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Locking in the incompressible limit for the element-free Galerkin method
Huerta, Antonio; Fernandez Mendez, Sonia
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. LACÀN - Centre Específic de Recerca de Mètodes Numèrics en Ciències Aplicades i Enginyeria
Volumetric locking (locking in the incompressible limit) for linear elastic isotropic materials is studied in the context of the element-free Galerkin method. The modal analysis developed here shows that the number of non-physical locking modes is independent of the dilation parameter (support of the interpolation functions). Thus increasing the dilation parameter does not suppress locking. Nevertheless, an increase in the dilation parameter does reduce the energy associated with the non-physical locking modes; thus, in part, it alleviates the locking phenomena. This is shown for linear and quadratic orders of consistency. Moreover, the biquadratic order of consistency, as in finite elements, improves the locking behaviour. Although more locking modes are present in the element-free Galerkin method with quadratic consistency than with standard biquadratic finite elements. Finally, numerical examples are shown to validate the modal analysis. In particular, the conclusions of the modal analysis are also confirmed in an elastoplastic example.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
Galerkin methods
Locking
Volumetric locking
Element-free Galerkin
Meshless
Meshfree
Galerkin, Mètodes de
info:eu-repo/semantics/submittedVersion
Article
Wiley and Sons
         

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