Théorie géométriquement exacte des coques en rotations finies et son implantation éléments finis

Abstract

ABSTRACT In this article, we review the significant progress on shell problem theoretical foundation and numerical implementation attained over a period of the last several years. First, a careful consideration of the three-dimensional finite rotations is given including the choice of optimal parameters, their admissible variations and the much revealing relationship between different parameters. A non-conventional derivation of the stress resultant shell theory is presented, which makes use of thevirtual work principle and local Cartesian frames. The presented derivation introduces no simplifying hypotheses regarding the shell balance equations, hence the resulting shell theory is referred to being the geometrically exact. The strain measures energy-conjugate to the chosen stress resultants are identified and the nature of the stress resultants with respect to the three-dimensional stress tensor is explained along with the resulting constitutive restrictions. Comments are made regarding a rather useful e...