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Geometrically nonlinear analysis of solids using an isogeometric formulation in boundary representation

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Abstract

This paper presents a geometrically nonlinear formulation in boundary representation for the isogeometric analysis of solids. The proposed formulation employs the parameterization of the scaled boundary finite element method. Thus, the geometry of the boundary is sufficient to describe the entire domain. In contrast to the scaled boundary finite element method, NURBS basis functions approximate the solution on the boundary and also in the interior of the domain. In this way, the exact geometry of the boundary is preserved and geometrically nonlinear problems are treated without further measures. The formulation is derived for two-dimensional domains with arbitrary number of boundaries. Numerical benchmarks evaluate the accuracy and efficiency of the formulation. Furthermore, the influence of the discretization in the interior of the domain and the performance of complex geometries is studied. The proposed formulation compares well with other numerical methods and is suitable for geometries that are designed in boundary representation.

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Acknowledgements

The authors wish to thank Clarissa Arioli and Bernd Simeon from the Technical University of Kaiserslautern for the fruitful discussions on the scaled boundary approach. The financial support of the DFG (German Research Foundation) under Grant No. KL1345/10-1 is gratefully acknowledged.

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  1. Chair of Structural Analysis and Dynamics, RWTH Aachen University, Mies-van-der-Rohe-Str.1, 52074, Aachen, Germany

    Margarita Chasapi & Sven Klinkel

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  1. Margarita Chasapi
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  2. Sven Klinkel
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Correspondence to Sven Klinkel.

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Chasapi, M., Klinkel, S. Geometrically nonlinear analysis of solids using an isogeometric formulation in boundary representation. Comput Mech 65, 355–373 (2020). https://doi.org/10.1007/s00466-019-01772-6

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  • DOI: https://doi.org/10.1007/s00466-019-01772-6

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