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Improvement of Classical Shell Theory and Its Application to Numerical Analysis of Stability for Shells

Research Project

Project/Area Number 63550420
Research Category

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

Allocation TypeSingle-year Grants
Research Field Building structures/materials
Research InstitutionNIHON UNIVERSITY

Principal Investigator

OZAWA Yoshitaka (1989)  College of Industrial Technology, NIHON University, Associate Prof., 生産工学部, 助教授 (00096794)

角野 晃二 (1988)  日本大学, 生産工学部, 教授 (70058585)

Co-Investigator(Kenkyū-buntansha) MITSUI Kazuo  College of Industrial Technology, NIHON University, Research assistant, 生産工学部, 助手 (80130615)
SUMINO Kohji  College of Industrial Technology, NIHON University, Lecturer, 生産工学部, 非常勤講師 (70058585)
小沢 善隆  日本大学, 生産工学部, 助教授 (00096794)
Project Period (FY) 1988 – 1989
Project Status Completed (Fiscal Year 1989)
Budget Amount *help
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1989: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1988: ¥1,700,000 (Direct Cost: ¥1,700,000)
KeywordsShell Theory / Stability / Nonlinear Oscillation / Buckling / 非線型振動
Research Abstract

It can be confirmed in the general theory of nonlinear elasticity of solid that the lost of stability can take place only in the form of static instability and the dynamic instability by no means take place, if the external forces have a potential. This means that the linearized equation for the stability of shell is self-adjoint mathematically. As the basic theory is originally in the form of solid, the stability equation for the shell obtained from any kinds of methodology should be self - adjoint definitely. But some equations of theories for stability of shells, eg. Vlassoy type equations, have inconsistency with a self-adjointness.
It is important to compose the basic equations consistent with the theory mentioned above, especially the self- adjoint property of the stability equations. In our study, the basic equations of shells are simplified under the following assumptions. 1) Rotations to the normal axis of the middle surface may be neglected. 2) The shell is sufficiently thin, therefore the shell is assumed to be loaded with loads distributed over the middle surface.
Under the two assumptions mentioned above, three types of equations, eg. the type considering the transverse shear deformation, Sanders type and Vlassoy type, are expressed. And then using these types equations respectively, numerical analysis of cylindrical shells and spherical shells under the non-conservative external forces are performed by using Galerkin method and finite difference method together with Newton - Raphson method. Consequently it was shown that the finite difference method is very effective to make up the stiffness matrix for the analysis of equilibrium state and the stability analysis. Furthermore the limit cycle described in complicated state were found out in the flutter domain by the usual method of analysis by using Calerkin method, finite difference method together with Newton - Raphson method, Newmark b method and the new method of stability analysis.

Report

(3 results)
  • 1989 Annual Research Report   Final Research Report Summary
  • 1988 Annual Research Report
  • Research Products

    (18 results)

All Other

All Publications (18 results)

  • [Publications] Kazuo MITSUI,Kohji SUMINO: "Stability Analysis of Circular Cylindrical Shells Subjected to Tangential Follower Force" Theoretical and Applied Mechanics. 37. 361-371 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Kohji SUMINO: "Chaos in Autonomous Elastic Systems" Theoretical and Applied Mechanics. 37. 315-325 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Kohji SUMINO: "Rheological Theory of Thin Elastic Shells" Bulletin of the International Association for Shell and Spatial Structures.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Yoshitaka OZAWA,Kazuo MITSUI,Kohji SUMINO: "Large Deflection Stability of Spherical Shells with Partial Load" Dynamics and Stability of Systems.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] 小沢善隆、角野晃二: "準静的非保存外力下の殼体の動的安定性に及ぼす材料粘性の影響I" 日本建築学会論文報告集.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Kazuo MITSUI, Kohji SUMINO: "Stability Analysis of Circular Cylindrical Shells Subjected to Tangential Follower Force" Theoretical and Applied Mechanics, 37 361-371, 1989.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Kohji SUMINO: "Chaos in Autonomous Elastic Systems" Theoretical and Applied Mechanics, 37 315-325, 1989.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Kohji SUMINO: "Rheological Theory of Thin Elastic Shells" Bulletin of IASS.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Yoshitaka OZAWA, Kazuo MITSUI, Kohji SUMINO: "Large Deflection Stability of Spherical Shells with Partial Load" Dynamics and Stability of Systems.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Yoshitaka OZAWA, Kohji SUMINO: "Effects of Visco-Elasticity to Dynamic Stability of Shell Under Quasi-Static Nonconservative Forces" Journal of AIJ.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] Kazuo MITSUI,Kohji SUMINO: "Stability Analysis of Circular Cylindrical Shells Subjected to Tangential Follower Force" Theoretical and Applied Mechanics. 37. 361-371 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Kohji SUMINO: "Chaos in Autonomous Elastic Systems" Theoretical and Applied Mechanics. 37. 315-325 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Kohji SUMINO: "Rheological Theory of Thin Elastic Shells" Bulletin of the International Association for Shell and Spatial Structures.

    • Related Report
      1989 Annual Research Report
  • [Publications] Yoshitaka OZAWA,Kazuo MITSUI,Kohji SUMINO: "Large Deflection Stability of Spherical Shells with Partial Load" Dynamics and Stability of Systems.

    • Related Report
      1989 Annual Research Report
  • [Publications] 小沢善隆,角野晃二: "準静的非保存外力下の殻体の動的安定性に及ぼす材料粘性の影響I" 日本建築学会論文報告集.

    • Related Report
      1989 Annual Research Report
  • [Publications] Koji SUMINO.: Theretical and Applied Mechanics. 37. (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] Kazuo MITSUI.・Koji SUMINO.: Theoretical and Applied Mechanics. 37. (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] Koji SUMINO.: Bulltin of IASS.

    • Related Report
      1988 Annual Research Report

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Published: 1988-04-01   Modified: 2016-04-21  

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