engleski

Towards locking-free meshless methods for analysis of shell-like structures

Locking phenomena still pose serious obstacles in meshless formulations for the analysis of shells and plates. The procedures that are used in the Finite Element Method to eliminate the locking effects are impracticable or less efficient in the meshless methods due to the non-polynomial character of meshless functions. In this contribution, the meshless formulations for shell-like structures based on the mixed Meshless Local Petrov-Galerkin (MLPG) paradigm are presented. The solid-shell approach is adopted, allowing the application of complete 3-D constitutive models without employing the rotational degrees of freedom. As the mixed MLPG method is not based on multi-field variational principles, the use of Lagrangian multipliers and the need to satisfy the complicated inf-sup conditions are avoided. Therefore, all independent field variables may be approximated by the same functions over the structure middle surface. The behavior of primal and mixed approaches in the thin plate limit is studied by using the consistency paradigm. It is shown that in the primal approach spurious constraints appear in the transversal shear strains, which leads to shear locking and sub-optimal convergence rates, while in the mixed paradigm locking is efficiently overcome by satisfying the Kirchhoff-Love conditions at the nodes of the model. Furthermore, the methods for avoiding the thickness locking effect are presented. Some peculiar features of the mixed MLPG method are also discussed, as well as the advantages of applying the mixed concept to the formulations based on classical shell theories. The validity of the theoretical predictions and the efficiency of the mixed algorithms are demonstrated by numerical examples.

meshless methods; MLPG method; locking; thin shells; mixed approach

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