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Extra info for Shell structures: theory and applications: volume 2 ; proceedings of the 9th SSTA Conference, Gdańsk - Jurata, Poland, 14 - 16 October 2009

Example text

Thin-plate theory for large elastic deformations. International Journal of Non-linear Mechanics 42: 233–240. Steigmann, D. 2008. Two-dimensional models for the combined bending and stretching of plates and shells based on three-dimensional linear elasticity. International Journal of Engineering Science 46: 654–76. and µ∗ = µµ−1 is the (two-dimensional) cofactor of µ. The Cayley-Hamilton formula may be used to confirm that The representation where κν , κτ and τ are the normal curvatures and twist of on the (ν, τ) – axes, then yields 2H = κν + κτ and These geometric formulae are essential to the systematic generalization of our procedure to the case of shells.

Continuum mechanics models of shell models. Considerable 14 elements have been proposed for the analysis of shells. The claim of this approach is to use finite elements of sufficiently high degree to recover the convergence property in an optimal order. This is called p-version finite element technology (where p is the degree of the interpolation polynomial). In this case, there is no need to use mixed formulations, and displacementbased finite element formulations can be applied. Finite elements with high-order interpolations have been utilized by Pitkäranta et al.

However, no gradual degradation is taken into account but a selective and constant knock-down of the material stiffnesses. This is what we call the ply discount model. From the above described approaches we choose the 2D-shell concept as basis of our further formulations. Firstly, some aspects on the shell formulation used for the simulations as well as the elasticity model employed are pointed out briefly followed by a more detailed derivation of the damage model. 1 Next, the relation between the Green-Lagrangian strains at a layer point with coordinate ξ 3 and the shell strains is written in matrix notation Remarks on the shell concept For the modeling of the laminae we employ quadrilateral shell elements which are state-of-the-art.

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