• Advances in nano research
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• 제12권2호
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• pp.139-150
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• 2022

This paper presents sets of explicit analytical equations that compute the static displacements of nanobeams by adopting the nonlocal elasticity theory of Eringen within the framework of Euler Bernoulli and Timoshenko beam theories. Castigliano's theorem is applied to an equivalent Virtual Local Beam (VLB) made up of linear elastic material to compute the displacements. The first derivative of the complementary energy of the VLB with respect to a virtual point load provides displacements. The displacements of the VLB are assumed equal to those of the nonlocal beam if nonlocal effects are superposed as additional stress resultants on the VLB. The illustrative equations of displacements are relevant to a few types of loadings combined with a few common boundary conditions. Several equations of displacements, thus derived, matched precisely in similar cases with the equations obtained by other analytical methods found in the literature. Furthermore, magnitudes of maximum displacements are also in excellent agreement with those computed by other numerical methods. These validated the superposition of nonlocal effects on the VLB and the accuracy of the derived equations.

• 대한기계학회논문집
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• 제17권1호
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• pp.215-222
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• 1993

본 연구에서는 판 스프링의 길이가 두께에 비하여 비교적 큰 것을 고려하여 판스프링의 기하학적 치수와 물성치들을 이용하여 판스프링의 강성과 조립된판 스프링 집합체의 강성을 예측할 수 있는 방법을 본 이론과 변형률 에너지이론을 적용하여 개 발하였고 그 개발된 방법으로 구한 강성예측치와 특성실험에서 얻은 강성치를 비교, 분석하여 판 스프링 강성해석 방법의 신뢰성을 보임과 동시에 독자적인 홀드다운스프 링 집합체의 특성해석 방법을 제시 하였다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2007년도 춘계학술대회 논문집
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• pp.549-550
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• 2007

• Structural Engineering and Mechanics
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• 제54권1호
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• pp.189-198
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• 2015

We present a torsion analysis of single-bent leaf flexure that is partially restrained, subject to a torsional load. The theoretical equations for the torsional angle are derived using Castigliano's theorem. These equations consider the partially restrained warping, and are verified using finite element analysis (FEA). A sensitivity analysis over the length, width, and thickness is performed and verified via FEA. The results show that the errors between the theory result and the FEA result are lower than 6%. This indicates that the proposed theoretical torsional analysis with partially restrained warping is sufficiently accurate.

• Nuclear Engineering and Technology
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• 제27권5호
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• pp.760-766
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• 1995

Young's Modulus와 단지 기하학적 테이타를 이용하여 흘드다운스프링의 탄성강성도를 해석하는 방법을 제시하였다. 제시된 이 방법은 엔지니어링 빔이론과 카스티릴아노 이론을 이용하여 판형흘드다운스프링의 탄성강성도 해석에 적용하였다. 이러한 방법의 효율성과 신뢰성을 보여주기 위하여 제안된 방법으로 부터의 탄성강성도를 여러가지 형태의 홀드다운스프링의 시험결과와 비교하였다. 이러한 결과비교에 의해 제안된 방법이 판형홀드다운스프링의 탄성강성도를 구하는데 있어서 효과적임을 입증하였다.

• Nuclear Engineering and Technology
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• 제28권6호
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• pp.583-593
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• 1996

An elastic stiffness formula of a leaf type holddown spring(HDS) assembly with a uniformly tapered width from $w_0$ to $w_14$ over the length, has been analytically derived based on Euler beam theory and Castigliano's theorem. Elastic stiffnesses of the tapered-width leaf type HDSs(TW-HDSs) designed in the same dimensional design spaces as the KOFA HDSs have been evaluated from the derived formula, in addition, a parametric study on the elastic stiffness of the TW-HDSs has been carried out. Analysis results show that, as the effects of axial and shear force on the elastic stiffness of He TW-HDSs have been 0.15~0.21% of the elastic stiffness, most of the elastic stiffness is attributed to the bending moment, and that elastic stiffnesses of the TW-HDSs have been about 32~33% higher than those of the KOFA HDSs. It is found that the number of leaves composing a HDS assembly could be lessened by one under the conditions that the TW-HDSs have been adopted in KOFA.

• 대한기계학회논문집A
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• 제21권1호
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• pp.180-187
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• 1997

A formula for estimating the elastic stiffness of TW-HDS with a uniformly tapered width from w$_{0}$ to w$_{1}$ over the length, has been analytically derived based on Euler beam theory and Castigliano's theorem. Elastic stiffnesses of the TW-HDSs designed in the same dimensional design spaces as the KOFA HDSs have been estimated from the derived formula, in addition, a sensitivity study on the elastic stiffness of the TW-HDSs has been carried out. Analysis results show that elastic stiffnesses of the TW-HDSs have been by far higher than those of the KOFA HDSs, and that, as the effects of axial and shear force on the elastic stiffness have been 0.15-0.21%, most of the elastic stiffness is attributed to the bending moment. As a result of sensitivity analysis, the elastic stiffness sensitivity at each design variable is quantified and design variables having remarkable sensitivity are identified. Among the design variables, leaf thickness is identified as that of having the most remarkable sensitivity of the elastic stiffness.

• 대한기계학회논문집A
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• 제21권8호
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• pp.1276-1290
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• 1997

The previous elastic stiffness formulas of leaf type holddown spring assemblies(HDSs) have been corrected and extended to be able to consider the point of taper runout for the TT-HDS and all the strain energies for both the TT-HDS and the TW-HDS based on Euler beam theory and Castigliano'stheorem. The elastic stiffness sensitivity of the leaf type holddown spring assemblies was analyzed using the derived elastic stiffness formulas and their gradient vectors obtained from the mid-point formula. As a result of the sensitivity analysis, the elastic stiffness sensitivity at each design variable is quantified and design variables having remarkable sensitivity are identified. Among the design variables, leaf thickness is identified as that of having the most remarkable sensitivity of the elastic stiffness. In addition, it was found that the sensitivity of the leaf type HDS's elastic stiffness is exponentially correlated to the leaf thickness.

• 한국해양공학회지
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• 제23권4호
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• pp.91-99
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• 2009

Many longitudinally arranged pipes in ships are subject to considerable displacement loads caused by the hull girder bending of ships and/or thermal loads in some special pipes through which fluids with highly abnormal temperatures are conveyed. As these loads may cause failure in the pipes or their supporting structures, loops have been widely adopted as a measure to prevent such failure, with the idea that they can lower the stress level in a pipe by absorbing some portion of these loads. But since such loops have some negative effects, such as causing extra manufacturing cost and occupying extra space, the number and dimensions of the loops need to be minimized. This research developed design formulas for pipe loops, modeling them as a spring element, for which the axial stiffness is calculated based on the beam theory, incorporating the effects of the curvature of loop corners and the flexibility of the straight portion of the pipe. The accuracy of the proposed design formulas was verified by comparing two results respectively obtained by the proposed formulas and MSC/NASTRAN. The paper ends with a sample application of the proposed formulas showing their efficiency.