• International Journal of Aeronautical and Space Sciences
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• 제13권4호
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• pp.458-467
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• 2012

In this study, the linear viscoelastic response of a rectangular laminated plate is investigated. The viscoelastic properties, expressed by two basic spring-dashpot models, that is Kelvin and Maxwell models, is assumed in the range to investigate the influence of viscoelastic coefficients to mechanical behavior. In the present study, viscoelastic responses are performed for two popular equivalent single-layered theories, such as the first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT). Compliance and relaxation modulus of time-dependent viscoelastic behavior are approximately determined by Prony series. The constitutive equation for linear viscoelastic material as the Boltzmann superposition integral equation is simplified by the convolution theorem of Laplace transformation to avoid direct time integration as well as to improve both accuracy and computational efficiency. The viscoelastic responses of composite laminates in the real time domain are obtained by applying the inverse Laplace transformation. The numerical results of viscoelastic phenomena such as creep, cyclic creep and recovery creep are presented.

• 소성∙가공
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• 제18권1호
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• pp.20-25
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• 2009

A finite element analysis was carried out for a 4:1 planar contraction die for polymer melts using the viscoelastic constitutive equation of Leonov. Viscoelastic fluids showed significant differences in pressure drop and birefringence in contraction and expansion flows. The pressure drop was higher and the birefringence smaller in expansion than in contraction flow. The difference increased with increasing flow rate. The nonlinear Leonov model was shown to describe the viscoelastic effects observed in experiments.

• 한국유변학회:학술대회논문집
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• 한국유변학회 2000년도 추계 학술발표회 논문집
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• pp.3-6
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• 2000

• 한국유변학회:학술대회논문집
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• 한국유변학회 2001년도 춘계 학술발표회 논문집
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• pp.25-28
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• 2001

• Journal of Mechanical Science and Technology
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• 제14권1호
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• pp.19-29
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• 2000

A viscoelastic finite element analysis is presented to investigate residual stresses occurred in a laminated cylindrical shell during cure. An incremental viscoelastic constitutive equation that can describe stress relaxation during the cure is derived as a recursive formula which can be used conveniently for a numerical analysis. The finite element analysis program is developed on the basis of a 3-D degenerated shell element and the first order shear deformation theory, and is verified by comparing with an one dimensional exact solution. Viscoelastic effect on the residual stresses in the laminated shell during the cure is investigated by performing both the viscoelastic and linear elastic analyses considering thermal deformation and chemical shrinkage simultaneously. The results show that there is big difference between viscoelastic stresses and linear elastic stresses. The effect of cooling rates and cooling paths on the residual stresses is also examined.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 춘계학술대회논문집
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• pp.289-294
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• 2001

Three kinds of viscoelastic damper model, which has a non-linear spring as an element is studied analytically and numerically. The behavior of the damper model shows non-linear hysteresis curves which is qualitatively similar to those of real viscoelastic materials. The motion is governed by a non-linear constitutive equation and an additional equation of motion. Harmonic balance method is applied to get analytic solutions of the system. The frequency-response curves show that multiple solutions co-exist and that the jump phenomena can occur. In addition, it is shown that separate solution branch exists and that it can merge with the primary response curve. Saddle-node bifurcation sets explain the occurrences of such non-linear phenomena.

• 한국소음진동공학회논문집
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• 제12권1호
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• pp.57-64
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• 2002

Three kinds of viscoelastic damper model, which has a non-linear spring as an element is studied analytically and numerically The behavior of the damper model shows non-linear hysteresis curves which is qualitatively similar to those of real viscoelastic materials. The motion is governed by a non-linear constitutive equation and an additional equation of motion. Harmonic balance method is applied to get analytical solutions of the system. The frequency-response curves sallow that multiple solutions co-exist and that the jump phenomena can occur. In addition, it is shown that separate solution branch exists and that it can merge with the primary response curve. Saddle-node bifurcation sets explain the occurrences of such non-linear Phenomena.

• Korea-Australia Rheology Journal
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• 제16권4호
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• pp.183-191
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• 2004

High Deborah or Weissenberg number problems in viscoelastic flow modeling have been known formidably difficult even in the inertialess limit. There exists almost no result that shows satisfactory accuracy and proper mesh convergence at the same time. However recently, quite a breakthrough seems to have been made in this field of computational rheology. So called matrix-logarithm (here we name it tensor-logarithm) formulation of the viscoelastic constitutive equations originally written in terms of the conformation tensor has been suggested by Fattal and Kupferman (2004) and its finite element implementation has been first presented by Hulsen (2004). Both the works have reported almost unbounded convergence limit in solving two benchmark problems. This new formulation incorporates proper polynomial interpolations of the log­arithm for the variables that exhibit steep exponential dependence near stagnation points, and it also strictly preserves the positive definiteness of the conformation tensor. In this study, we present an alternative pro­cedure for deriving the tensor-logarithmic representation of the differential constitutive equations and pro­vide a numerical example with the Leonov model in 4:1 planar contraction flows. Dramatic improvement of the computational algorithm with stable convergence has been demonstrated and it seems that there exists appropriate mesh convergence even though this conclusion requires further study. It is thought that this new formalism will work only for a few differential constitutive equations proven globally stable. Thus the math­ematical stability criteria perhaps play an important role on the choice and development of the suitable con­stitutive equations. In this respect, the Leonov viscoelastic model is quite feasible and becomes more essential since it has been proven globally stable and it offers the simplest form in the tensor-logarithmic formulation.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 추계학술대회
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• pp.1672-1677
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• 2003

In this paper, the spectral element model is derived for the vibration and stability analyses of an axially moving viscoelastic beam subjected to axial tension. The viscoelastic material is represented by using a one-dimensional constitutive equation of hereditary integral type. The accuracy of the present spectral element model is first verified by comparing the eigenvalues obtained by the present spectral element model-based SEM with those obtained by the exact theory and the conventional FEM. The effects of viscoelasticity on the vibration and stability of an example moving viscoelastic beam are numerically investigated.

• 대한토목학회논문집
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• 제30권4D호
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• pp.387-393
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• 2010

본 논문에서는 아스팔트 포장의 균열 성장을 분석하기 위해서 확장유한요소법을 사용하였다. 또한 아스팔트의 점탄성 효과를 고려하기 위하여 맥스웰 체인을 이용한 점탄성 구성방정식을 사용하였으며, 균열 모델로는 선형점성균열 모델을 사용하였다. 특히 점탄성 구성방정식을 구성할 때 측정을 통해 얻어지는 온도별 변형계수와 지연시간을 Prony 급수를 이용해 재구성한 크리프 곡선을 직접 사용하지 않고 연속적인 미분이 가능한 멱승 로그 식으로 대체하여 사용하였다. 멱승 로그 식으로 완화시간 스펙트럼(relaxation spectrum)을 계산하여 맥스웰 체인의 부분탄성계수(partial moduli)를 도출하였다. 멱승 로그 적정 식을 통해 구한 맥스웰 체인의 부분 탄성계수는 크리프 곡선을 직접 이용하는 방법으로 구한 부분 탄성계수 보다 안정적인 형태의 곡선을 나타내어 해석을 용이하게 해준다. 개발된 정적균열 해석 모듈을 이용하여 아스팔트 시편의 온도별 정적균열 성장 실험 결과를 성공적으로 모사할 수 있었다.