Isogeometric analysis of topologically complex shell structures
| Autor: | Sung-Kie Youn, Pilseong Kang |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Surface (mathematics)
Applied Mathematics Linear elasticity Mathematical analysis General Engineering Shell (structure) Geometry Isogeometric analysis Computer Graphics and Computer-Aided Design Finite element method Mathematics::Numerical Analysis Numerical integration Trimming Normal Analysis Mathematics |
| Zdroj: | Finite Elements in Analysis and Design. 99:68-81 |
| ISSN: | 0168-874X |
| Popis: | In the conventional isogeometric analysis, a topologically complex shell structure is required to be modeled using multiple NURBS patches. In the CAD industry, however, the topologically complex shell structure is conveniently and efficiently created via trimming techniques rather than constructing multiple untrimmed NURBS patches. With this feature, the isogeometric analysis which enables to handle the topologically complex shell structure with a single NURBS patch is presented in this paper. In the present method, the information of the topologically complex shell structure composed of the untrimmed surface and trimming curves is directly utilized into isogeometric shell analysis. For numerical integration, a special integration scheme is adopted considering the inside or the outside of the trimmed boundaries which are described by the trimming curves. For the shell formulation, the degenerated shell element based on the Reissner-Mindlin theory is employed. The exact surface normal vectors and their analytic derivatives are adopted into the formulation. The shell formulation is validated with linear elastic benchmark problems. Then linear elastic problems of topologically complex shell structures are dealt with using the proposed procedures, and the effectiveness is illustrated. The isogeometric analysis methodology for topologically complex shell structures is presented.Isogeometric analysis of topologically complex shell structures is performed by using trimmed NURBS surfaces and exact normal vectors.The basic concept of the Trimmed Surface Analysis is adopted and appropriately modified to shell structures.The exact normal vectors, which are directly calculated by NURBS surface expression are used in the shell formulation based on the Reissner-Mindlin degenerated shell element.The analytic derivatives of the direction vectors, which are directly calculated by NURBS surface expression are also employed in the shell formulation.With numerical examples, it is shown that the present method for topologically complex shell structures, which cannot be treated by the conventional isogeometric analysis without multiple patches, gives appropriate solutions. |
| Databáze: | OpenAIRE |
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