engleski

Locking effects in a 3-D MLPG meshless approach for the analysis of plates and shells

The main aim of the contribution is to discuss the causes and methods for the elimination of the locking effects that appear in a three-dimensional (3-D) continuum meshless approach for the shell-like structures based on the Meshless Local Petrov-Galerkin (MLPG) method. The solid-shell concept allowing the implementation of complete 3-D material models is adopted for the description of shell kinematics, and the geometry of a shell is described mathematically exactly. The local weak forms (LWF) of the 3-D equilibrium equations, written over the local sub-domains surrounding the node couples, serve as the governing equations. Depending on the choice of unknown field variables, it is possible to derive various purely displacement-based (primal) as well as mixed formulations. In the mixed algorithms, the global system of equations is closed by employing suitable collocation procedures. In all cases, all unknown variables are approximated by using the same meshless functions in the directions tangential to the structure middle surface, while polynomials are applied in the thickness direction. The Poisson’s thickness locking and transversal shear locking effects are theoretically exposed by considering the classical displacement-based approach for the plates that employs the linear displacement distribution over the plate thickness. Thereafter, suitable procedures for their alleviation in the primal and mixed formulations are explained. Thereby, a special attention is dedicated to revealing the mechanism of eliminating the shear locking phenomena in the mixed approach. Suitable illustrative numerical examples demonstrate the validity of the theoretical assumptions and the numerical efficiency of the discussed algorithms.

MLPG method; shells; shear locking

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