• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.311-326
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• 2011

In this paper, we adopt discontinuous Galerkin methods with penalty terms namely symmetric interior penalty Galerkin methods, to solve nonlinear viscoelasticity type equations. We construct finite element spaces and define an appropriate projection of u and prove its optimal convergence. We construct extrapolated fully discrete discontinuous Galerkin approximations for the viscoelasticity type equation and prove ${\ell}^{\infty}(L^2)$ optimal error estimates in both spatial direction and temporal direction.

• 대한수학회보
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• 제49권4호
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• pp.829-850
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• 2012

In this paper, we adopt symmetric interior penalty discontinuous Galerkin (SIPG) methods to approximate the solution of nonlinear viscoelasticity-type equations. We construct finite element space which consists of piecewise continuous polynomials. We introduce an appropriate elliptic-type projection and prove its approximation properties. We construct semidiscrete discontinuous Galerkin approximations and prove the optimal convergence in $L^2$ normed space.

• 토지주택연구
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• 제11권2호
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• pp.95-104
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• 2020

This study aims to explore a purely mechanistic pavement analysis approach where viscoelasticity and fracture of asphalt mixtures are considered to accurately predict deformation and damage behavior of flexible pavements. To do so, the viscoelastic and fracture properties of designated pavement materials are obtained through experiments and a fully mechanistic damage analysis is carried out using a finite element method (FEM). While modeling crack development can be done in various ways, this study uses the cohesive zone approach, which is a well-known fracture mechanics approach to efficiently model crack initiation and propagation. Different pavement configurations and traffic loads are considered based on three main functional classes of roads suggested by FHWA i.e., arterial, collector and local. For each road type, three different material combinations for asphalt concrete (AC) and base layers are considered to study damage behavior of pavement. A concept of the approach is presented and a case study where three different material combinations for AC and base layers are considered is exemplified to investigate progressive damage behavior of pavements when mixture properties and layer configurations were altered. Overall, it can be concluded that mechanistic pavement modeling attempted in this study could differentiate the performance of pavement sections due to varying design inputs. The promising results, although limited yet to be considered a fully practical method, infer that a few mixture tests can be integrated with the finite element modeling of the mixture tests and subsequent structural modeling of pavements to better design mixtures and pavements in a purely mechanistic manner.

• 대한기계학회논문집A
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• 제20권7호
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• pp.2148-2158
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• 1996

Uncoupled, quasi-static and linear thermoviscoelastic problems are analyzed in time domain by the finite element approximation which is developed using the principle of virtual work and viscoelasticity matrices instead of shear and bulk relaxation functions as in usual formulations. The material is assumed to be isotropic, homegeneous and thermorheologically simple, which means that the temperature-time equivalence postulate is effective. The stress-strain laws are expressed by relaxation-type hereditary integrals. In spatial and time discritizations, isoparametric quadratic quadrilateral finite elements and linear time variations are adopted. For explicit derivations, the viscoelastic material is assumed to behave standard linear solid in shear and elastically in dilatation. Two-dimensional examples are solved under general temperature distributions T = T(x, t), and compared with other opproximate solutions to show the versatility of the presented analysis.

• Structural Engineering and Mechanics
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• 제40권6호
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• pp.783-800
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• 2011

This paper addresses the finite strip formulations for the stability analysis of viscoelastic composite plates with variable thickness in the transverse direction, which are subjected to in-plane forces. While the finite strip method is fairly well-known in the buckling analysis, hitherto its direct application to the buckling of viscoelastic composite plates with variable thickness has not been investigated. The equations governing the stiffness and the geometry matrices of the composite plate are solved in the time domain using both the higher-order shear deformation theory and the method of effective moduli. These matrices are then assembled so that the global stiffness and geometry matrices of a moderately thick rectangular plate are formed which lead to an eigenvalue problem that is solved to determine the magnitude of critical buckling load for the viscoelastic plate. The accuracy of the proposed model is verified against the results which have been reported elsewhere whilst a comprehensive parametric study is presented to show the effects of viscoelasticity parameters, boundary conditions as well as combined bending and compression loads on the critical buckling load of thin and moderately thick viscoelastic composite plates.

• 대한기계학회논문집
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• 제16권8호
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• pp.1429-1437
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• 1992

본 연구에서는 이완형 물성방정식을 바탕으로 하며 프와송 비가 일정하다는 가정을 하지 않는다. 또한 점탄성 지배방정식에 변분원리를 적용하고 유도되어진 식 에 유한요소해법을 사용하여 시스템 기본해석을 위한 연립방정식을 유도한다. 이와 함께 점탄성 물성함수의 유도 및 응력계산을 위한 공식화 과정도 설명한다. 제시된 방법론의 타당성 및 정확성을 보이기 위해서 평면응력 및 평면변형 문제의 변위 및 응력을 수치해석하여 이론해와 비교 검토하며, 아울러 시간증분의 변화와 Gauss poi- nts수가 수치정확도에 끼치는 영향을 조사한다.

• 한국전기전자재료학회논문지
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• 제23권5호
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• pp.358-363
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• 2010

The polishing pad is important element for polishing characteristic such as material removal rate(MRR) and within wafer non-uniformity(WIWNU) in the chemical mechanical planarization(CMP). The result of the viscoelasticity measurement shows that 1st elastic modulus is increased and 2nd elastic modulus is decreased when the top pad is thickened. The finite element analysis(FEA) was conducted to predict characteristic of polishing behavior according to the pad thickness. The result of polishing experiment was similar with the FEA, and it shows that the 1st elastic modulus affects instantaneous deformation of pad related to MRR. And the 2nd elastic modulus has an effect on WIWNU due to the viscoelasticity deformation of pad.

• Structural Engineering and Mechanics
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• 제1권1호
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• pp.103-118
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• 1993

The near field is discretized into finite elements, and the far field into infinite elements. Closed form far-field solutions to three fundamental problems are used as the shape functions of the infinite elements. Such infinite elements are capable of transmitting all surface and body waves. An efficient scheme to integrate numerically the stiffness and mass matrices of these elements in presented. Results agree closely with those obtained by others.

• 소성∙가공
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• 제13권2호
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• pp.180-187
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• 2004

A computer code was developed to simulate the filling stage of the injection/compression molding process by a finite element method. The constitutive equation used here was the compressible Leonov model. The PVT relationship was assumed to follow the Tait equation. The flow-induced birefringence was related to the calculated flow stresses through the linear stress-optical law. Simulations of a disk part under different process conditions including the variation of compression stroke and compression speed were carried out to understand their effects on birefringence variation. The simulated results were also compared with those by conventional injection molding.

• Composites Research
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• 제27권4호
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• pp.174-181
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• 2014

본 연구에서는 탄소섬유 강화 복합재의 점탄성 성질을 적용한 유한요소 해석에 대해서 기술하였다. 고온의 성형과정에서 발생하는 가장 중요한 문제 중 하나는 잔류응력의 발생이다. 잔류응력으로 인해 성형이 끝난 후 뒤틀림, 균열이 일어 날 수 있으며 이는 완성품에 심각한 결함을 가져올 수 있다. 잔류응력의 주요 원인은 점탄성이며 고온의 성형과정에서 열팽창계수의 차이와 수지의 시간 및 온도에 대한 물성의 변화로 인해 발생하는 탄소섬유 강화 복합재의 특징이다. 화학 수축도 잔류응력에 많은 영향을 주며 이를 고려한 뒤틀림 예측에서 오차를 줄일 수 있는 중요한 요소이다. 본 연구는 복합재 성형에 사용된 온도변화에 대한 경화도와 점탄성 효과, 화학수축을 유한요소 해석으로 수행하기 위한 기법을 연구하고, 점탄성의 영향성을 연구하였다. 기존에 연구되어 있는 논문을 참고하여 서브루틴의 타당성을 검증한 후 나아가 복합재의 적층각의 변화에 따른 응력과 변형을 해석해 봄으로써 실제 복합재의 성형 시 발생하는 휨 현상에 대한 예측방법을 제시하였다.