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1992 Fiscal Year Final Research Report Summary

Fundamental Study on Nonlinear Finite Element Method to Achieve High Accuracy

Research Project

Project/Area Number 02650062
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 材料力学
Research InstitutionUniversity of Tsukuba

Principal Investigator

WATANABE Osamu  Institute of Engineering Mechanics University of Tsukuba, Associate Professor, 構造工学系, 助教授 (80111368)

Project Period (FY) 1990 – 1992
KeywordsFinite Element Method / Constitutive Equation / Variational Principle / Numerical Analysis / Hypoelasticity / Hyperelasticity
Research Abstract

The finite element method is widely used in the structural analysis of engineering products for the reasonable design and developments. The present study is concerned with the constitutive equation and variational principles and their effects on numerical analysis in order to achieve high accuracy in the non-linear finite element analysis during three years from 1990 to 1992. Hypoelasticity, defined as the rate type constitutive equation, is used to describe plastic behaviors of metal alloys, on the other hand, hyperelasticity, defined as the potential type constitutive equation, is used for rubber materials. Hypoelasticity widely used with Jaumann stress derivative gives oscillation in stress-deformation curve if linear kinematic hardening law is adopted in simple shear problem. Hyperelasticity, based on Green-Lagrange strain measured from the undeformed configuration, cannot predict accurately the experimental fact that shear stress respond behind shear deformation in simple shear problem. For the analysis of hyperelasticity, the employed mixed variational principle does not include the initial stress term, which significantly affects bifurcation analysis. In order to overcome such shortcomings in constitutive equation and mixed variational principles, the following points are studied consecutively.
(1) By using rotationless strain regarded as the generalized logarithmic strain, hyperelastic constitutive equation is proposed.
(2) Theoretical aspects of hypoelasticity is studied from the viewpoint of corotational equation and non-coaxiality relating to intermediate configurations.
(3) Constitutive equation for large plastic strain is formulated based on internal time theory and compared to the experiments.
(4) Mixed variational principles taking account of the initial stress term and stability of solutions are studied theoretically.
(5) Numerical analysis of hypo and hyperelasticity is carried out by using rotationless strain.

  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] 渡部 修: "非回転ひずみを用いた超弾性理論(非圧縮性構成式)" 日本機械学会論文集,A編. 57. 154-161 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 渡部 修,原田 隆: "Green形構成式を用いた平面ブロックの弾性大変形シミュレーション" 日本機械学会論文集,A編. 57. 1808-1814 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 渡部 修: "亜弾性体の共回転構成式と非共軸性" 日本機械学会論文集,A編. 57. 2965-2974 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 渡部 修: "超弾性構成式と混合型変分限理における体積拘束" 日本機械学会論文集,A編. 58. 84-92 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 渡部 修: "超弾性体の解の安定性" 日本機械学会論文集,A編. 58. 310-318 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 木下 伸,渡部 修: "非回転ひずみを用いた超弾性体の有限要素解析(2次元平面ブロックのせん断変形)" 日本機械学会論文集,A編. 58. 2328-2335 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Watanabe, O.: "Hyperelasticity Theory Based on Irrootational Strain (Constitutive Equation for Incompressible Materials)" Trans. JSME, Ser.A,. Vol.57, No.533. 154-161 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Watanabe, O., Harada, T.: "Large Deformation Analysis of Elastic Plane Block using the Green-Rate Constitutive Equation" Trans. JSME, Ser.A,. Vol.57, No.540. 1808-1814 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Watanabe, O.: "Corotational Equation and Its Noncoaxiality in Hypoelasticity" Trans. JSME, Ser.A,. Vol.57, No.544. 2965-2974 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Watanabe, O.: "Volume Constraint in Hyperelastic Constitutive Equation and Mixed Variational Principle" Trans. JSME, Ser.A,. Vol.58, No.545. 84-92 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Watanabe, O.: "Stability of Solutions for Hyperelasticity" Trans. JSME, Ser.A,. Vol.58, No.546. 310-318 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Watanabe, O.: "Hyperelasticity Theory based on Rotationless Strain (Constitutive Equation for Incompressible Materials)" JSME International Journal, Series I. Vol.35, No.1. 53-61 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Watanabe, O.: "Finite Strain Plasticity using Internal Time Theory" Plastic Flow and Creep, (Ed. Zbib, H. M.), ASME AMD-. Vol.135/MD-Vol.31. 175-187 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Watanabe, O.: "Constitutive Equation and Mixed Variational Principle of Hyperelasticity using Rotationless Strain" Finite Inelastic Deformations-Theory and Applications, IUTAM Symposium Hannover/Germany, (Ed. Besdo, D., Stein, E.), Springer-Verlag. 227-236 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Watanabe, O., Harada, T.: "Large Deformation Analysis of Elastic Plane Block using the Green-Rate Constitutive Equation" JSME International Journal, Series I. Vol.35 No.4. 413-419 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kishita, S., Watanabe, O.: "Structural Analysis of Hyperelasticity Using Rotationless Strain (Shear Deformation of 2-Dimensional Plane Block)" Trans. JSME, Ser.A,. Vol.58, No.556. 2328-2335 (1992)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1994-03-24  

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