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Modeling of structures by finite elements. Vol. 3: Shells. (Modélisation des structures par éléments finis. Vol. 3: Coques.) (French) Zbl 0831.73003

Paris: Hermes. xxvi, 564 p. (1992).
This last volume (of a series of three) is concerned with the modelling of shells by finite element methods. It also comprises two chapters and one annex:
Chapter 5 (200 pages): Shells of revolution. Main topics include the geometrical description, the associate variational formulation, the main finite elements for axisymmetrical shells, and a careful study on how to take care of non-axisymmetrical behaviours.
Chapter 6 (256 pages): Shells with a general shape. Main topics comprise the geometrical description through representation of the middle surface by a set of two parametric coordinates; the associate variational formulations for a model including the effect of shear strains (Reissner/Mindlin/Naghdi approximations) and the hypothesis of plane stresses; the approximation by curved isoparametric elements, plane facet DKT elements and curved facet DKT elements; some comments about other kind of theories (like thoses of Kirchhoff-Love-Koiter) and the associated finite element methods.
Annex A (54 pages): RE-FLEX Software. This software is thoroughly described in Volume 1. In this annex three elements are specifically described: one for the approximation of axisymmetrical shells including transverse shear strains, one for general shells, the triangular element DKT 18, and one quadrangular element for general shells with transverse shear effects.
In spite of the complications inherent to thin shell theories and approximations, this last volume benefits from the great qualities of clarity of the authors. I recommend these lectures to any reader interested in the approximation of thin shell problems by finite element methods.

MSC:

74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74S05 Finite element methods applied to problems in solid mechanics
74K15 Membranes