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Meshless analysis of shear deformable shells: boundary and interface constraints

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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.

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Acknowledgments

The first author would like to thank CNPq (Conselho Nacional de Desenvolvimento Tecnológico) for his PhD grant and CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível 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 Técnico, Lisbon for many proficuous conversations on the subject.

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  1. Polytechnic School at the University of São Paulo, São Paulo, Brazil

    Jorge C. Costa & Paulo M. Pimenta

  2. Institute of Continuum Mechanics, Leibniz Universität Hannover, Hannover, Germany

    Peter Wriggers

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  1. Jorge C. Costa
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Correspondence to Jorge C. Costa.

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Costa, J.C., Pimenta, P.M. & Wriggers, P. Meshless analysis of shear deformable shells: boundary and interface constraints. Comput Mech 57, 679–700 (2016). https://doi.org/10.1007/s00466-015-1253-z

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