meshing the cross-section into several fibers. A new nonlinear solution procedure based on the combination of the Newton-Raphson equilibrium iterative algorithm and the constant work method for adjusting the incremental load factor is proposed for solving nonlinear equilibrium equations. The nonlinear inelastic behavior predicted by the proposed program compares well with previous studies. Coupling effects of three primary sources of nonlinearity, geometric imperfections, and residual stress are investigated and discussed in this paper.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2001.11a
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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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.319-326
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• 2001

In this paper, 3-D frame design using refined plastic-hinge analysis accounting for local buckling is developed. This analysis accounts for material and geometric nonlinearities of the structural system and its component members. Moreover, the problem associated with conventional refined plastic-hinge analyses, which do not consider the degradation of the flexural strength caused by local buckling, is overcome. Efficient ways of assessing steel frame behavior including gradual yielding associated with residual stresses and flexure, second-order effect, and geometric imperfections are presented. In this study, a model consisting of the width-thickness ratio is used to account for local buckling. The proposed analysis is verified by the comparison of the LRFD results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.810-816
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• 2001

In this paper, we theoretically analyzed the NRRO(the non-repeatable run-out) of a ball bearing with geometric imperfection. The quasi-static and dynamic analysis of a ball bearing was performed to calculate the displacement of shaft center caused by the form errors while the shaft is rotating. From consideration of the generating mechanism of NRRO, it is found that the waviness of one ball generates vibrations with nf$\sub$b/${\pm}$f$\sub$c/(where n is odd) components. Also it is confirmed that the outer race waviness of the order n = jZ${\pm}$1 generates vibration with jZf$\sub$c/ components. The form errors of ball bearing elements were precisely measured and NRRO of a ball bearing was calculated using the measured data. It is concluded that the ball bearings must has large ball number and small ball diameter to obtain low NRRO.

• Structural Engineering and Mechanics
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• v.77 no.4
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• pp.523-533
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• 2021

The present study investigates the lateral torsional buckling behaviour of pultruded glass fiber reinforced polymer (GFRP) simply supported channel beams subjected to uniform bending about their major axis. A parametric study by varying the sectional geometry and span of channel beams is carried out by using ABAQUS software. The accuracy of the FE models was ensured by verifying them against the available results provided in the literature. The effect of geometric nonlinearity, geometric imperfections, and the dependency of finite element mesh on the lateral torsional buckling were carefully considered in the FE model. Lateral torsional buckling (LTB) strengths obtained from the numerical study were compared with the theoretical LTB strengths obtained based on the Eurocode 3 approach for steel sections. The comparison between the numerical strengths and the design procedure proposed in the literature based on Eurocode 3 approach revealed disagreements. Therefore, a simplified improved design procedure is proposed for the safe design strength prediction of pultruded GFRP channel beams. The proposed equation has been provided that might aid the structural engineers in economically designing the pultruded GFRP channel beams in the future.

• Structural Engineering and Mechanics
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• v.86 no.3
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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.

• Steel and Composite Structures
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• v.42 no.4
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• pp.513-538
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• 2022

This paper reports on experiments addressing the buckling and collapse behavior of an innovative built-up cold-formed steel (CFS) columns. The built-up column consists of four individual CFS lipped channels, two of them placed back-to-back at the web using two self-drilling screw fasteners at specified spacing along the column length, while the other two channels were connected flange-to-flange using one self-drilling screw fastener at specified spacing along the column length. In total, 12 experimental tests are reported, covering a wide range of column lengths from stub to slender columns. The initial geometric imperfections and material properties were determined for all test specimens. The effect of screw spacing, load-versus axial shortening behaviour and buckling modes for different lengths and screw spacing were investigated. Nonlinear finite element (FE) models were also developed, which included material nonlinearities and initial geometric imperfections. The FE models were validated against the experimental results, both in terms of axial capacity and failure modes of built-up CFS columns. Furthermore, using the validated FE models, a parametric study was conducted which comprises 324 models to investigate the effect of screw fastener spacing, thicknesses and wide range of lengths on axial capacity of back-to-back and flange-to-flange built-up CFS channel sections. Using both the experimental and FE results, it is shown that design in accordance with the American Iron and Steel Institute (AISI) and Australia/New Zealand (AS/NZS) standards is slightly conservative by 6% on average, while determining the axial capacity of back-to-back and flange-to-flange built-up CFS channel sections.