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Communication Dans Un Congrès Année : 2021

Nodal-Boundary Finite-Element Method for the Signorini Problem In Two Dimensions

Résumé

The various numerical solution methods targeting the Signorini problem differ in their treatment of the complementarity boundary conditions. In the finite element method, the needed application of a Newton impact-law either produces chattering or induces energy dissipation while Nitsche's and penalty methods do not strictly enforce the impenetrability condition with the obstacle. Also, the up-wind finite volume approach does not conserve energy for multiple spatial dimensions. Hence, a new methodology called the Nodal Boundary method is proposed for treatment of Signorini conditions within the framework of Finite Element. Similarly to mass redistribution techniques, this method defines the motion of contact nodes based on internal nodes. However, this method does not require computation of a modified mass matrix. Applications of the derived scheme on different settings of the Signorini problem are presented. It is found that, while energy is not always conserved, this method allows for existence of periodic solutions together with the elimination of chattering at contact.
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hal-04010691 , version 1 (01-03-2023)

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  • HAL Id : hal-04010691 , version 1

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David Urman, Mathias Legrand. Nodal-Boundary Finite-Element Method for the Signorini Problem In Two Dimensions. ASME 2021 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, ASME, Aug 2021, Virtual, Online, United States. ⟨hal-04010691⟩
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