• 대한전자공학회논문지SD
• /
• 제45권8호
• /
• pp.11-16
• /
• 2008

본 논문에서는 먼저 RTP(Rapid Thermal Processor) 장치를 스트레스 측정에 용이한 구조로 제작하고 PC에서 통합 공정관리 시스템을 설계하였다. 다음으로는 Large deformation 이론을 바탕으로 반도체 웨이퍼 표면의 변형검사를 위한 레이져 인터페로미터리를 구성하였다. 궁극적으로 이러한 레이져장치로부터 웨이퍼 표면의 영상을 추출하고 세선화, 블록화 그리고 스트레스 분포도의 순서로 영상처리 하여 스트레스로 인한 웨이퍼 표면의 변형을 검사하였다. 실험을 하기 위해 변형이 이루어지도록 웨이퍼의 후면을 1mm정도 갈아낸 후 약 1000도에서 $3\sim4$회 열처리를 수행하였으며, 열처리를 가한 영상과 가하지 않은 영상을 통하여 웨이퍼 열처리 후 심각한 변형이 이루어졌음을 알 수 있었다.

• 국제초고층학회논문집
• /
• 제3권3호
• /
• pp.231-241
• /
• 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
• /
• 제4권3호
• /
• pp.229-249
• /
• 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.

• 한국정밀공학회:학술대회논문집
• /
• 한국정밀공학회 1995년도 추계학술대회 논문집
• /
• pp.736-739
• /
• 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
• /
• 제21권2호
• /
• pp.121-136
• /
• 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.

• 한국광학회지
• /
• 제24권6호
• /
• pp.324-330
• /
• 2013

편향법을 이용하여 면적이 비교적 크고 거울과 같이 산란이 거의 없는 물체의 3차원 측정을 하였다. 편향법을 통해 얻은 왜곡 무늬로부터 위상과 기울기를 구하기 위해 푸리에변환 방법을 이용하였고, 구한 기울기로부터 높이를 구하기 위해 최소자승법을 이용하였다. 웨이퍼에 미세 응력을 주었을 때 변형을 편향법을 이용하여 측정할 수 있음을 확인하였다.

• Steel and Composite Structures
• /
• 제13권1호
• /
• pp.71-89
• /
• 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
• /
• 제16권2호
• /
• pp.111-121
• /
• 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
• /
• 제71권6호
• /
• pp.669-682
• /
• 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
• /
• 제86권6호
• /
• pp.731-738
• /
• 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.