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Méthode combinée volumes finis et meshless local Petrov Galerkin appliquée au calcul de structures

Abstract : This work concerns the development of a new numerical method entitled "Meshless Local Petrov- Galerkin (MLPG) combined with the Finite Volumes Method (FVM)" applied to the structural analysis. It is based on the resolution of the weak form of the partial differential equations by a method of Petrov Galerkin as in finite elements, but the approximation of the field of displacement introduced into the weak form does not require grid. The displacements and strains are given with the various nodes by local interpolation by using moving least squares (MLS). The values of the nodal strains are expressed in terms of interpolated nodal values independently of displacements, by simply imposing the strain displacement relationship directly by collocation at the nodal points. The procedure of calculation for this method is implemented in a computer code developed in MATLAB. The developed code was validated on a certain number of test cases by comparison with analytical solutions and finite elements results like ABAQUS. The whole of these tests showed a good behaviour of the method (about 0.0001% of errors in compared to the exact solution). The approach is also extended for the study of the thin beams and the dynamic analysis and stability.
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https://hal.univ-lorraine.fr/tel-01748434
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Mohammad-Réza Moosavi. Méthode combinée volumes finis et meshless local Petrov Galerkin appliquée au calcul de structures. Autre. Université Henri Poincaré - Nancy 1, 2008. Français. ⟨NNT : 2008NAN10080⟩. ⟨tel-01748434⟩

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