engleski

On mixed Meshless Local Petrov-Galerkin (MLPG) approach for thin plate analysis

A new MLPG method based on the mixed formulation proposed is developed for plate analysis. In contrast to available meshless formulations for modeling of plate and shell deformation responses , in this approach, both strains and displacements are approximated independently by using the Moving Least Square (MLS) interpolation scheme. Discretization is performed by nodes located on the upper and lower plate surfaces. The local symmetric weak form (LSWF) of equilibrium equations is derived over local sub-domains, surrounding the nodes, by using strains as independent variables. The unknown nodal strains are then replaced by the values calculated from the independently interpolated nodal displacements. For that purpose the standard strain-displacement relationships are enforced at the nodes by means of collocation approach. In this way, a closed system of equations may be assembled on the global level with only nodal displacements as unknown variables. The strain and displacement fields are interpolated by using the same 2-D MLS functions in the in-plane directions, while simple polynomials are employed in the normal direction. The proposed formulation is superior in comparison to fully displacement approach. In a thin plate limit, the shear locking effect is alleviated without increasing the order of the approximation functions, or constructing special shape functions for rotations. Computational costs associated with differentiation of MLS functions over the entire domain are eliminated by using the present mixed approach. In addition, the lower-order of MLS function required for strain interpolation enables the use of smaller support domains than in fully displacement formulation. Like in displacement formulations, a special care should be taken for elimination of undesired thickness locking phenomena which occur if a 3-D solid concept is applied. The accuracy and numerical efficiency of the proposed approach will be demonstrated by numerical examples.

MLPG; mixed formulation; plates; MLS; shear locking

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