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Finite bending of plates into cylindrical shells

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Summary

The use of finite components of strain and a linear stress-strain relation shows that a plate can be bent into a cylindrical shell whose section is given by rn cos nθ=an, where n=(3−2σ)−1, σ being the Poisson’s ratio. The case (σ=1/2) and the one given by r2/5 cos2/5 θ=a2/5, (σ=1/4) are discussed in detail.

References

  1. [1]

    Seth, B. R.,Non-linear continuum mechanics, « Proc. Ind. Sci. Cong. », Part II (1955) — Presidential address to the section of Mathematics at the 42nd session of the Indian Science Congress.

  2. [2]

    Signorini, A., « Rend. Lincei », 12 (1930); 18 (1933); 8 (1950). A complete list of his papers is given in reference (1).

  3. [3]

    Novozilov V. V.,Foundation of the theory of non-linear elasticity, Moscow, 1948Ttheory of Thin Shells, Groningen, 1959.

  4. [4]

    Seth, B. R., « Phil. Tran. Roy. Soc. London ». A 234 (1935), pp. 231–264.

  5. [5]

    —— ——, ZAMM, 37 (1957), 393–398.

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To Antonio Signorini on his 70th birth day.

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Seth, B.R. Finite bending of plates into cylindrical shells. Annali di Matematica 50, 119–125 (1960) doi:10.1007/BF02414507

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Keywords

  • Cylindrical Shell
  • Finite Component