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Moving least‐squares approximation with discontinuous derivative basis functions for shell structures with slope discontinuities
Author(s) -
Zhang Zhiqian,
Noguchi Hirohisa,
Chen JiunShyan
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2362
Subject(s) - classification of discontinuities , cartesian coordinate system , moore–penrose pseudoinverse , moment (physics) , mathematical analysis , basis (linear algebra) , mathematics , basis function , matrix (chemical analysis) , shell (structure) , singularity , geometry , inverse , physics , engineering , classical mechanics , materials science , civil engineering , composite material
Moving least‐squares approximation with discontinuous derivative basis functions (MLSA‐DBF) is introduced for analysis of shell structures with slope discontinuities. To deal with shells with arbitrary slope discontinuities, the Cartesian coordinate is introduced in the construction of MLSA on the shell surface. The possible causes of singularity in the moment matrix of MLSA on the shell surface with slope discontinuities are identified, and the Moore–Penrose pseudoinverse is used to obtain the generalized inverse of the singular moment matrix resulting from linear dependency and insufficient influence nodes in the MLSA. Following the proposed formulations for shear deformable shell structures with slope discontinuities in the Cartesian coordinates, several numerical examples are analyzed to demonstrate the performance, validity, accuracy, and convergence properties of the proposed MLSA‐DBF approach. Copyright © 2007 John Wiley & Sons, Ltd.