Hierarchic Isogeometric Analysis for Shell Structures

Abstract eng:
It is evident that Kirchhoff-Love models are mechanically sufficient in most applications of thinwalled shells; however it turned out that the C1-continuity requirement was a serious obstacle in early finite element derivations. This was the reason that most models resorted to a Reissner/Mindlin kinematics including transverse shear deformations and requiring only C0-continuity; it is well known though that low order finite elements suffer from various locking phenomena and need special treatments. In the last two decades two main tendencies in shell modeling and discretization can be recognized. On the one hand higher order shell models have been developed including higher order effects; this is done either in the sense of multi-director formulations or as multi-layer models, following quasi apriori p- or h-discretizations through the thickness. The theoretical starting point may be a threedimensional continuum or a shell formulation based on dimensional reduction. On the other hand a strong tendency appeared to return to Kirchhoff-Love formulations using rotation-free finite elements. A promising version is the Isogeometric Analysis (IGA) using either smooth subdivision surfaces or NURBS-based Finite Elements exploiting the higher order inter-element continuity of up to Cp-1, p being the degree of NURBS basis functions. This approach is followed in the present contribution. First an overview is given on the described current tendencies in shell modeling [1]. The main part of the contribution concentrates on a novel modeling strategy following a hierarchic approach from low to high order shell formulations [3]. It starts from a NURBS discretization for a 3-parameter Kirchhoff/Love model satisfying a priori C1- continuity, see for example [2]. This procedure is extended to higher order formulations like the 5-parameter Reissner/Mindlin and the threedimensional 7-parameter model introducing the difference vector to the rotated normal as it is described in classical formulations for thin-walled structures or as it is used also in [4] in the context of subdivision surfaces. In the present version it should be noted that this hierarchical concept naturally does not show shear locking however still needs modifications for the in-plane strains like the NURBS-DSG (Discrete Strain Gap) extension [5] to avoid membrane locking.

• Export as: BibTeX | MARC | MARCXML | DC | EndNote | NLM | RefWorks
• Add to your basket