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• W48765511 abstract "ao (2) Abstract: Shear-locking is a well studied phenomenon in the conventio nal displacement ap- proach of the Finite Element Method (FEM). Although not veryelegant and mathematically soundly, the reduced/selective integration technique is,in general, the chosen option. However, for approximations based on unstructured data, like the one s used on meshless methods, it is not possible to relay on a concept such asreduced integration due to the non-polinomial character of the approximation. Therefore it is necessary to develop new strategies to overcome this problem. In this work two proposals are reviewed and critically analy zed, namely a method based on a change of variables (which proves to be, in fact, a mixed appr oach) and the construction of the approximation fields based on the reproduction of the Kirchh off assumption on the thin limit (it is shown that this procedure originate a rank deficiency in th e equations system). The two procedures are applied to the Element Free Galerkin ( EFG) method analysis of beams and its relative numerical performance is compared. For the sake of completeness, tests are also carried out with the traditional variables and approximati on. The merits and drawbacks of each approach are discussed. The presence of locking (whether is shear, membrane or volumetric) in the numerical solutions solely based on the approximation of the generalized displacement fields can lead to totally er- roneous solutions. In the displacement version of the FEM is usual to overcome such a problem resorting the reduced/selective integration schemes. It c an be proved that this procedure is equiv- alent to a certain class of mixed formulations, see Malkus and Hughes (10). However, this can hardly be extended to meshless methods due to the non-polinomial character of the approxi- mations, e. g., Moving Least Squares (MLS), Reproducing Kernel Particle Methods (RKPM), natural neighbour co-ordinates (Sibson co-ordinates) or enriched Shepard functions (used in the h-p Cloud method). A poor integration of the weak form lead, in general, to unsatisfactory re- sults. Thus, alternative procedures were proposed. In the f ollowing, a brief review is presented: Change of variables. By a simple change of the independent variables, it is possible to construct a locking-free formulation, as proposed by Cho and Atluri (3). This change does not increase the total number of degrees of freedom, although it can be interpreted as a mixed formulation." @default.
• W48765511 created "2016-06-24" @default.
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• W48765511 date "2005-01-01" @default.
• W48765511 modified "2023-09-24" @default.
• W48765511 title "On the procedures to eliminate shear locking in meshless methods" @default.
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