Contribution à l’étude d’éléments finis spéciaux pour des simulations numériques à trois dimensions précises

DJAHARA, Hossam (2024) Contribution à l’étude d’éléments finis spéciaux pour des simulations numériques à trois dimensions précises. Doctoral thesis, Faculté des Sciences et de la technologie.

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Abstract

This thesis presents the validation of newly developed high-order finite elements for analyzing various structures and material behavior in both linear and nonlinear regimes. These elements are based on the Space Fiber Rotation (SFR) concept, known for its effectiveness. SFR enables a spatial rotation of a three-dimensional virtual fiber within the element, introducing six Degrees of Freedom (DOFs) per node (Three translation and three rotation), which enhances the approximation of the classical displacement field. The novel elements include conforming (SFR20) and non-conforming (SFR20I) Hexahedral 20-node elements. The incompatible modes approach is utilized in the non-conforming element formulation to avoid numerical deficiencies related to Poisson’s ratio locking. High-order elements are chosen to address mesh refinement requirements for low-order elements and mesh distortion issues. The validation process involves linear validation with reduced integration and performance assessment through distortion, aspect ratio, and convergence tests across various structures. Additionally, nonlinear validation is conducted by implementing the elements and the plasticity model in Abaqus software in the form of User defined ELement (UEL) and User defined MATerial subroutine, respectively. Overall, the proposed elements demonstrate superior performance, particularly in handling mesh distortion.

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