A large deformation, rotation-free, isogeometric shell

Conventional finite shell element formulations use rotational degrees of freedom to describe the motion of the fiber in the Reissner–Mindlin shear deformable shell theory, resulting in an element with five or six degrees of freedom per node. These additional degrees of freedom are frequently the sou...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2011-03, Vol.200 (13), p.1367-1378
Main Authors: Benson, D.J., Bazilevs, Y., Hsu, M.-C., Hughes, T.J.R.
Format: Article
Language:English
Subjects:
Applied sciences
Convergence
Deep drawing
Deformation
Degrees of freedom
Exact sciences and technology
Forming
Formulations
Fundamental areas of phenomenology (including applications)
Isogeometric analysis
Mathematical analysis
Metal stamping
Metals. Metallurgy
NURBS
Physics
Production techniques
Rotation-free
Rotational
Shells
Solid mechanics
Structural and continuum mechanics
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Summary:Conventional finite shell element formulations use rotational degrees of freedom to describe the motion of the fiber in the Reissner–Mindlin shear deformable shell theory, resulting in an element with five or six degrees of freedom per node. These additional degrees of freedom are frequently the source of convergence difficulties in implicit structural analyses, and, unless the rotational inertias are scaled, control the time step size in explicit analyses. Structural formulations that are based on only the translational degrees of freedom are therefore attractive. Although rotation-free formulations using C 0 basis functions are possible, they are complicated in comparison to their C 1 counterparts. A C k -continuous, k ⩾ 1, NURBS-based isogeometric shell for large deformations formulated without rotational degrees of freedom is presented here. The effect of different choices for defining the shell normal vector is demonstrated using a simple eigenvalue problem, and a simple lifting operator is shown to provide the most accurate solution. Higher order elements are commonly regarded as inefficient for large deformation analyses, but a traditional shell benchmark problem demonstrates the contrary for isogeometric analysis. The rapid convergence of the quadratic element is demonstrated for the NUMISHEET S-rail benchmark metal stamping problem.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2010.12.003