Finite Element Analysis of Thermorheologically Simple Viscoelastic Solids

열유동학적으로 단순한 점탄성체의 유한요소해석

  • 심우진 (금오공과대학교 기계설계공학과) ;
  • 박인규 (금오공과대학교 기계설계공학과)
  • Published : 1996.03.01

Abstract

In this paper, the finite element formulation for the thermal analysis of quasi-static, uncoupled, homogeneous, isotropic and linear viscoelastic problems is presented based on the principle of virtual work. The viscoelastic material is assumed to be thermorheologically simple, which is well known material property in a large class of high polymers. The variational formulation and the finite element equation in matrix from are derived. Effective generation and storage of the hereditary stiffness matrices are given in detail especially for the case of the steady state temperature distribution T=T(x). Some numerical examples are given and compared with published results to show the versatility of the derived finite element formulations.

준-정적 선형 2차원 열점탄성 문제들의 유한요소해석을 위하여 가상일의 원리를 근거로 하여 새로운 변분공식과 유한요소방정식을 유도한다. 이때 점탄성 재료는 열유동학적으로 단순한 물성을 갖는다. T=T(x)일 경우에 유전적 강성행렬들의 효율적이고 단순화된 계산과정을 소개한다. 몇몇 예제를 해석하고 기존의 발표된 수치결과들과 비교 검토하여 정확성 및 경제성을 입증한다.

Keywords

References

  1. Elastic and Creep Properties of Filamentous Materals Leaderman, H.
  2. J. Amer. Chem. Soc. v.72 Mechanical Properties of Substances of High Molecular Weight Ferry, J.D.
  3. J. Appl. Phys. v.23 Time-Temperature Dependence of Linear Viscoelastic Behaviour Schwarzl F.;Staverman, A.J.
  4. Rheol. Elast. Temperature-Frequency Relationships of Dielectric and Mechanical Properties of Polymers Payne, A.R.;Mason P(Ed.);Wookey, N.(Ed.)
  5. Trans. Soc. Rheol. v.4 Stress Analysis for Linear Viscoelastic Materials with Temperature Variation Morland L.W.;Lee, E.H.
  6. J. Appl. Mech. On Transient Thermal Stresses in Viscoelastic Materials with Temperature-Dependent Properties Muki, R.;Sternhberg, E.
  7. Int. J. Eng. Sci. v.5 Thermal Stresses in Viscoelastc Thin-Walled Tube with Temperatutr-Dependent Properties Lockett, F.J.;Morland, L.W.
  8. Nuc. Eng. Design v.4 An approximate Method for Thermoviscoelastic Stress Analysis Taylor, R.L.;Chang, T.Y.
  9. Int. J. Num. Meth. Eng. v.2 Thermomechanical Analysis of Viscoelastic Stress Analysis Taylor, R.L.;Pister, K.S.;Goudreau, L.
  10. Comp. Meth. Appl. Mech. Eng. v.25 A Finite Element Method for Thermoviscoelastic Analysis of Plane Problems Srinatha H.R.;Lewis, R.W.
  11. Int. J. Num. Meth. Eng. v.38 Application of High-Order Quadrature Rules to Time-Domain Boundary Element Analysis of Viscoelasticity Lee, S.S.;Westmann, R.A.
  12. 대한기계학회 논문집 v.16 no.8 유전 적분형 물성방정식에 근거한 선형 점탄성 문제의 시간영역 유한요소해석 심우진;이호섭
  13. 한국전산구조공학회 논문집 v.6 no.2 유전적분형 선형점탄성문제의 유한요소법에 의한 효율적 해석 심우진;이성희
  14. Computational Engineering, PCCE'93 Seoul Efficient Finite Element Formulation for Linear Viscoelastic Analysis Based on Herditary-Type Constitutive Equations Sim, Woo-Jin;Lee, Sung-Hee;Kwak, B.M(Ed.);Tanaka, M.(Ed.)
  15. Theory of Viscoelasticity(2nd Edn.) Christensen, R.M.
  16. The Finite Element Method(3rd Edn.) Zienkiewicz, O.C.
  17. Advanced Strength and Applied Elasticity(3rd Edn.) Ugural, A.C.;Fenster, S.K.