Structural Engineering and Mechanics

  • 제7권2호
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  • Pages.159-180
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  • 1999
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

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Fundamental theory of curved structures from a non-tensorial point of view

  • Paavola, Juha (Helsinki University of Technology, Laboratory of Structural Mechanics) ;
  • Salonen, Eero-Matti (Helsinki University of Technology, Laboratory of Structural Mechanics)
  • 발행 : 1999.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

The present paper shows a new non-tensorial approach to derive basic equations for various structural analyses. It can be used directly in numerical computation procedures. The aim of the paper is, however, to show that the approach serves as an excellent tool for analytical purposes also, working as a link between analytical and numerical techniques. The paper gives a method to derive, at first, expressions for strains in general beam and shell analyses, and secondly, the governing equilibrium equations. The approach is based on the utilization of local fixed Cartesian coordinate systems. Applying these, all the definitions required are the simple basic ones, well-known from the analyses in common global coordinates. In addition, the familiar principle of virtual work has been adopted. The method will be, apparently, most powerful in teaching the theories of curved beam and shell structures for students not familiar with tensor analysis. The final results obtained have no novelty value in themselves, but the procedure developed opens through its systematic and graphic progress a new standpoint to theoretical considerations.

키워드

참고문헌

  1. Flugge, W. (1966), Stresses in Shells. Springer-Verlag.
  2. Flugge, W. (1972), Tensor Analysis and Continuum Mechanics. Springer-Verlag.
  3. Green, A.E. and Zerna, W. (1954), Theoretical Elasticity. Oxford, New York.
  4. Irons, B.M. and Ahmad, S. (1980), Techniques of Finite Elements. Ellis Horwood.
  5. Malvern, L.E. (1969), Introduction to the Mechanics of a Continuous Medium. Prentice-Hall Inc., Englewood Cliffs.
  6. Morley, L.S.D. (1984), "A facet-like shell theory", Int. J. Engng Sci. 22(11/12), 1315-1327. https://doi.org/10.1016/0020-7225(84)90024-7
  7. Morley, L.S.D. (1987a), "'Practical' components of vectors and tensors", Int. J. Engng Sci. 25(1), 37-53. https://doi.org/10.1016/0020-7225(87)90133-9
  8. Morley, L.S.D. (1987b), "Tensor calculus of locally Cartesian coordinates on a curved surface" , Int. J. Engng Sci. 25(2), 253-263. https://doi.org/10.1016/0020-7225(87)90010-3
  9. Novozhilov, V.V. (1964), Thin Shell Theory. P. Noordhoff Ltd. Translation.
  10. Oden, J.T. (1967), Mechanics of Elastic Structures. McGraw-Hill.
  11. Washizu, K. (1975), Variational Methods in Elasticity and Plasticity. 2nd ed., Pergamon Press Ltd.
  12. Wempner, G. (1981), Mechanics of Solids with Applications to Thin Bodies. 2nd ed., Sijthoff & Noordhoff.

피인용 문헌

  1. Coping with Curvilinear Coordinates in Solid Mechanics vol.32, pp.1, 2004, https://doi.org/10.7227/IJMEE.32.1.1
  2. Strain and stress analysis of a curved tapered beam model vol.72, pp.4-5, 1999, https://doi.org/10.1016/S0045-7949(98)00335-6