• Journal of the Institute of Electronics Engineers of Korea SD
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• v.45 no.8
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• pp.11-16
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• 2008

In this paper, firstly we made of the rapid thermal processor equipment with the specifically useful structure to measure wafer stress. Secondly we made of the laser interferometry to inspect the wafer surface curvature based on the large deformation theory. And then the wafer surface fringe image was obtained by experiment, and the full field stress distribution of wafer surface comes into view by signal processing with thining and pitch mapping. After wafer was ground by 1mm and polished from the back side to get easily deformation, and it was heated by three to four times thermal treatments at about 1000 degree temperature. Finally the severe deformation between wafer before and after the heat treatment was shown.

• International Journal of High-Rise Buildings
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• v.3 no.3
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• pp.231-241
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• 2014

Ductile fracture is one of the most common failure modes of steel beam-to-column connections in moment resisting frames. Most proposed evaluation methods of the plastic deformation capacity of a beam until ductile fracture are based on steel beam tests, where the material's yield strength/ratio, the beam's moment gradient, and loading history are the most important parameters. It is impossible and unpractical to cover all these parameters in real tests. Therefore, a new attempt to evaluate a beam's plastic deformation capacity through analysis is introduced in this paper. Another important issue is about the loading histories. Recent years, the effect on the structural component under long-duration ground motion has drawn great attentions. Steel beams tends to experience a large number of loading cycles with small amplitudes during long-duration earthquakes. However, current research often focuses on the beam's behavior under standard incremental loading protocols recommended by respective countries. In this paper, the plastic deformation capacity of steel beams subjected to long duration ground motions was evaluated through analytical methodology.

• Advances in nano research
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• v.4 no.3
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• pp.229-249
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• 2016

In this paper, buckling characteristics of nonhomogeneous functionally graded (FG) nanobeams embedded on elastic foundations are investigated based on third order shear deformation (Reddy) without using shear correction factors. Third-order shear deformation beam theory accounts for shear deformation effects by a parabolic variation of all displacements through the thickness, and verifies the stress-free boundary conditions on the top and bottom surfaces of the FG nanobeam. A two parameters elastic foundation including the linear Winkler springs along with the Pasternak shear layer is in contact with beam in deformation, which acts in tension as well as in compression. The material properties of FG nanobeam are supposed to vary gradually along the thickness and are estimated through the power-law and Mori-Tanaka models. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. Nonlocal equations of motion are derived through Hamilton's principle and they are solved applying analytical solution. Comparison between results of the present work and those available in literature shows the accuracy of this method. The obtained results are presented for the buckling analysis of the FG nanobeams such as the effects of foundation parameters, gradient index, nonlocal parameter and slenderness ratio in detail.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.736-739
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• 1995

The meshless adaptive method based on multiple scale analysis is developed to simulate large deformation problems. In the procedure, new particles are simply added to the orginal particle distribution because meshless methods do not require mesh structures in the formulations. The high scale component of the approximated solution detects the localized region where a refinement is needed. The high scale component of the second invariant od Green-Lagrangian strain tensor is suggested as the new high gradient detector for adaptive procedures. The feasibility of the proposed theory is demonstrated by a numerical experiment for the large deformation of hyperelastic materials.

• Structural Engineering and Mechanics
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• v.21 no.2
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• pp.121-136
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• 2005

This paper presents the implementation of the Blatz-Ko hyperelastic compressible model in a finite element program to deal with large deformation problems. We show analytically and numerically that the minimum number of increment steps in the Newton-Raphson algorithm depends on material properties and applied loads. We also show that this dependence is related to the orientation preservation principle. So we propose a convergence criteria based on the sign of eigenvalues of the deformation gradient matrix.

• Korean Journal of Optics and Photonics
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• v.24 no.6
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• pp.324-330
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• 2013

Phase-measuring deflectometry is a full-field gradient measuring technique that lends itself very well to testing specular optical surfaces. We have measured deformation of a large specular surface by deflectometry. In this work, we have used a Fourier-transform method to get the phase from a measured deformed fringe pattern, and we have used least squares method to obtain the height information of the specular surface from the calculated slope. Experimentally, we have confirmed that deflectometry can be used for deformation measurement of a specular surface like that of a wafer.

• Steel and Composite Structures
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• v.13 no.1
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• pp.71-89
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• 2012

The paper investigates beam lateral buckling stability according to linear and non-linear models. Closed form solutions for single-symmetric cross sections are first derived according to a non-linear model considering flexural-torsional coupling and pre-buckling deformation effects. The closed form solutions are compared to a beam finite element developed in large torsion. Effects of pre-buckling deflection and gradient moment on beam stability are not well known in the literature. The strength of singly symmetric I-beams under gradient moments is particularly investigated. Beams with T and I cross-sections are considered in the study. It is concluded that pre-buckling deflections effects are important for I-section with large flanges and analytical solutions are possible. For beams with T-sections, lateral buckling resistance depends not only on pre-buckling deflection but also on cross section shape, load distribution and buckling modes. Effects of pre-buckling deflections are important only when the largest flange is under compressive stresses and positive gradient moments. For negative gradient moments, all available solutions fail and overestimate the beam strength. Numerical solutions are more powerful. Other load cases are investigated as the stability of continuous beams. Under arbitrary loads, all available solutions fail, and recourse to finite element simulation is more efficient.

• Journal of Welding and Joining
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• v.16 no.2
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• pp.111-121
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• 1998

It is well recognized that a excessive temperature gradient from the junction of head to skirt in axial direction in a hot pressure vessel can cause unpredicted high thermal stress at the junction and/or in axial direction of a skirt. this thermal stress resulting from axial thermal gradient may be a major cause of unsoundness of structural integrity. In case of cyclic operation of hot pressure vessels, the thermal stress becomes one of the primary design consideration because of the possibility of fracture as a result of cyclic thermal fatigue and progressively incremental plastic deformation. To perform thermal stress analysis of the junction and cylindrical skirt of a vessel, or, at least, to inspect quantitatively the magnitude and effect of thermal stress, the temperature profile of the vessel and skirt must be known. This paper demonstrated the temperature distribution and thermal stress analysis for the junction of skirt to head using F.E. analysis. Effect of air pocket in crotch space was quantitatively investigated to minimize the temperature gradient causing the thermal stress in axial direction. Effect of the skirt height on thermal stresses was also studied. Analysis results were compared with theoretical formulas to verify th applicability to the strength calculation in design field.

• 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.

• Structural Engineering and Mechanics
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• v.86 no.6
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• pp.731-738
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• 2023

This article presents an analytical approach to explore the bending behaviour of of two-dimensional (2D) functionally graded (FG) nanobeams based on a two-variable higher-order shear deformation theory and nonlocal strain gradient theory. The kinematic relations are proposed according to novel trigonometric functions. The material gradation and material properties are varied along the longitudinal and the transversal directions. The equilibrium equations are obtained by using the virtual work principle and solved by applying Navier's technique. A comparative evaluation of results against predictions from literature demonstrates the accuracy of the proposed analytical model. Moreover, a detailed parametric analysis checks for the sensitivity of the bending and stresses response of (2D) FG nanobeams to nonlocal length scale, strain gradient microstructure scale, material distribution and geometry.