TY - JOUR

T1 - Meshless analysis of shear deformable shells

T2 - boundary and interface constraints

AU - Costa, Jorge C.

AU - Pimenta, Paulo M.

AU - Wriggers, Peter

N1 - Funding Information: 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.

PY - 2016/4

Y1 - 2016/4

N2 - 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.

AB - 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.

KW - Element-free Galerkin

KW - Interfaces

KW - Multi-region Problems

KW - Nitsche’s Method

KW - Thick shells

UR - http://www.scopus.com/inward/record.url?scp=84955581288&partnerID=8YFLogxK

U2 - 10.1007/s00466-015-1253-z

DO - 10.1007/s00466-015-1253-z

M3 - Article

AN - SCOPUS:84955581288

VL - 57

SP - 679

EP - 700

JO - Computational mechanics

JF - Computational mechanics

SN - 0178-7675

IS - 4

ER -