engleski

Mixed Meshless Local Petrov-Galerkin (MLPG) approach for shell analysis

The mixed meshless approach, based on the Local Petrov-Galerkin method, according to the formulation presented in is developed for analysis of shell structures. In contrast to the well-known displacement based meshless methods, besides the displacement the strain and stress are approximated independently. The strain interpolation is used in order to alleviate the undesired shear locking phenomenon in the thin shell limit. The thickness locking is eliminated by means of the interpolation of the transversal normal stress component. Thus, in addition to the displacement components, the independent variables are the five strain components and the transversal normal stress component. Discretization of the shell continuum is performed by the nodes located on the upper and lower surfaces. All variables are approximated by the simple polynomial functions in the transversal directions, and by means of the modified Moving Least Square (MLS) interpolation, which possesses Kronecker Delta property, in the in-plane directions. The concept of a three dimensional solid is used and the shell geometry is described exactly by employing a parametric mapping technique. To obtain the discretized governing equations with only the nodal displacements as unknown variables, the nodal strain and stress values are replaced by the displacement components using the collocation approach. The proposed algorithm possesses considerable advantages in comparison to the standard fully displacement formulations. In a thin structural limit, the shear locking effect is fully suppressed even when low order MLS functions are used. In addition, the low order of the MLS interpolation enables the use of relatively small support domain, which significantly contributes to numerical efficiency. Differentiation of the MLS functions over the entire domain is also avoided, which further increases the numerical efficiency in terms of computational costs and stability. The accuracy and robustness of the proposed formulation are demonstrated by the numerical examples.

mixed approach; MLPG method; MLS functions; locking

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