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Isogeometric analysis of multi-patch solid-shells in large deformation

Isogeometric analysis of multi-patch solid-shells in large deformation In the context of isogeometric analysis (IGA) of shell structures, the popularity of the solid-shell elements benefit from formulation simplicity and full 3D stress state. However some basic questions remain unresolved when using solid-shell element, especially for large deformation cases with patch coupling, which is a common scene in real-life simulations. In this research, after introduction of the solid-shell nonlinear formulation and a fundamental 3D model construction method, we present a non-symmetric variant of the standard Nitsche’s formulation for multi-patch coupling in association with an empirical formula for its stabilization parameter. An selective and reduced integration scheme is also presented to address the locking syndrome. In addition, the quasi-Newton iteration format is derived as solver, together with a step length control method. The second order derivatives are totally neglected by the adoption of the non-symmetric Nitsche’s formulation and the quasi-Newton solver. The solid-shell elements are numerically studied by a linear elastic plate example, then we demonstrate the performance of the proposed formulation in large deformation, in terms of result verification, iteration history and continuity of displacement across the coupling interface.Graphic AbstractIn the context of isogeometric analysis (IGA), after introduction of the solid-shell nonlinear formulation and a fundamental 3D model construction method, we present a non-symmetric variant of the standard Nitsche’s formulation for multi-patch coupling in association with an empirical formula for its stabilization parameter. An selective and reduced integration scheme is also introduced to address the locking syndrome. In addition, the quasi-Newton iteration format is derived as solver, together with a step length control method. The second order derivatives are totally neglected by the adoption of the non-symmetric Nitsche’s formulation and the quasi-Newton solver. The performance of the proposed formulation in large deformation is demonstrated by several examples.[graphic not available: see fulltext] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Mechanica Sinica" Springer Journals

Isogeometric analysis of multi-patch solid-shells in large deformation

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References (49)

Publisher
Springer Journals
Copyright
Copyright © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2021
ISSN
0567-7718
eISSN
1614-3116
DOI
10.1007/s10409-020-01046-y
Publisher site
See Article on Publisher Site

Abstract

In the context of isogeometric analysis (IGA) of shell structures, the popularity of the solid-shell elements benefit from formulation simplicity and full 3D stress state. However some basic questions remain unresolved when using solid-shell element, especially for large deformation cases with patch coupling, which is a common scene in real-life simulations. In this research, after introduction of the solid-shell nonlinear formulation and a fundamental 3D model construction method, we present a non-symmetric variant of the standard Nitsche’s formulation for multi-patch coupling in association with an empirical formula for its stabilization parameter. An selective and reduced integration scheme is also presented to address the locking syndrome. In addition, the quasi-Newton iteration format is derived as solver, together with a step length control method. The second order derivatives are totally neglected by the adoption of the non-symmetric Nitsche’s formulation and the quasi-Newton solver. The solid-shell elements are numerically studied by a linear elastic plate example, then we demonstrate the performance of the proposed formulation in large deformation, in terms of result verification, iteration history and continuity of displacement across the coupling interface.Graphic AbstractIn the context of isogeometric analysis (IGA), after introduction of the solid-shell nonlinear formulation and a fundamental 3D model construction method, we present a non-symmetric variant of the standard Nitsche’s formulation for multi-patch coupling in association with an empirical formula for its stabilization parameter. An selective and reduced integration scheme is also introduced to address the locking syndrome. In addition, the quasi-Newton iteration format is derived as solver, together with a step length control method. The second order derivatives are totally neglected by the adoption of the non-symmetric Nitsche’s formulation and the quasi-Newton solver. The performance of the proposed formulation in large deformation is demonstrated by several examples.[graphic not available: see fulltext]

Journal

"Acta Mechanica Sinica" – Springer Journals

Published: May 1, 2021

Keywords: Isogeometric; Solid-shell; Nitsche; Patch coupling; Quasi-Newton

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