engleski

On an efficient MLPG formulation for shell analysis

A meshless formulation based on the local Petrov- Galerkin approach is developed for analysis of shell structures. A 3-D solid concept usually used in the finite element formulations is adopted, and the exact shell geometry may be described. The shell continuum is discretized in the parametric space defined in the normalized coordinates by the nodes located on the upper and lower surfaces, and it is than mapped into the global Cartesian coordinates. According to the Petrov-Galerkin approach, the local weak form of the 3-D equilibrium equations is derived over both the cylindrical and the prismatic local sub-domains surrounding the couple of nodes positioned on the opposite surfaces in the parametric space. The mixed approach using the strain and the transversal stress interpolations is applied. The interpolation in the in-plane directions is performed by the modified moving least squares functions obeying Kronecker delta property with a high accuracy, while the linear polynomial functions are used for the approximation over the shell thickness. In order to derive a closed system of the global discretized equations with the displacements as unknown variables, the nodal strain and stress values are replaced by the displacement components using the independent displacement interpolation. The results obtained by means of the integration over the cylindrical and the prismatic local subdomains are compared one another. The superiority of the formulation using the prismatic integration domain is demonstrated, in which more stable solutions and monotonic convergence are exhibited. All undesired locking phenomena are suppressed by both approaches.

MLPG method; shells; 3-D solid; mixed formulation; MLS

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