Meshless analysis of shear deformable shells

boundary and interface constraints

authored by: Jorge C. Costa, Paulo M. Pimenta, Peter Wriggers
Abstract: Meshless methods provide a highly continuous approximation field, convenient for thin structures like shells. Nevertheless, the lack of Kronecker Delta property makes the formulation of essential boundary conditions not straightforward, as the trial and test fields cannot be tailored to boundary values. Similar problem arise when different approximation regions must be joined, in a multi-region problem, such as kinks, folds or joints. This work presents three approaches to impose both kinematic conditions: the well-known Lagrange multiplier method, used since the beginning of the element free Galerkin method; a pure penalty approach; and the recently rediscovered alternative of Nitsche’s method. We use the discretization technique for thick Reissner–Mindlin shells and adapt the weak form as to separate displacement and rotational degrees of freedom and obtain suitable and separate stabilization parameters. This approach enables the modeling of discontinuous shells and local refinement on multi-region problems.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Universidade de Sao Paulo
Type: Article
Journal: Computational mechanics
Volume: 57
Pages: 679-700
No. of pages: 22
ISSN: 0178-7675
Publication date: 04.2016
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-015-1253-z (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{2f4fd9af9f3f4d7cbf024801a21a47bc,
title = "Meshless analysis of shear deformable shells: boundary and interface constraints",
abstract = "Meshless methods provide a highly continuous approximation field, convenient for thin structures like shells. Nevertheless, the lack of Kronecker Delta property makes the formulation of essential boundary conditions not straightforward, as the trial and test fields cannot be tailored to boundary values. Similar problem arise when different approximation regions must be joined, in a multi-region problem, such as kinks, folds or joints. This work presents three approaches to impose both kinematic conditions: the well-known Lagrange multiplier method, used since the beginning of the element free Galerkin method; a pure penalty approach; and the recently rediscovered alternative of Nitsche{\textquoteright}s method. We use the discretization technique for thick Reissner–Mindlin shells and adapt the weak form as to separate displacement and rotational degrees of freedom and obtain suitable and separate stabilization parameters. This approach enables the modeling of discontinuous shells and local refinement on multi-region problems.",
keywords = "Element-free Galerkin, Interfaces, Multi-region Problems, Nitsche{\textquoteright}s Method, Thick shells",
author = "Costa, {Jorge C.} and Pimenta, {Paulo M.} and Peter Wriggers",
note = "Funding Information: The first author would like to thank CNPq (Conselho Nacional de Desenvolvimento Tecnol{\'o}gico) for his PhD grant and CAPES (Coordena{\c c}{\~a}o de Aperfei{\c c}oamento de Pessoal de N{\'i}vel Superior) for supporting his exchange stay at the Leibniz University of Hannover. The second author acknowledges the support of the CNPq under the grant 303091/2013-4 as well as expresses his gratitude to the Alexander von Humboldt Foundation for the Georg Forster Research Award that made possible his stay at the University of Duisburg-Essen and the Leibniz University of Hannover. Also, we thank Prof. Carlos Tiago, at Instituto Superior T{\'e}cnico, Lisbon for many proficuous conversations on the subject.",
year = "2016",
month = apr,
doi = "10.1007/s00466-015-1253-z",
language = "English",
volume = "57",
pages = "679--700",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "4",
}