A simplified Kirchhoff–Love large deformation model for elastic shells and its effective isogeometric formulation
Autor: | Alessandro Reali, Antonio Madeo, Josef Kiendl, Domenico Magisano, Giovanni Garcea, Leonardo Leonetti |
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Rok vydání: | 2019 |
Předmět: |
Mechanical Engineering
Computation Computational Mechanics General Physics and Astronomy 010103 numerical & computational mathematics 01 natural sciences Measure (mathematics) Displacement (vector) Computer Science Applications 010101 applied mathematics Nonlinear system Third order symbols.namesake Mechanics of Materials symbols Applied mathematics Polygon mesh 0101 mathematics Reduction (mathematics) Newton's method Mathematics |
Zdroj: | Computer Methods in Applied Mechanics and Engineering. 354:369-396 |
ISSN: | 0045-7825 |
Popis: | Isogeometric Kirchhoff–Love elements have received an increasing attention in geometrically nonlinear analysis of elastic shells. Nevertheless, some difficulties still remain. Among the others, the highly nonlinear expression of the strain measure, which leads to a complicated and costly computation of the discrete operators, and the existence of locking, which prevents the use of coarse meshes for slender shells and low order NURBS, are key issues that need to be addressed. In this work, exploiting the hypothesis of small membrane strains, we propose a simplified strain measure with a third order polynomial dependence on the displacement variables which allows an efficient evaluation of the discrete quantities. Numerical results show practically no difference to the original model, even for very large displacements and composite structures. Patch-wise reduced integrations are then investigated to deal with membrane locking in large deformation problems. An optimal integration scheme for third order C 2 NURBS, in terms of accuracy and efficiency, is identified. Finally, the recently proposed Newton method with mixed integration points is used for the solution of the discrete nonlinear equations with a great reduction of the iterative burden with respect to the standard Newton scheme. |
Databáze: | OpenAIRE |
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