Simulation of linear elastic structural elements using the Petrov–Galerkin finite element method

Abstract: In this contribution, it is demonstrated that the mesh sensitivity of linear elastic Reissner–Mindlin finite‐element plate formulations can be significantly reduced by using a Petrov–Galerkin‐based approach. In contrast to the usual Bubnov–Galerkin method, Petrov–Galerkin methods are generally characterized by the fact that the test function and the trial function are approximated using different shape functions. To provide an overview, established Petrov–Galerkin methods for 2D solid elements, which have been shown to reduce mesh sensitivity, are reviewed first. It is then investigated whether a suitable Petrov– Galerkin plate formulation can be developed. In this context, it is demonstrated that a full Petrov–Galerkin method leads to problems in the treatment of transverse shear locking. However, the proposed partial Petrov–Galerkin method shows the desired mesh‐insensitive behavior.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Simulation of linear elastic structural elements using the Petrov–Galerkin finite element method ; day:06 ; month:09 ; year:2023 ; extent:8 ; Proceedings in applied mathematics and mechanics ; (06.09.2023) (gesamt 8)

Contributors, Places and Time

• Creator: Zähringer, Felix ; Betsch, Peter

Further information

• DOI: 10.1002/pamm.202300110
• URN: urn:nbn:de:101:1-2023090615212969686322
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 10:58 AM CEST