engleski

A locking free meshless formulation for thin shell analysis

An efficient elimination of the undesired locking phenomena in the numerical analysis of thin shell structures has been a challenge for many years. A special attention has been directed to the suppressing of the shear locking effect. The well known finite element method has mostly been applied. In the present contribution, a meshless computational strategy based on the local Petrov-Galerkin approach is proposed. In contrast to the traditional finite element method, the computational model is discretized only by the nodes which do not need to be connected into elements. A mixed meshless approach using the strain and stress interpolations is applied. The 3-D solid concept usually used in the finite element formulations is adopted, and the exact shell geometry is described. The interpolation in the in-plane directions is performed by the moving least squares functions and the linear polynomial functions are used for the approximation over the shell thickness. The integration is performed over the prismatic local sub-domain surrounding the couple of nodes positioned on the opposite surfaces in the parametric space. A closed system of the global discretized equations with only the displacements as unknown variables is derived by using the collocation approach and the independent displacement interpolation. The numerical efficiency of the proposed formulation is demonstrated by the numerical examples. Both the thickness and the shear locking effects are completely suppressed.

meshless methods; locking phenomena; thin shells; 3-D concept

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